THE NEW BUSINESS ARITHMETIC REVISED EDITrON LIBRARY OF THE UNIVERSITY OF CALIFORNIA GIFT OF Class THE NEW Business Arithmetic A TREATISE ON Commercial Calculations REVISED EDITION J. A. LYONS & COMPANY NEW YORK CHICAGO 6 APR 4 19H GIFT COPYRIGHT. 1906, BY POWERS & LYONS PREFACE Since the great majority of those who study Arithmetic need to use it in the transaction of the practical affairs of life, a text- book on the subject, should be especially practical. It has been the aim in the preparation of this work to represent the business methods of the times. While a few problems are intended to illustrate some principle, by far the greater number show the application of Arithmetic to the actual business transactions of the day. In this practical character we believe the book will be found unequaled. The principles of each successive topic are carefully developed by appropriate exercises, so graded that the mind of the student must inevitably grasp the relations of the whole subject, and when the work is completed, comprehend it, not as a mass of loosely-connected details, but as a unified whole. Since good methods economize time and energy, secure rapid- ity and accuracy in calculation, and strengthen the reasoning powers, the aim has been to present each subject in the most clear and concise manner, showing the reason for every operation performed, in order that the student may learn to rely upon the principle involved and not merely seek for a result. The treatment of the fundamental rules of Arithmetic has been made simple, and is free from all effort to exalt these rules into complex and difficult propositions. A clear explanation, followed by an abundance of well graded problems, will enable the pupil to readily master the foundation work of Arithmetic. The work in Fractions is made plain by giving brief, clear and accurate definitions, and simple, concise and logical solutions of concrete problems. Compound Numbers are explained by showing their relation to simple numbers, while the exercises and problems deal with facts found in every-day life. The subject of Percentage and its applications is made most 3 - . - - - : 4 PREFACE thorough and practical. A system of analysis is employed which must inevitably fix the principles clearly in the mind of the learner. Equation of Payments, Averaging Accounts and Partnership have been emphasized according to the demand of business. That the reasoning powers of the pupil may be strengthened and his ability to think independently of pencil and tablet may be increased, several hundred problems for oral solution have been added. The work undoubtedly now contains an abundance of material, not only for giving facility in computations, but for correct training in arithmetical thought. We have made an earnest effort to present such a work to teachers and students as will meet with their approval and suit their wants. We believe by a thorough study of the work young men and women will go out into the business world intelligent persons with ability to apply their knowledge. THE AUTHOR. CONTENTS PAGE: DEFINITIONS 7 NOTATION AND NUMERATION 8 ADDITION 13 SUBTRACTION 18 MULTIPLICATION 22 DIVISION 30 FACTORING 37 CANCELLATION ' 38 GREATEST COMMON DIVISOR 40 LEAST COMMON MULTIPLE 41 FRACTIONS 44 Reduction 46 Addition : 52. Subtraction 55 Multiplication 58 Division 64 DECIMAL FRACTIONS 74 Reduction 77 Addition 79 Subtraction 81 Multiplication 82 Division 83 COMPOUND NUMBERS 85 UNITED STATES MONEY 86 Addition 87 Subtraction 89 Multiplication 90 Division 91 SHORT METHODS 92. BILLS 97 REDUCTION OF DENOMINATE NUMBERS 105 United States Money 105 Canada Money 105 English Money 106 Avoirdupois Weight 108 Trov Weight \ 110 Apothecaries' Weight Ill Comparison of Weights 112 Long Measure 113 Surveyors' Long Measure 115 Square Measure 115 Board Measure 118 Surveyors' Square Measure 119 Cubic Measure 123 Liquid Measure 125 Apothecaries' Fluid Measure 126 Dry Measure 126 Comparison of Dry and Liquid Measures 127 Time 128 Circular Measure 130' REDUCTION OF DENOMINATE FRACTIONS 134- 6 6 CONTENTS DENOMINATE NUMBERS Addition 139 Subtraction 141 Multiplication 143 Division 144 LONGITUDE AND TIME 146 RATIO 154 Proportion 155 Compound Proportion 158 MEASUREMENTS USED IN BUSINESS 161 PERCENTAGE 167 PROFIT AND Loss 183 MARKING GOODS 190 TRADE DISCOUNT 193 BILLS 197 COMMISSION 205 INSURANCE 213 Fire Insurance 214 Marine Insurance 217 Life Insurance 219 INTEREST 225 Sixty Days Method 232 Six Per Cent Method 233 Cancellation Method 235 Common Bankers' and Exact Interest Compared 236 Annual Interest 243 Compound Interest 245 COMMERCIAL PAPER 250 Partial Payments 255 Annual Interest, with Partial Payments 260 TRUE DISCOUNT % 261 BANK DISCOUNT 264 STOCKS AND BONDS 268 EXCHANGE 277 Domestic Exchange 278 Foreign Exchange 281 BANKS AND BANKING 284 National Banks 284 Savings Banks 287 TAXES 292 CUSTOMS OR DUTIES 295 EQUATION OF ACCOUNTS 299 CASH BALANCE 311 PARTNERSHIP 313 INVOLUTION 328 EVOLUTION. 329 Square Root 330 Applications of Square Root 332 Cube Root 334 Applications of Cube Root MENSURATION 338 Plane Figures 339 Solids 341 Metric System 345 Value of Moneys 350 STATUTORY WEIGHTS! . ... 352 ARITHMETIC DEFINITIONS 1. Arithmetic is the science of numbers and their use. 2. A Unit is a single thing ; as, one, one man, one horse. 3. A Number is one or more units ; as 1, 3, 9, 6 boys. 4. The Unit of a Number is one of the kind expressed by the number. The unit of 9 is 1, the unit of 20 feet is 1 foot. 5. An Integer is a whole number. 6. Like Numbers are those which are composed of the same kinds of units. Thus 25 and, 34 ; 3 yards and 10 yards. 7. An Abstract Number is one used without reference to any particular thing or quantity. Thus 15; 64; 280. 8. A Concrete Number is one used with reference to some particular thing or quantity. Thus 25 dollars ; 14 days ; 100 men. Concrete numbers are called denominate numbers because the de- nomination or kind is named. 9. A Sign is a character used to indicate an operation, or ex- press the qualities or relations of numbers. A Solution is a process of computation used to obtain a re- quired result. 10. A Problem is a question for solution. llT An Example is a problem solved, illustrating a principle or rule. 12. A Principle is a truth upon which the solution is founded. 13. An Analysis is a statement of the successive steps in a solution. 14. An Explanation is a statement of the reasons for the manner of solving a problem. 15. A Rule is a direction for solving problems. 7 NOTATION AND NUMERATION 16. Notation is the art of writing numbers by means of characters. 17. Numeration is the art of reading numbers written by characters. Two systems of Notation are in general use: the Roman and the Arabic. The Roman is supposed to have been invented by the Romans and employs seven capital letters to express num- bers. The Arabic is said to be derived from the Arabs and em- ploys ten characters called figures. ARABIC NOTATION 18. Figures are characters used to represent numbers. There are ten figures : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Zero, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. The Figure 0, Zero or Cipher, expresses no units, or nothing, when standing alon,e. The other nine figures express the num- ber of units shown by. their names. These figures are called digits. 19. To express numbers greater than nine and less than one hundred, two figures are written side by side ; as, thirty-six, 36 ; seventy-two, 72. 20. To express numbers greater than ninety-nine, three or more figures are written side by side ; as, one hundred eighty-five, 185 ; two thousand six hundred twenty-four, 2624. 21. When figures are written side by side, the one at the right expresses units or ones, the next tens, the next hundreds, the next thousands, etc. 22. The Simple Value of a figure is the value it expresses when standing alone, or in unit's place ; as 3, 7, 9. 23. The Local Value of a figure is the value it expresses when used with other figures to represent a number, 8 NOTATION AND NUMERATION 9 In the number 345, the figure 5 expresses a simple value, and the figures 3 and 4 express local values. 24. The Order of a Unit takes its name from the place it occupies. A figure in the first place expresses units of the first order ; in the second place, units of the second 'order, etc. When a figure stands in the second place it represents tens; in the third place hundreds ; in the fourth place thousands, etc. One ten is written 10 One ten and four, fourteen 14 Two tens, twenty 20 Two tens and seven, twenty-seven 27 Three tens, thirty . ; 30 One hundred, one ten and seven, one hundred seventeen. . . . 117 Three hundred, five tens and nine, three hundred fifty-nine. . 359 Six thousand, five hundreds, nine tens and two, is read, six thousand five hundred ninety-two 6592 NOTE. In reading whole numbers the word AND should not be used. Thus, seven hundred fifty-four, not seven hundred and fifty-four. Copy and read the following numbers : ' 1. 297 5. 1790 9. 3096 2. 472 6. 4607 10. 7006 3. 685 7. 9218 11. 8200 4. 920 8. 2030 12. 6303 Write the following in figures : 13. One hundred forty-six. 14- Seven hundred ten. 15. Six hundred three. 16. Two hundred ninety. 77. Five hundred thirty-eight. 18 Three thousand seven hundred nineteen. 19. Six thousand nine hundred twenty-seven. 20. Four thousand sixty-four. 21. Seven thousand four hundred one. 22. Five thousand forty. 23. Nine thousand six hundred ninety-six. 24> Eight thousand eight hundred. 10 NEW BUSINESS ARITHMETIC 25. Seven units of the first order and two of the second. 26. Nine units of the fourth order, three of the third, two of the second and one of the first. 27. Five units of the third order, one of the first. 28. Six units of the fourth order, seven of the second, two of the first. 25. For convenience, figures are arranged in periods of three places each ; the first three at the right being called units or one's period; the next three the thousand's period; the next three the million's period, etc. Quadrillions. Trillions, Billions, 6th period. 5th period, 4th period, TABLE Millions, 3d period, Thousands. 2d period, 546, 897, to t-i o 534, ,000 -a ffi HO e rt c 3^3: o- p ct a- o 2 2. 3 s a i H W 3 g -- 3 2 6 05 Or 3* 3* i!l Units, 1st period, Periods. 9 8 ~~T? Figures. % % Places. *Z$ General Principles 1. Ten units of any order equal one unit of the next higher order.. .Ten units equal one ten; ten tens equal one hundred; ten hundreds equal one thousand, etc. 2. Removing a figure one place to the left increases its value ten times. Removing a figure one place to the right decreases its -value ten times. To Write Numbers a. Begin at the left and write the figures belonging to the highest period. b. Write the hundreds, tens and units of each period in their order, putting a cipher in the place of any order that is omitted. NOTATION AND NUMERATION 11 To Read Numbers a. Begin at -the right and point off the numbers into periods of three figures each. b. Begin at the left and read each period separately, giving the name to each period except the last. Read the following: 1. 384 5. 136042 9. 147002001 2. 9328 6. 100420 10. 3073640240 3. 11765 7. 9793642 11 73260479142 4. 29470 8. 3106053 12. 48600752052 Write the following numbers : 13. Ninety-seven. 14. Three hundred sixty-eight. 15. Two thousand four hundred seventy-five. 16. Thirty-seven thousand one hundred ninety-six. 17. One hundred thirty-six thousand three hundred twenty-seven. 18. Five million three hundred six thousand five hun- dred three. ROMAN NOTATION 26. Roman Notation employs seven capital letters to ex- press numbers, as follows : Letters I, V, X, L, C, D, M. ' Values 1, 5, 10, 50, 100, 500, 1000. These letters may be combined to express numbers according to the following principles : 1. Repeating a letter repeats its value. Thus, II represents 2 ; XX, 20 ; CCCC, 400 ; DD, 1000. 2. When a letter is placed after one of greater value, its value is to be added to that of the greater. Thus, VI represents 6 ; XV, 15 ; XXI, 21 ; DC, 600 ; DCX, 610. 3. When a letter is placed before one of greater value, its value is to be taken from the greater. Thus, IX represents 9 ; XL, 40 ; XC, 90 ; CD, 400. 12 NEW BUSINESS ARITHMETIC 4- When a letter of any value is placed between two letters, each of greater value, its value is taken from the sum of the other two. Thus, XIV represents 14 ; XIX, 19 ; LIX, 59 ; CXL, 140. 5. A bar placed over a letter increases its value one thousand times. Thus, X~ represents 10000 ;lCL, 40000; CD", 400000. 27. TABLE OF ROMAN NOTATION Roman Arabic. Roman. Arabic. Roman. Arabic. Roman. Arabic. I, 1. IX, 9. XX, 20. xc, 90. II, 2. x, 10. XXI, 21. c, 100. III, 3. XIII, 13. XXX, 30. ccc, 300. IV, 4. XIV, 14. XL, 40. D, 500. V, 5. XV, 15. L, 50. DCC, TOO. VI, 6. XVIII, 18. LX, 60. M, 1000. VIII, 8. XIX, 19. LXXX, 80. MD, 1500. 28. Express by Roman notation : 1. Eighteen. 2. Twenty-three. 8. Fifty-eight. 4. Ninety-nine. 5. Eighty-four. 6. One hundred eighty-eight. 7. One hundred ninety-nine. 8. Five hundred seventeen. 9. Six hundred forty-five. 10. Seven hundred sixty-one. 11. 12. 13. 14- 15. 428. 975. 1116. 23480. 76103. 29. Express by Arabic notation : 1. XXIX. 2. LXVIII. 8. CLXIV. 4. CXXIV. 5. cccxxxm. 6. DCLVI. 7. MDLVIII. 8. CLIL 9. VDXXII. 10. DX. 11. CXIX. 12. XICCIV. 13. MMDCXVIIL 14. VDXLIV. 15. MDLXXII. ADDITION 30. Addition is uniting two or more numbers into one num- ber. 31. The Sum or Amount is the number obtained by adding. 32. The Sign of addition is an upright cross +, and is read plus. When it is placed between two numbers, it shows that they are to be added. $3 + $2 is read 3 dollars plus 2 dollars, and means that 2 dollars are to be added to 3 dollars. The sign $ is used for dollars, c. or cts. for cents. 33. The Sign of equality is two horizontal lines =, and is read equal or arc equal to. 2 -\- 5 = 7 is read 2 plus 5 equal 7. 34. When the amount of each column is less than ten. 1. A farmer raised 232 bushels of corn, 142 bushels of wheat and 223 bushels of oats; how many bushels did he raise in all? Find the sum of each of the following : 1 2 3 4 5 6 232 323 245 312 437 1102 142 242 321 243 140 1312 223 324 132 412 321 4132 597 7. What is the sum of 321, 142 and 323? 8. What is the amount of 213, 152 and 401 ? 9. What is the sum of 3232, 2323 and 4102 ? 10. I paid $212 for a wagon, $150 for one horse, $210 for another horse, and $11 for a set of harness. What did I pay for all? 13 14 NEW BUSINESS ARITHMETIC 35. When the sum of any column is greater than 9. 1. Find the sum of 3164, 2247, 4234 and 3232. EXPLANATION. The sum of the units 2, 4, 7 and 4 is 17 units or 1 ten and 7 units ; write the 7 units under the col- umn of units and add 1 ten to the column of tens. The sum of the tens 1, 3, 3, 4 and 6 is 17 tens or 1 hundred and 2247 ^ tens; write the tens under the column of tens and add 4234 the * hundred to tne column of hundreds. The sum of the hunci reds ! 2, 2, 2 and 1 is 8 hundreds; write under the column of hundreds. The sum of the thousands 3, 4, 2 and 19877 ^ * S ^ thousands or 1 ten-thousand and 2 thousands; write the 2 thousands under the column of thousands and the 1 ten-thousand in the place of ten-thousands. The result 12877 is the sum required. 1. Units of the same order are written in the same column ; and when the sum in any column is 10 or more than 10, it produces one or more units of a higher order, which must be added to the next column. This process is sometimes called "carrying the tens." 2. In adding, learn to pronounce the partial results without naming the numbers separately; thus instead of saying 2 and 4 are 6 and 7 are 13, simply pronounce the results 6, 13, 17, etc. From the foregoing examples and illustrations we deduce the following : To Add Whole Numbers a. Write the numbers so that figures of the same order are in the same column. b. Begin at the right and add each column separately. c. When the sum of any column is greater than 9, place the right-hand figure of the result under the column added and add the remaining figure or figures to the next column. d. Write at the left the sum of the last column. PROBLEMS m 24 (8) 265 432 (5) 1362 to 3420 (V 9416 32 314 864 1487 1862 3624 46 286 526 4532 1425 1583 84 627 893 2386 6347 2436 ADDITION 15 ,8) (9) (10) (11) (12) (IS) 234 979 9140 94187 -71758 986756 562 2864 6968 71849 3680 863694 846 52 8947 48197 797 387623 324 715 7968 89471 36425 890124 118 3680 5392 19478 943628 1369479 462 9289 18364 26480 102154 279562 367 360 27147 62849 864209 8325791 214 14006 38297 56783 579135 2345678 14. 128 + 324 + 116 + 893 + 246 + 427 = how many? 15. 1265 + 3482 + 2149 + 3625 + 1304 + 107 = how many? 16. 28603 + 24567 + 39042 + 16841 + 40218 = how many ? 17. Find the sum of $347, $962, $375, $842 and $636. 18. What will be the amount of $3476, $1924, $4822, $3965 and $7180? 19. Add 8765 feet, 5678 feet, 6758 feet, 7685 feet and 3629 feet. 20. Add forty-nine, seventy-six, three hundred twenty-five, nine thousand six hundred thirty-three, five thousand one hun- dred ten and sixty-two thousand four hundred eleven. 21. Find the sum of three hundred seventy, two thousand eighty-one, seven thousand four hundred sixteen, fifty thousand one hundred twenty-nine and four hundred forty-four thousand six hundred ninety-three. 22. A paid $762 for hogs, $1869 for cattle, $3796 for horses and then had $9240 remaining. How much had he at first? 28. I sold six cows that weighed as follows: 1824 pounds, 1369 pounds, 964 pounds, 2217 pounds, 1746 pounds, 1940 pounds. How many pounds did they all weigh ? 24. A farmer bought four farms. He paid $3221 for the first, $5680 for the second, $4216 for the third and $2645 for the fourth. How much did he pay for all ? 25. I paid $212 for a wagon, $154 for one horse, $210 for an- other horse and $65 for a set of harness. What did I pay for all ? 16 NEW BUSINESS ARITHMETIC 26. R. D. Lyman bought four lots. He paid $2232 for the first, $3124 for the second, $1485 for the third and $2238 for the fourth. Find the cost of the four lots. 27. A merchant paid $746 for calico, $294 for linen, $2864 for shoes, $212 for toys and $1169 for carpets. How much did he pay for all ? 28. A farmer raised 1278 bushels of corn, 1642 bushels of wheat, 765 bushels of oats, 367 bushels of rye, 93 bushels of bar- ley and 160 bushels of buckwheat. Find the number of bushels of grain he raised. (29) (SO) (31) (32) (33) (34) 476 + 908 + 126 + 443 + 180 + 1265 = x 390 + 371 + 324 + 298 + 976 + 3428 = x 915 + 569 + 503 + 876 + 209 + 1456 = x 207 + 245 + 891 + 569 + 314 + 9234 = x 841 + 703 + 736 + 137 + 563 + 1867 = x 632 + 421 + 5.17 + 910 + 842 + 2854 = x 234 + 127 + 143 + 347 + 175 + 3629 = x 143 + 354 + 274 + 256 + 224 + 2872 = x 536 + 781 + 531 + 324 + 135 + 3428 = x 245 + 436 + 275 + 463 + 253 + 9234 = x x + *" + x + x + x + x = x 35. The proprietors of a college paid $2675 for rent, $6286 for teachers, $824 for school furniture, $269 for lights and $970 for fuel. Find the total expense. 36. A bankrupt firm's resources are cash $740, dry-goods $1965, boots and shoes $1647, Brown's note $1278, office furniture $280 and real estate $2394. Find the total resources of the firm. 37. I bought four horses for $85 each. I sold the first for $12 more than cost, the second for $16 more than cost, the third for $26 more than cost and the fourth for $41 more than cost. How much money did I receive for all? 38. A, B, C and D form a partnership. A invests $2640, B invests $3160, C invests $1125 more than A and B together, and D invests as much as A. and C together. How much 4id they all invest in the business ? ADDITION 17 39. A stock dealer bought 218 sheep for $568, 319 hogs for $1162, 123 calves for $2316, 24 oxen for $695 and 11 horses for $957. How many head of stock did he buy and how much did they cost? 40. I sold a house for $3278 and a lot for $1360. I lost $392 on the house and $125 on the lot. What did both cost me? 41. Find the sum of $618, $974, $1243, $7896, $20374, $36345, $9289, $33696, $180, $49270 and $37025. (42) (4?) (44) (45) (46) 852 - f 895 + 967 + 58378 + 47114 = x 734 - -f 766 + 3833 + 64956 4- 89725 = X 3383 - f 677 + 592 + 7895 + 65836 = X 7930 - -f 2814 + 5745 + 6384 + 85684 = X 496 - f 5920 + 824 + 5463 + 78912 ' === - X 757 - f 6782 + 978 + 981 + 97865 = X 2183 - f 588 + 684 + 4752 + 65438 = X 3652 - -f 676 + 756 + 3946 + 99914 = X 1138 - f 983 + 1492 + 895 + 88827 = X 2795 - f 1495 + 767 + 1574 + 77715 == X 676 - f 6 ?4 + 4543 + 6388 + 66624 = X 764 - -f- 542 + 786 + 5946 -f 55568 = X . 842 - f 721 + 692 + 7892 + 89735 = X 13798 - f 2987 + 370 + 1147 + 97814 = X X + x 4- x -f- x i ., = X (47) (48) (49) (50) (5*1) 790 9999 49 123456 213579 965 8989 428 789012 486420 1208 7897 3695 654321 397531 9669 36925 16378 210987 124683 375 52963 875692 913579 610793 92648 13579 3346279 806421 239701 30245 97531 963015 793519 896543 89762 496894 97892 421608 528647 24689 345678 496835 988997 134569 765432 876543 9469358 657893 174682 234567 6543210 642086 798979 212345 98898 9876543 59371 397856 167890 SUBTRACTION 36. Subtraction is taking one number from another. 37. The Minuend is the number from which we subtract. 38. The Subtrahend is the number to be taken from the minuend. 39. The Remainder or Difference is the number left or remaining after subtracting. 40. The Sign of subtraction is a short horizontal line , and is called minus; when placed between two numbers it shows that the second is to be subtracted from the first. G -- 2 is read 6 minus 2, and means that 2 is to be subtracted from 6. The minuend and subtrahend must be like numbers; thus, 5 dollars from 9 dollars leave 4 dollars ; 5 apples from 9 apples leave 4 apples ; but it would be absurd to say 5 apples from 9 dollars, or 5 dollars from 9 apples. 41. When each -figure in the minuend is greater than its cor- responding figure in the subtrahend. 1. From 958 subtract 324. SOLUTION MINUEND 958 SUBTRAHEND 324 DIFFERENCE OR REMAINDER 634 Find the difference or remainder in each of the following : (2) (3) (4) (5) (6) (7) 67 98 86 876 676 925 35 26 31 334 415 213 8. Bought a house for $547 and sold it for $315. What was my loss? 9. Bought a farm for $620 and sold it for $855. What was my gain? 10. A and B together bought real estate for $6985. A paid $4130. How much did B pay? 18 SUBTRACTION 19 11. A farmer had 4687 bushels of wheat and sold 2380 bush- els. How many bushels remained? 12. A man having 96489 bricks, sold 34375 of them. How many had he left ? 13. In a factory 86955 yards of cloth were made in one week, of which 36520 yards were sold. How many yards remained? 4:2. When the figures in the minuend are not all greater than the corresponding figures in the subtrahend. 1. From 834 lake 378. SOLUTION EXPLANATION. Since 8 units cannot be subtracted from 834 4 units, add 1 ten of 3 tens to units, thus leaving 2 tens 378 and giving 14 units; 8 units from 14 units leaves 6 units. Since 7 tens cannot be subtracted from 2 tens, add 1 hun- 456 dred of the 8 hundreds, thus leaving 7 hundreds and giving 12 tens ; 7 tens from 12 tens leave 5 tens, 3 hundreds from 7 hundreds leaves 4 hundreds. The result, 456, is the difference required. From the preceding illustrations we have the following: To Subtract Whole Numbers a. Write the subtrahend under the minuend so that figures of like order are in the same column. b. Begin at the right and subtract each column separately. c. If the lower figure is greater than the upper, add ten to the upper figure and subtract the lower from it. Take one from next upper figure and proceed as before. NOTES. 1. The sum of the remainder and subtrahend equals the minuend. 2. The difference between the minuend and remainder equals the subtrahend. PROBLEMS ft) 873 538 (S) (4) (5) (6) (7) 6423 1969 8146 3176 9076 3862 1408 4377 2907 4567 ft) 5097 3809 ft) 76377 45761 * (10) 67777 46699 (11) 900076 899934 (12) 767340 5039 20 NEW BUSINESS ARITHMETIC IS. From 962 take 824. 14. 6593 1807 = how many? 15. 80014 43190 = how many? 16. From 35467 take 12479. 17. From 94100 take 5007. 18. Take 307709 from 604562. 19. Take 42620 from 58364. 20. Subtract ten thousand six hundred forty-two from fifteen thousand fifteen. 21. From one million nine thousand six take twenty thou- sand four hundred. 22. What is the difference between two million seven thou- sand eighteen, and one hundred five thousand seventeen? 28. A man receiving a salary of $2450, spent for family ex- penses $968. How much had he left? 24. A farm that cost $6200 was sold at a loss of $743. For how much was it sold? 25. B has $8000 and owes $3749. How much will he have after paying what he owes? 26. Bought land for $9000, sold half for $6175 and the re- mainder for $7140. What did I gain on the land? 27. A man having $10000 lost $140. How much had he left? 28. A builder agreed to build a church for $31840; it cost him $27196. What was his gain? 29. A man m commenced business with $3760, and at the end of two years had $6708. How much did he gain? SO. A merchant bought goods of a manufacturer amounting to $3180 and paid him cash amounting to $1892. How much does he still owe the manufacturer? 31. The distance from New York to Queenstown is 2890 miles. After having sailed 1640 from New York, how far is a vessel from Queenstown ? 82. A bought a lot and built a house upon it. The lot cost him $1625. He paid for carpenter work on the house $2340 ; for mason work $428; for plastering $534; for plumbing $246; for painting $186, and for fencing, grading, etc., $125. He then sold both house and lot for $6800. What was his gain ? SUBTRACTION 21 S3. Find the balance of the following accounts:. DR. MILLER & MILLER CR. 1905 1905 an. 1 Balance, $125.60 an. 5 Cash, $125.60 an. 4 Mdse.,30da., 246.24 an. 9 Sight Draft, 325.00 fan. 6 Mdse., 2/10, 563.42 an. 12 Ret'd Goods, 25.94 [an. 9 Mdse., 10 da., 327.64 an. 26 Note, 30 da. 400.00 an. 24 Mdse., 30 da., 297.29 34. DR. BROWNING, KING & CO. CR. 1905 Feb. Feb. Feb. Feb. 10 15 18 26 $300.00 100.00 31.65 126.34 1905 Feb. Feb. Feb. Feb. Feb. Feb. Feb. 1 4 6 12 20 22 24 Balance $327.65 124.00 75.26 24.37 62.43 126.34 316.24 35. DEPOSITORS' LEDGER, BANKERS' NATIONAL BANK Accounts Balance Deposit Checks in Detail Total Checks Balance $ 25.00 136.00 1. Adams, Wm. $ 324.36 $1000.00 624.37 $785.37 $538.99 324.00 2. Allison, W. K. 462.85 1114.60 476.21 ***** *** ** 1000.00 3. Brown, F. C. 1142.61 3125.00 724.36 ? ? 41.25 4. Dennis & Co. , W. E. 25.60 784.00 63.00 ? ? 216.40 5. Fern Bros. & Co. 284.36 936.24 317.42 ? ? 400.00 6. Henry & Henry 924.65 824.35 75.63 ? . ? 369.80 7. Lamson & Bro. 2346.80 2143.84 421.00 ? ? 8. Mann & Smith 9175.20 924.81 725.14 725.14 ? 362.24 9. Nero Mfg. Co. 1146.24 475.60 436.43 ? ? 824.36 10. Mano Eng. Co. 3174.38 976.97 642.63 ? ? ***** f ** ***** ** ) ? ? Proof Bal. + Dep. - Total Checks = Bal. MULTIPLICATION 43. Multiplication is taking one number as many times as there are units in another. It is a short method of adding equal numbers ; thus, 2 cents + 2 cents + 2 cents + 2 cents = 4X2 cents = 8 cents. 44. The Multiplicand is the number to be taken ; as, 2 cents in the above. 45. The Multiplier is the number which shows how many times the multiplicand is taken; as, 4 in the above. 46. The Product is the number obtained by multiplying; as, 8 cents in the above. 47. The Sign of multiplication is an oblique cross X, and is read times when the multiplier is placed first, and multiplied by when the multiplicand is first. When placed between two num- bers it shows that one is to be multiplied by the other. 4X2 cents is read 4 times 2 cents and means that 2 cents are taken 4 times in addition, or that 2 cents are multiplied by 4. The multiplicand and multiplier are called factors, as they both together produce the product. The multiplicand may be either an abstract or a concrete number. The multiplier must always be an abstract number. The product is an abstract or concrete number according as the multiplicand is abstract or concrete. Multiplication is a short method, of performing addition when the numbers to be added are equal. MULTIPLICATION TABLE 1X1=1 2X1=2 3X1=3 4X1=4 1X2=2 2X2=4 3X2=6 4X2=8 1X3=3 2X3=6 3X3=9 4 X 3 = 12 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 1X6=6 2 x 6 = 12 3 X 6 = 18 4 X 6 = 24 1X7=7 2 X 7 = 14 3 X 7 = 21 4 X 7 = 28 1X8=8 2 X 8 = 16 3 X 8 = 24 4 X 8 = 32 1X9=9 2 X 9 = 18 3 X 9 = 27 4 X 9 = 36 1 X 10 = 10 2 X 10 = 20 3 X 10 = 30 4 X 10 = 40 1 X 11 = 11 2 X 11 = 22 3 X 11 = 33' 4 X 11 = 44 1 X 12 = 12 2 X 12 = 24 3 X 12 = 36 4 X 12 = 48 22 MULTIPLICATION 23 5X1=5 6X1=6 7X1=7 8 X 1=8 5 X 2 = 10 6 X 2 = 12 7 x 2 = 14: 8 X 2 = 16 5 X 3 = 15 6 X 3 = 18 7 X 3 = 21 8 X 3 = 24 5 X 4 = 20 6 X 4 = 24 7 X 4 = 28 8 X 4 = 32 5 X 5 = 25 6 X 5 = 30 7 X 5 = 35 8 X 5 = 40 5 X 6 = 30 6 X 6 = 36 7 X 6 = 42 8 X 6 = 48 5X 7 = 35 6 X 7 == 42 7 X 7 = 49 8 X 7 = 56 5 x 8 = 40 6 X 8 = 48 7 X 8 = 56 8 X 8 = 64 5 x 9 = 45 6 X 9 = 54 7 X 9 = 63 8 X 9 = 72 5 X 10 = 50 6 X 10 = 60 7 X 10 = 70 8 X 10 = 80 5 X 11 = 55 6 X 11 = 66 7 X 11 = 77 8 X 11 = 88 5 X 12 = 60 6 x 12 = 72 7 X 12 = 84 8 X 12 = 96 9X1= 9 10 X 1 = 10 11 X 1= 11 12 X 1 = 12 9 X 2 = 18 10 X 2= 20 11 X 2= 22 12 X 2 = 24 9 X 3 = 27 10 X 3 = 30 11 X 3= 33 12 X 3= 36 9 x 4 = 36 10 X 4 = 40 11 X 4 = 44 12 X 4= 48 9 X 5 = 45 10 X 5 = 50 11 X 5= 55 12 X 5= 60 9 X 6 = 54 10 X 6 == 60 11 X 6= 66 12 X 6 = 72 9 X 7 = 63 10 X 7 = 70 11 X 7= 77 12 X 7 = 84 9 X 8 = 72 10 X 8= 80 11 X 8 = 88 12 X 8 = 96 9 x 9 = 81 10 X 9 = 90 11 X 9 = 99 12 X 9 = 108 9 X 10 = 90 10 X 10 = 100 11 x 10 = 110 12 X 10 = 120 9 X 11 = 99 10 x 11 = 110 11 X 11 = 121 12 X 11 = 132 9 X 12 = 108 10 X 12 = 120 11 x 12 = 132 12 X 12 = 144 48. When the multiplier consists of one figure. 1. Multiply 436 by 4. EXPLANATION. 4 times 6 units are 24 units, or 2 tens and 4 units; write the 4 units in units' place, and add the 2 tens to the product of tens. 4 times 3 tens are 12 tens, plus the 2 tens (from the product of units) are 14 tens, or 1 hundred and 4 tens; write the 4 tens in tens' place and add the 1 MULTIPLICAND MULTIPLIER PRODUCT SOLUTION 436 4 1744 hundred to the product of hundreds. 4 times 4 hundreds are 16 hundreds, plus the 1 one hundred are 17 hundreds, or 1 thousand and 7 hundreds; write the 7 hundred in hundreds' place, and the 1 thousand in thousands' place. The result, 1744, is the product required. Find the product of each of the following : (2) (3) (4) (5) (6) (7) 1624 2436 1837 3262 8425 2987 234567 24 NEW BUSINESS ARITHMETIC (8) (9) (10) (11) (12) 3204 4624 3285 4623 8423 89465 6327 7 14. Multiply 12687 by 2. IS. Multiply 32346 by 6. 15. Multiply 43745 by 3. 19. Multiply 49728 by 7. 16. Multiply 81968 by 4. 20. Multiply 27856 by 8. 17. Multiply 32643 by 5. 21. Multiply 38769 by 9. 22. In 1 gallon there are 4 quarts. How many quarts are there in 2647 gallons? 23. A man receives $2645 a year. How much does he receive in 5 years? 24. What will it cost to dig a ditch 7 miles long at $273 per mile? 25. What will 8 acres of land cost at $259 per acre ? 26. When flour is selling at $9 per barrel, what will 3642 bar- rels cost? 27. If a man walks 6 miles an hour, how many miles will he walk in 16 days by traveling 8 hours each day? 28. If a bank clears $37293 each year, how much will it clear in 7 years? 49. When the multiplier is expressed by more than one figure. 1. Multiply 436 by 243. MULTIPLICAND MULTIPLIER PARTIAL PRODUCTS PRODUCT SOLUTION 436 243 1308 1744 872 105948 EXPLANATION. The product of 436 by 3 units is 1308 units; write so the right-hand figure is in units' place. The product 436 by 4 tens is 1744 tens; write so the right-hand fig- ure is in tens' place. The product of 436 by 2 hundreds is 872 hundreds; write so the right-hand figure is in hundreds' place. Add the partial products. This gives 105948, the product required. 1. When the multiplier contains two or more figures, the several re- sults obtained by multiplying by each figure are called partial products. 2. When there are ciphers between the significant figures of the mul- tiplier, pass over them, and multiply by the significant figures only. MULTIPLICATION 25 From the preceding examples and illustrations we deduce the following : To Multiply Whole Numbers a. When the multiplier contains two or more figures, write it under the multiplicand so that figures of the same order are in the same column. b. Begin at the right and multiply the multiplicand by each figure of the multiplier, and write the first figure of each product under the figure of the multiplier that produced it. c. Add the partial products. NOTES. 1. When there are ciphers at the right of the multiplier or multiplicand, place the right-hand figure of the multiplier under the right- hand figure of the multiplicand and multiply as if there were no ciphers. 2. After multiplying annex to the product as many ciphers as there are at the right of both the multiplier and multiplicand. >V9, P3SS PROBLEMS (2) (3) (4) (5) (6) (7) Multiply 365 463 268 796 397 1584 by 47 36 52 68 286 674 8. Multiply 368 by 43. 12. Multiply 8765 by 574. 9. Multiply 4096 by 246. 13. Multiply 3700 by 1420. 10. Multiply 1628 by 250. U. Multiply 12000 by 900. 11. Multiply 2374 by 2300. 15. Multiply 7324 by 2364. 16. At $436 per acre, what will 394 acres cost? 17. Find the cost of 368 hogsheads of tobacco at $567 per hogshead. 18. A drover bought 763 head of oxen at an average of $67 per head. What did they cost him? 19. How many feet are there in 150 miles, if there are 5280 feet in 1 mile? 20. In 1 pound there are 7000 grains. How many grains are there in 1260 pounds? 21. A factory employs 236 men at an average of $147 per month. What amount do they all receive? 26 NEW BUSINESS ARITHMETIC 22. A manufacturer sold 328 self-binding reapers at $469 each. How much did he receive for them ? 23. If 1 barrel of flour weighs 200 pounds, what will 760 barrels weigh? 24. What will 894 bushels of wheat weigh if 1 bushel weighs 60 pounds? 25. A farmer bought 207 acres of land at $80 per acre. What was the cost? 26. In 1 hogshead there are 63 gallons. How many gallons are there in 3267 hogsheads? 27. How many cubic inches are there in 2362 gallons, if 1 gallon contains 231 cubic inches? 28. If in 1 bushel of apples there are 56 pounds, how many pounds are there in 942 bushels ? 29. Find the cost of 2450 bushels of wheat at 85 cents per bushel. 80. If a man takes 30300 steps each day for 260 days, how many steps does he take? 81. If a boy writes 1605 words an hour, how many words will he write in 40 days by working 12 hours each day? 82. A man bought 420 loads of corn, 36 bushels in each load. How many pounds did he buy if each bushel weighs 56 pounds? 88. I sold 18 carloads of hogs, 35 hogs in each car, at 10 cents per pound. The hogs averaged 320 pounds. How much did I receive for the whole lot? SPECIAL CASES IN MULTIPLICATION a. To multiply by 10, 100 or 1 with any number of ciphers following. b. To multiply when the multiplier has ciphers at the right. c. To multiply when there are ciphers at the right of each term. d. To multiply when the unit figure of the multiplier is one. e. To multiply when the left-hand figure of the multiplier is one. f. To multiply by 11, 22, etc. g. Cross multiplication. MULTIPLICATION 27 Illustration a. 32 X 100 = 32 and the addition of two ciphers, or 3200. EXAMPLES. 49 X 100 ; 53 X 10 ; 645 X 10 ; 327 X 100. b. 24 X 90 = 9 X 24 and the addition of one cipher, or 2160. EXAMPLES. 25 X 80 ; 84 X 600; 36 X 200; 71 X 800. c. 90 X 80 = 9 X 8 and the addition of two ciphers, or 7200. EXAMPLES. 240 X 30; 3600 X 900; 2500 X 2500; 90 X 910. d. 243 X 21 == 243 X 21 486 5103 EXAMPLES. 294 X 31 ; 846 X 51 ; 327 X 601 ; 426 X 701. e. 374 X 16 = 374 X 16 2244 5984 EXAMPLES. 427 X 17; 375 X 104; 724 X 19 ; 562 X 109. f. 3452 X 11 = 37972. Write 2 as the first figure, (5 + 2) as the second, (5 + 4) as the third, (3 + 4) as the fourth and 3 as the fifth. Carry when necessary. To multiply by 33, multiply each addition by 3, then add the carrying number. EXAMPLES. 3463 X 11; 4234 X 22; 3714 X 33; 4637 X 55; 9876 X 11; 7964 X 66. gm 64 X 76 = 4864. (6X4) = units. Write the 4 and carry the 2. 2 4 (6X6) + (4X7) = tens' place. Write the 6 and carry the 6 + (6 X ?) = hundreds' place; 4864 the desired result. EXAMPLES. 1. 24 X 36 = x 2. 94 X 63 = x 62 X 47 x 38 X 45 = x 74 X 39 =_ 57 X 67 =_ x x 28 NEW BUSINESS ARITHMETIC PROBLEMS IN ADDITION, SUBTRACTION AND MULTIPLICATION 50. 1. Bought 230 bushels of corn at 40 cents a bushel and 365 bushels of wheat at 80 cents a bushel. What did both cost? 2. A teacher receives a salary of $1300 a year and pays $360 for board, $200 for clothing, $100 for books and $45 for other expenses. What does he save in the year? 3. A merchant bought 288 barrels of flour for $1960 and sold it at $8 a barrel. How much did he gain ? 4. A farmer bought 34 head of cattle at $18 a head and sold them at $21 a head. How much did he gain by the operation? 5. A lawyer has an income of $4325 a year, and his daily expenses are $4. What will he save in a year of 365 days? 6. A sold a farm of 360 acres at $45 an acre; B sold one of 280 acres at $60 an acre. Which received the greater sum, and how much? 7. A farmer sold 263 bushels of wheat at $1 a bushel. He received in payment 23 yards of cloth at $4 a yard, and the bal- ance in groceries. What did) the groceries cost him ? 8. I sold 17 cows at $36 apiece and for them received 65 tons of hay at $9 a ton and the remainder in money. How much money did I receive? 9. A man bought a house for $2867. He expended in repair- ing it $16 for plumbing, $73 for carpenter work, $48 for painting. He then sold the house for $3265. What did he gain ? 10. Two persons start from the same point and travel in oppo- site directions, one at the rate of 45 miles a day and the other 36 miles a day. How far apart will they be in 16 days? 11. A dealer bought 535 barrels of pork at $8 a barrel. He sold 245 barrels of it at $10 a barrel and the remainder at $7 a barrel. What did he gain or lose? 12. Mr. Brown has an income of $12650 a year. He spends $1650 for house rent and twice as much for other expenses. How much does he save in a year? MULTIPLICATION 29 IS. A sold 3 houses. For the first he received $2875, for the second $230 more than the first, and for the third as much as the first two. How much did he receive for all? 14. Mr. C bought 14 cows at $23 each, 7 horses at $96 each, 34 oxen at $57 each, and 300 sheep at $2 each. He sold the whole for $3842. What did he gain? 15. A merchant having $7632 deposited in his bank, drew out for the purchase of dry-goods, $1867; groceries, $362; boots and shoes, $218; hardware, $160. What amount had he left in the bank? DIVISION 51. Division is finding how many times one number is con- tained in another. 52. The Dividend is the number to be divided. 53. The Divisor is the number by which to divide. 54. The Sign of division is a short horizontal line with a dot above and one below it -=-. The divisor follows the dividend as $6 -^ 2 or $6 -4- $2. It may be written jf^ 2) $6, or $6(2, 2 55. The Quotient is the number obtained by dividing, and shows how many times the divisor is contained in the dividend. 1. When the dividend does not contain the divisor an exact number of times, the part of the dividend left is called the remainder, and it must be less than the divisor. 2. As the remainder is always a part of the dividend, it is always of the same name and kind. 3. When there is no remainder, the division is said to be exact. 4. When the process of dividing is performed mentally, and the re- sults only are written, the operation is termed Short Division. 5. When the whole process of division is written, the operation is termed Long Division. SHORT DIVISION 56. When the divisor consists of one figure. 1. Divide 693 by 3. SOLUTION DIVISOR 3)693 DIVIDEND QUOTIENT 231 Find the quotient of each of the following: m W (4) (5) (6) (7) 2)864 3)936 5)550 2)6248 3)9636 4)4884 (8) (9) (10) (11) (12) (13) 2)8624 3)9306 4)80480 3)30609 2)20840 5)5055 80 DIVISION 31 14. Divide 1712 by 8. SOLUTION 8)1712 214 Solve the following problems: (15) (16) (17) (18) (19) (20) 4)1720 5)3675 6)4992 7)2674 8)9296 9)11916 21. At $9 a barrel how many barrels of flour can be bought for $10926 ? 22. How many calves can I buy with $2940 at $7 per head? 23. Eight men own 22824 sheep. If they have the same number, how many has each? 24. Five men invest equally in business. The total invest- ment was $23770. How much did each invest? 25. When broadcloth was selling at $6 per yard I paid $97362 for an invoice. How many yards did I buy? LONG DIVISION 57. When the divisor is expressed by more than one figure. 1. Divide 5848 by 43. SOLUTION 43)5848(136 43 154 129 258 258 From the preceding we induce the following : To Divide Whole Numbers o. Write the divisor on the left of the dividend. b. Find how many times the divisor is contained in the least number of figures which will contain it at the left of the dividend, and write the result in the quotient at the right. 32 NEW BUSINESS ARITHMETIC c. Multiply this quotient figure by the divisor, subtract the product from the figures of the dividend used and to the remain- der bring down the next figure of the dividend, which divide as before, and so continue until all the figures of the dividend have been brought down and used. d. If, after bringing down a figure, the divisor is too large to be contained in the dividend, ivrite a cipher in the quotient and bring down the next figure in the dividend. e. If there is a remainder in the quotient it should be written at the right of the quotient with the divisor under it. NOTES. 1. If any remainder be equal to or greater than the divisor,, the quotient figure is too small, and must be increased. 2. If the product of the divisor by the quotient figure be greater than the dividend, the quotient figure is too large, and must be diminished. PROBLEMS 2. Divide 7668 by 36. 6. Divide 24492 by 78. 3. Divide 1666 by 49. 7. Divide 11808 by 246. 4. Divide 3484 by 52. 8. Divide 49815 by 369. 5. Divide 20995 by 85. 9. Divide 1720 by 5. 10. Divide 32740 by 154. 11. Divide 32572 by 34. 12. Divide 1554768 by 216. 13. Divide 93840 by 63. Remainder 33. U. Divide 10557312 by 32. 15. Divide 3931476 by 278. 16. Divide 352417 by 29. Remainder 9. 17. Divide 75088 by 52. 18. Divide 1674918 by 189. 19. Divide 42647 by 92. Answer, 463|i. 20. Divide 163513 by 497. 21. Divide 127960 by 267. 22. Divide 36928 by 69. 28. At $76 each, how many horses can be bought for $9728? 24. 274 wagons cost $29592. What was the average price per wagon? 25. B paid $19872 for 207 acres of land. What was the price per acre? 26. A farmer raised 9765 bushels of wheat on 223 acres. What was the yield per acre? DIVISION 33 27. A manufacturing company made a profit of $37840 in 215 days. What was the daily profit? 58. When there are ciphers at the right of the divisor. I. Divide 34216 by 900. EXPLANATION. Cut off the ciphers at the right of the di- SOLUTION visor and the same number of 9|00)342|16 figures from the right of the 38 QUOTIENT. 16 REMAINDER dividend. Divide the remain- ing figures of the dividend by the remaining figures of the divisor. To the remainder, if any, annex the figures cut off from the dividend. PROBLEMS 2. Divide 362076 by 60. 3. Divide 350000 by 14000. 4. Divide 28520 by 1500. 5. Divide 18065 by 1200. 6. Divide 1720800 by 3600. 7. Divide 968050 by 12900. 8. Divide 836290 by 1780. 9. Divide 924000 by 2640. 10. Divide 7802030 by 6070. II. At $150 each, how many horses can be bought for $11250? 12. A real estate dealer received $8640 for 36 lots. What was the average price of the lots ? PROBLEMS IN ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION 59. 1. A merchant owes $59, $84, $36 and $17. He pays $42. How much does he still owe? 2. A bought four bills of goods amounting to $740, $965, $342 and $196. He paid $1262 on them. How much does he still owe for the goods? 3. A laborer bought a coat worth $16, a vest worth $3, and a pair of pants worth $5. How many days had he to work to pay for his suit, his services being worth $2 a day ? L I bought 95 bushels of wheat at 78 cents per bushel, and 34 NEW BUSINESS ARITHMETIC paid for it in cloth at 19 cents per yard. How many yards were required ? 5. Four men have $2890. The first has $610; the second $593 ; the third $975. How much has the fourth man? 6. A clerk's income is $898 a year and his expenses are $2 a day. How much will he save in two years of 365 days each? 7. How many pounds of cheese at 9 cents per pound must be given for 27 pounds of tea worth 80 cents a pound ? 8. A person sells 15 tons of hay at $22 per ton, and receives in payment a carriage worth $125, a cow worth $45, a colt worth $40, and the balance in cash. How much money ought he to receive ? 9. A deposited in bank $426, $743, $860, $910, $85, $1269 and $26. He withdrew from the bank $705, $210, $500. How much had he then in the bank ? 10. I sold 48 horses at $86 each, and with the money bought calves at $8 each. How many calves did I buy ? 11. I bought two pieces of land, one of 360 acres at $29 per acre, the other of 194 acres at $41 per acre. What did both pieces cost me? 12. A bought 175 cows at $23 each, and 268 hogs at $13 each. B bought 79 cows at $34 each, and 170 hogs at $11 each. How much more did A pay than B ? 13. I bought a farm for $2165, paying $725 cash, and the bal- ance in monthly payments of $120 each. How many monthly payments did I make? 14- A teacher receives a salary of $75 per month for 1 year. His board cost $20 per month, other expenses $180 for the year. With the balance of his money he buys books at $6 a volume. How many books can he buy ? 15. A man bought 26 tons of coal at $6 per ton. For how much must he sell it per ton to gain $52 on the 26 tons? 16. B had $9628, of which he invested $1860 in bank stock, $2108 in horses, $974 in hogs, $1218 in sheep, and the remainder in land. What did the land cost him? 17. A widow has a farm valued at $6720; also three houses worth $12530, $11324 and $9875. She has a daughter DIVISION 35 and two sons. To the daughter she gives one-fourth the value of the farm, and, one-third the value of the houses, and then divides the remainder equally among the boys. How much did each receive? 18. A is worth $960, B is worth five times as much as A, less $600, and C is worth three times as much as A and B and $300 more. What are B and C each worth and how much are they all worth? 19. A grocer bought 7 barrels of fish at $18 per barrel, but one barrel proved to be bad. This he sold for $5 less than cost, and the remainder at an advance of $3 per barrel. Did he gain or lose, and how much? 20. If a clerk's salary is $600 a year and his personal expenses $320, how many years before he will be worth $6600 if he has $1000 at the present time? 21. A man went into business with a capital of $1500; the first year he gained $800, the second year $950, the third year $700, and the fourth year $625, when he invested the whole in a cargo of tea and doubled his money. What was he then worth ? 22. A butcher bought 9 calves for $54, and 8 lambs for $16. How much more did he pay for a calf than a lamb? 28. A farmer sold to a grocer 380 pounds of pork, at 7 cents per pound ; 150 pounds of butter, at 17 cents per pound, and one cheese weighing 53 pounds, at 9 cents per pound, and received in payment 22 pounds of sugar, at the rate of 11 pounds for a dollar; 225 pounds of flour at 4 cents per pound; 15 pounds of tea, at 65 cents per pound; one half-barrel of fish, at $18 per barrel, and one set of dishes worth $27. Did the farmer owe the grocer, or the grocer the farmer, and how much ? 24. A speculator bought 200 bushels of apples for $90, and sold the same for $120. How much did he make per bushel ? 25. A milkman sold 120 quarts of milk, at 5 cents per quart, and took in payment one pig worth $1.50, and the balance in sheeting, at 10 cents per yard. How many yards did he receive? 26. A manufacturing company made 928 yards of cloth on Monday, 1142 yards on Tuesday, 1468 on Wednesday and 876 36 NEW BUSINESS ARITHMETIC yards on Thursday, and sold 1940 yards of it. How many yards remained ? 21. A man bought a farm, paying $1690 down. After mak- ing three other payments of $945, $765 and $2740, the amount unpaid was $3628. He sold the farm for $8278. What was his loss? 28. A merchant's store was insured for $21650, and his goods for $17645. The store was valued at $25000, and the goods at $22564. Both were destroyed by fire. What was his loss ? 29. A, B, C and D formed a partnership. A invested $720 more than B ; C invested $1280 less than B, and D invested $945 less than A and C together. What was the total investment if B invested $2450? 30. A speculator bought 200 acres of land at $45 per acre, and afterwards sold 150 acres of it for $11550; the balance he sold at a gain of $5 per acre, and received in payment $250 cash, and the balance in sheep at $5 each. How many sheep did he re- ceive ? What was his profit on the land ? FACTORING 60. An Exact Divisor of a number is a number that will be contained in it an integral number of times. 61. A Factor of a number is an integral divisor of the num- ber. The factors of 18 are 2, 3 and 3 ; of 30 are 2, 3 and 5. 62. A Prime Number is one which cannot be divided or separated into factors, except 1 and that number; as 3, 5, 7, 11 and 13. 63. A Composite Number is one which can be resolved or' separated into integral factors ; as 4, 6, 9, 10 and 12. 64. An Even Number is one that is exactly divisible by 2 ; as 8, 16, 24 and 30. 65. An Odd Number is one that is not exactly divisible by 2; as 5, 9, 7, 15 and 21. 66. A Prime Factor is one that is a prime number ; as 3, 11, J7 and 23. 67. Factoring is finding the factors of a number. 1. What are the prime factors of 42? SOLUTION 2)42 3)21 7 From the preceding definitions and example we have the fol- lowing : To Separate a Number Into Its Prime Factors a. Divide the given number by any prime factor. b. Divide the quotient, if a composite number, by any prime' factor and so continue dividing until the quotient is a prime- number. c. The divisors and the last quotient are the prime factors* 37 38 NEW BUSINESS ARITHMETIC Find the prime factors of the following numbers : 2. 9 11. 108 20. 300 29. 1347 8. 12 12. 120 21. 385 80. 2898 4. 18 13. 124 #& 465 81. 4292 5. 36 14. 186 28. 525 5. 9222 6. 35 15. 225 #4. 644 33. 8151 7. 42 16. 231 5. 656 54. 3476 8. 50 17. 288 26. 756 55. 5270 P. 66 18. 294 07. 1273 36. 8892 10. 96 IP. 297 28. 2920 57. 13717 CANCELLATION 68., Since dividing both dividend and divisor by the same number does not change the quotient, we may strike out or re- ject equal factors from both dividend and divisor without affect- ing the result. 69. Cancellation is striking out equal factors from both dividend and divisor. Cancellation is a short method of division-. 70. The Sign of cancellation is an oblique line, /; when drawn across a number, it shows the number has been cancelled ; as, , fy, and $. The most common method is to write the dividend above a horizontal line and the divisor beneath it, although a vertical line with the divisor on the left and the dividend on the right is sometimes used. If the dividend or divisor is a composite number it should first be re- solved into its prime factors, before beginning the operation of cancella- tion. 1. Divide 4X8X3X5X7 by 2X3X4X5. EXPLANATION. Strike out the fac- tors 3, 4 and 5 from both dividend SOLUHUJ* ... _,. _. , ,.. 4 and divisor. Since 2 in the divisor ity&V^y^y? * s a f ac t r f 8 in the dividend, we cancel these, leaving the factors 4 *v ' f X P X f> times 7 in the dividend, or 28, the quotient. CANCELLATION 39 We therefore have the following: To Find a Quotient by Cancellation a. Write the numbers composing the dividend above a hori- zontal line and those composing the divisor below it. b~ Cancel all factors common to both dividend and divisor. c. Multiply the remaining factors of the upper numbers or dividend together, and the remaining factors, if any, of the lower numbers or divisor together. Divide the upper product by the lower and the result will be the quotient desired. NOTES. 1. Rejecting a factor from any number is dividing the num- ber by that factor. 2. When a factor is cancelled, the unit, 1, is supposed to take its place. 3. One factor in the dividend will cancel only one equal factor in the divisor. 4. If all the factors or numbers of the divisor are cancelled, the prod- uct of the remaining factors of the dividend will be the quotient. 5. By many it is thought more convenient to write the factors of the dividend on the right of a vertical line, and the factors of the division on the left. Solve the following problems by cancellation : 2. Divide 3X7X4X5X11 by 5X7X4X3. 3. Divide 2X4X6X8X 10 by 2X4X5X6. 4. Divide 8X6X 12 X 15 by 5X3X4X2X3. 5. Divide 9 X 8 X 6 X 18 by 2 X 3 X 4 X 3 X 3. 6. Divide 7 X 6 X 3 X 1* by 2 X 3 X 2 X 7. 7. Divide 4 X 6 X 12 X 15 XS by 2X3X6X5X4. 8. Divide 3X6X9X 12 X 24 by 3X4X6X8X5. 9. How many yards of calico at $.08 per yard will pay for 14 bushels of turnips at $.28 per bushel? 10. If 8 yards of cloth cost $32, what will 19 yards cost? 11. How many hogs at $9 each will pay for 36 barrels of flour at $6 each ? 12. I exchanged 48 dozen of eggs at 10 cents per dozen for sugar at 8 cents per pound. How many pounds did I get? 13. I bought 8 boxes of boots, each containing 9 dozen pairs at $18 per dozen, and gave in payment 12 loads of wheat of 54 bushels each. What did I receive per bushel for the wheat ? 40 NEW BUSINESS ARITHMETIC 14. A cubic yard is 3 feet deep, 3 feet long and 3 feet wide. How many cubic yards in 24 feet long, 18 feet wide and 6 feet deep? GREATEST COMMON DIVISOR 71. A Common Divisor of two or more numbers is a number that will divide them integrally. 72. The Greatest Common Divisor of two or more numbers is the greatest number that will divide them integrally, or is the product of all their common prime factors. Numbers are said to be prime to each other when they have no common divisor. If a number divides two or more others, it will also divide their sum and difference, and also the sum and difference of any product of them, because it divides them when they are taken separately. Hence if one number divide the whole of another number, and also one part of it, it will divide the other part also. Thus, 9 divides 45 and 27, and also their difference, 18. 1. Find the Greatest Common Divisor of 84 and 203. EXPLANATION. Write the smaller number SOLUT as the divisor and the larger as the dividend. 84)203(2 We know that the G. C. D., whatever it is, 168 must divide 84, and if it divides 84 it will also 35)84(2 divide twice that number or 168. If it divides 70 203 and 168 it must divide their difference, 35, ~7T\oK/9 according to the principle laid down above. Repeating this argument until the end, it must _~. divide 7 and 14, and as 7 is contained in 14 7)14(2 without a remainder, 7 is the largest number 14 that will divide itself and 14, and hence is the G. C. D. From the preceding principles and explanations we have the following rule: To Find the Greatest Common Divisor a. Divide the greater number by the less, and then the less by the remainder ' f until nothing is left. b. The last divisor will be the Greatest Common Divisor. LEAST COMMON MULTIPLE 41 NOTE. 1. If it is desired to find the G. C. D. of more than two num- bers, first find the G. C. D. of two of them, and then find the G. C. D. of that and another, and so on. 2. Find the greatest common divisor of 247 and 323. 3. Find the greatest common divisor of 316 and 664. 4. What is the greatest common divisor of 532 and 1274? 5. What is the greatest common divisor of 741 and 1273 ? 6. What is the greatest common divisor of 1313 and 4108? 7. What is the greatest common divisor of 468 and 1266 ? 8. What is the greatest common divisor of 224, 280 and 336 ? 9. I have four rooms, respectively 16, 20, 24 and 32 feet wide. How wide must carpet be that will just fit each room? 10. The sides of a lot are 112, 126, 140 and 168 feet. What is the greatest length of boards that can be used in fencing it without cutting them? 11. A farmer has four pieces of land. The first has 240 acres ; the second, 180 acres ; the third, 300 acres ; the fourth, 360- acres. He wishes to divide them into the largest possible fields of equal side. How many acres will there be in each field? LEAST COMMON MULTIPLE 73. A Multiple of a number is any number that will integrally contain it. Thus, 18, 24 and 30 are multiples of 6. 74. A Common Multiple of two or more numbers is any num- ber that will integrally contain each of them. Thus, 24 is a com- mon multiple of 2, 4, 6 and 8. 75. The Least Common Multiple of two or more numbers is the least number that will integrally contain each of them. Thus, 36 is the least common multiple of 6, 12 and 18. 76. The Least Common Multiple contains all the prime fac- tors of each of the given numbers. It is plain that the least common multiple of numbers that have no common factor is the product. But if the numbers, have a common factor, that factor is to be taken only once unless 42 NEW BUSINESS ARITHMETIC it is repeated in any of the numbers, in which case it must be used as many times as a factor of the multiple, as the greatest number of times it appears in any of the given numbers. 1. Find the least common multiple of 4, 6, 9 and 12. EXPLANATION. Write the numbers in a SOLUTION horizontal line. Since 2 is a factor of some of 2)4, 6, 9, 12 the numbers, we know that it must be a fac- 2)2, 3, 9, 6 tor f t* 16 L. C. M., hence we divide as many ON-, o Q o' numbers as possible by 2 and bring down the quotients and undivided numbers below. By inspection we see that 2 is again a factor of 2 X 2 X 3 X 3 = 36 L. C. M. some O f t h e numbers brought down, and hence another 2 must be a factor of the L. C. M. We therefore divide by 2 and bring down the quotients and undivided numbers again. We next divide by 3 for a like reason and bring down as before. We now have but 3 left, and as we would gain nothing by dividing it by itself, we multiply together the several divisors and last quotient, and the result is the L. C. M. sought. Suggestion. The L. C. M. of 12, 9, 6 and 4 cannot be less than 12 ; 12 contains all of the factors of itself, 6 and 4 and 3, one of the factors of 9. It therefore remains to multiply the remain- ing factors 12 and 3 to find the L. C. M., which is 36. From this example we derive the following rule : To Find The Least Common Multiple a. Write the numbers in a horizontal line. b. Divide by any prime number that will exactly divide one or more of the given numbers, and write the quotients and undivided numbers beneath. Continue to divide until no number will divide more than one of the quotients. c. Multiply the several divisors and the last quotient together and the result will be the L. C. M. 2. What is the least common multiple of 27, 45, 63 and 81 ? 3. What is the least common multiple of 10, 12, 14, 16 and 18? Find the L. C. M. of the following: 4. 32 ; 48, 64 and 80. 7. 3, 6, 9, 12, 15, 21 and 24. 5. 18, 30, 42 and 60. 8. 30, 40, 50, 60, 70 and 80. 6. 32, 48, 72 and 96. 9. 7, 14, 28, 56, 112 and 224. LEAST COMMON MULTIPLE 43 10. What is the smallest piece of land that can be divided into fields of 16, 24 or 30 acres each? 11. What is the least amount of money with which you can purchase chickens at 12 cents each, ducks at 20 cents each, tur- keys at 60 cents each or geese at 75 cents each? 12. How many bushels will a bin contain from which 9, 18 or 30 bushels can be taken an even number of times ? IS. A can shear 42 sheep in a day, B 63, and C 54. What is the number of sheep in the smallest flock that would furnish exact days' labor for each of them shearing alone ? FRACTIONS 77. A Fraction is one or more of the equal parts of a unit. 78. A Fractional Unit is one of the equal parts of a unit, as, one-third, one-fourth, one-seventh. 79. A Fraction is one or more fractional units, as, one-half, three-fourths, seven-ninths. 80. The Unit of a Fraction is the thing divided. The unit of the fraction two-thirds of a dollar, is $1 ; of four-fifths is 1 ; of six-elevenths of a bushel is 1 bushel. 81. A Fraction is expressed by writing one number above and another below a short horizontal line ; as, one-fifth, J ; three- fourths, j. 82. The Terms of a fraction are the two numbers used to express it. 83. The Denominator shows the number of parts into which the unit is divided and is written below the line. 84. The Numerator shows the number of parts (fractional units) taken, and is written above the line. In bushels, 5 is the denominator and shows the unit (1 bushel) is divided into 5 equal parts; 4 is the numerator and shows that 4 of the 5 equal parts are taken. is the fractional unit. 85. A Fraction is read by naming the number and kind of fractional units; as, f, three-fifths; $|, two-sevenths of a dollar; $ bushel, nine-twentieths of a bushel. Read the following fractions : 1. i- 4. TV 7. TV- 10. 2. 1. 5. A. 8. TV 11. 8. i. 6. A 9. if. 12. 44 FRACTIONS 45 Write the following in the form of fractions : 13. Three-fifths. 19. Twelve-fourteenths. 14. Six-sevenths. 20. Sixteen-twentieths. 15. Seven-elevenths. 21. Eight twenty-sixths. 16. Ten forty-sevenths. 22. Thirty- four seventy-fifths. 17. Forty-one sixtieths. 23. Sixty-nine eighty-ninths. 18. Fifty-six seventy-firsts. 24- Ninety-three ninety-sixths. 86. A Proper Fraction is one whose numerator is less than its denominator; as, , J, -$. 87. An Improper Fraction is one whose numerator equals or exceeds its denominator; as, -f, f, V. 88. A Mixed Number is one expressed by an integer and a fraction; as, 3J, read three and one- fourth; the word and being placed between the integer and fraction. 89. A Complex Fraction is one which has a fraction in one or both of its terms; as, y T T^"' The fi rst is read one-half over two-thirds, etc. 90. A Compound Fraction consists of two or more single fractions joined together by the word of; as, ^ of f of f . 91. Reduction is changing the form of a number or fraction without changing its value; 2 may be changed to f ; 3 to *-\ $ to 3; f to i, while the value is not altered. A Fraction is an indicated division, the numerator being the dividend, the denominator being the divisor and the value of the fraction the quotient. The value of the fraction is the ratio existing between the numerator and denominator. Therefore, 1. Increasing the numerator increases the value of the fraction. 2. Diminishing the denominator increases the value of the fraction. 3- Diminishing the numerator diminishes the value of the frac- tion. 4. Increasing the denominator diminishes the value of the fraction. 46 NEW BUSINESS ARITHMETIC 5. Increasing both numerator and denominator the same num- ber of times does not alter the value of the fraction, for the ratio between them remains the same. 6. Diminishing both numerator and denominator in the same proportion does not alter the value of the fraction. REDUCTION OF FRACTIONS 92. Reduction of Fractions consists in changing their form without altering their value. A fraction is in its lowest terms when its numerator and de- nominator have no common divisor. As fractions may be reduced to lower terms by division, they may also be reduced to higher terms by multiplication. ORAL PROBLEMS 1. -J = how many whole ones? f, f, -J-, f. 2. -f = how many fourths? How many halves? 6 _ f 1 t I 1 # TT tf, 7, ?, 2T> T5, TS- 1 l _ * III 4- 32" T^> > > ? 5. Change f f to thirds. 6. Change f 1 to twelfths, to sixths, to thirds. 7. How many halves in \\, &, if, II? 5. How many thirds in |, -J-J, f f, f |? 9. Compare | with if; I with }-jj-; $ with ff. 93. To reduce fractions to their lowest terms. 1. Reduce |% to its lowest terms. SOLUTION )= 3)11 = I From the solution we have the following rule: To Reduce Fractions to Lowest Terms a. Divide both terms of the fraction by any number that will divide them without a remainder. b. Divide this result as before, and so continue to divide until no number will divide both without a remainder. FRACTIONS 4 7 c. The last result will be the fraction in its lowest terms. 2. Reduce iff to its lowest terms, HI, ftf, 3. Reduce the following to their lowest terms : |fj, ff $, rVA, rfftV, && 4. Express in its simplest form the quotient of 125 divided b} 625. 5. Express in its simplest form the quotient of 272 divided by 425. 6. Divide 873 by 3395 and express the quotient in the lowest terms or simplest form. 7. Divide 323 by 437 and express the quotient in the lowest terms or simplest form. ORAL PROBLEMS 1. In one apple are how many halves? 4ths? 2. Two peaches equal how many half peaches? fourth peaches ? 8. -| equals how many 4ths ? 8ths ? 12ths ? 4. i equals how many 8ths? 12ths? 24ths? 36ths? 5. | equals how many 8ths? 12ths? 24ths? 36ths? 6. f equal how many 8ths? 12ths? 24ths? 36ths? 7. f equals how many 8ths? 12ths? 24ths? 36ths? 8. f equal how many IGths? 24ths? 40ths? 64ths? 9. | equal how many 16ths? 24ths? 40ths? 64ths? 10. How many 36ths in | ? in f ? in T % ? 11. How many 48ths in f ? f ? T V A? A? 94. To reduce fractions to higher terms. Since fractions are reduced to lower terms by dividing both terms by a common factor, they are reduced to higher terms by multiplying both terms by a common factor. 1. Reduce f to a fraction having 20 for its denominator. SOLUTION 20 -T- 4 = 5 j}_ X 5 = 15 4 X 5 = 20 Therefore we have the following rule: 48 NEW BUSINESS ARITHMETIC To Reduce Fractions to Higher Terms a. Divide the required denominator by the denominator of the fraction in order to find how many times the terms of the fraction must be increased. b. Multiply both terms of the fraction by the quotient as found above. 2. Reduce f to a fraction whose denominator is 15. 3. Reduce f to a fraction whose denominator is 35. 4. Reduce f to a fraction whose denominator is 63. 5. Reduce T V to a fraction whose denominator is 180. 6. Reduce ^f to a fraction whose denominator is 128. 7. Reduce if to a fraction whose denominator is 375. 8. Reduce j 7 ^ to a fraction whose denominator is 896. 9. Reduce |f to a fraction whose denominator is 918. 10. Reduce -f Jf to a fraction whose denominator is 2840. 95. To reduce improper fractions to whole or mixed numbers. ORAL PROBLEMS 1. What is a unit? What is a mixed number? 2. How many ones in -f? -f? |? \ 2 ? 3. How many ones in y? V? ? if? 4. Reduce to units V, , V, W- 5. V T === 7i; 7i is a mixed number. 6. * = how many units and what part of a unit? 7. -V = what mixed number? ? V? V? 8. Reduce to whole or mixed numbers: - 2 g 5 , > "V", f ?, f and 1J to fractions having the least common denominator. ADDITION OF FRACTIONS 98. Addition of Fractions is the process of finding the sum of two or more fractional numbers. We have seen that no quantities can be added together except they are of the same kind or denomination. Not only must frac- tions be parts of the same kind of units, but they must have the same denominators before they can be added. FRACTIONS 53 ORAL PROBLEMS 1. What is the sum of J, f and |? 2. What is the sum of f, f\ and J? 5. A has J and B f. How many eighths have both? How many units? 4. Find the sum of ^ and ^ ; J and J ; J and J. 5. Find the sum of and | ; f and f ; f and f . 0. Find the sum of f and f ; J and f ; T 7 2 and, f . 7. Find the sum of 2J and 3 ; 4 J and 5 J ; 3 and 4J. 5. Find the sum of 3| and 6j; 3f and 4&; 7f and J. 0. One boy has $3| and another has $2J. How many dol- lars have both? 10. A boy rode 3J miles in a wagon, 11 J miles in a train, and walked 2^ miles. How far did he go in all? 11. How many years are 12f years and 18J years? 12. How many hours are 15f hours and 17J hours? 13. What is the sum of 3J bushels, 4J bushels and 5f bushels? 14. How many dollars in $2J + $3| + $6 T 7 ^ and WRITTEN PROBLEMS 1. Find the sum of J, f, f and f . SOLUTION The L. C. M. of 2, 3, 4 and 6 is 12. 4 = A A + A + A + = = A = af . From the preceding problem and explanation we have the fol- lowing : To Add Fractions a. Reduce the fractions to their least common denominator. b. Add the numerators and under their sum write the denomi- nator. c. In mixed numbers, add the whole numbers and fractions separately, then add their sums. 64 NEW BUSINESS ARITHMETIC NOTE. If the mixed numbers are small, they may be reduced to im- proper fractions, and then added after the usual method. 2. Add i, f , f and f. 6. Add {, , 1 and H- 3. Add A, A, A and A- 7. Add *, A, H and If. 4. Add I, |, i and A 8. Add 7f, 9f, llf and 9f. 5. Add |, i, i and i P. Add 6f, 7 T V, 8}i and 9^. 10. What fraction is equal to 1 + 2f + 3} + 4f + 5f + 6f? 11. What is the sum of 17f, 18 T 5 , 26^ and lOf ? 1. Add 41, ITS, 2ff, Sf* and 5 A. 13. What fraction is equal to + i + i + A + A + A? 14. What is the sum of 125f, 327A and 25i? 15. What is the sum of iff, 8f, 3 A and 14|? 15. I have four fields. The first contains 17J acres; the sec- ond, llf- acres; the third, 21f acres; the fourth, 19 A acres. How many acres have I ? 17. Jones paid $7| for a coat, $2J for a hat, $3|- for pants, $1 for a vest and $4f for shoes. What did he pay for all ? 18. A merchant bought 38J yard,s of calico, 103f yards of muslin, 80f yards of flannel and 26J yards of gingham. How many yards did he buy? 19. A family used f of a ton of coal in September, T 7 ^ of a ton in October, | of a ton in November, ff of a ton in December and 1J tons in January. How much did they use in the five months ? 20. A farmer received $7 for a hog, $23 J for a cow, $11| for a sheep and $123 A f r a horse. How much did he receive for all? 21. A man invested $2460f in land, $1432. f in cotton and $1314f in mining stock. What was his total investment? 22. A has on deposit in a savings bank $46f , B has on deposit $28A, C has on deposit $76J and D has on deposit $96|. What is the total amount of their deposits? 28. A collector received from one man $5^%, from another $11|, from another $18 T %, and from another $lf. How much did he collect in all? FRACTIONS 55 4. Add 1026H, 1875|, 5634f and 4327f. 25. A lady went shopping, and expended for car fare J of a dollar, for thread J of a dollar, for needles T V of a dollar, for gloves 1J dollars, for a hat 7J dollars, for a dress 32 ^ dollars. What was the total amount of her expenditures ? 26. A farmer sold 437 bushels of corn for $127i; 268 T 5 2 bushels of wheat for $186 T 7 for taxes; $16& for advertis- ing and $38f for expenses in selling it. He collected $37 in rent for the property while he owned it, and sold it for $4000 in cash. How much was his gain? MENTAL REVIEW OF ADDITION AND SUBTRACTION 10O. To add two fractions whose numerators are each 1, take the sum of the denominators for the numerator, and the prod- uct of the denominators for the denominator of the sum. Thus, } + 1 = A. 58 NEW BUSINESS ARITHMETIC Find the value of: i. i+f e. i+f a. 2. i+f 7. T V+i m i+f 3. i+f 5. i+A. 13. i+rV. -4. i+f 5. i+f 14. m. 5. i+A-. m i+f J5. i+f 100 A. To subtract fractions whose numerators are each 1, take the difference of the denominators for the numerator and the product of the denominators for the denominator of the remainder. Thus, i i=Vo. Find the value of : 5. i-i 9. 6. i-i 10. J-4. 5. i-i 7. * A. iJ. f- 1. 4. 1-i. . i-i. w. i-i. 100B. To add two fractions whose numerators are greater than 1, take the sum of the products of the numerator of each by the denominator of the other for the numerator, and the product of the denominators for the denominator of the sum. Thus, f -f- }=}}. (2 X 4 + 3 X 3 = 17, and 3 X 4 = 12.) Find the value of: 1. f+t. 5. t+i 9. e. m. 10. m. 7. |+f W. f+ T 3 T. 4. *+f . i+f ^. 4+i 100C... To subtract two fractions whose numerators are greater than 1, take the difference of the products of the numera- tor of each by the denominator of the other for the numerator, and the product of the denominators for the denominator of the re- mainder. Thus, f f = T V (3 X 3 2 X 4 = 1, and 3 X 4 = 12.) MULTIPLICATION OF FRACTIONS 101. A fraction is multiplied by multiplying the numerator or dividing the denominator. FRACTIONS 59 ORAL PROBLEMS 1. At $i for 1 dozen eggs, what is the cost of 3 dozen? 2. At $| for a chicken, what will 5 chickens cost? 3. If a boy has f of a bushel, what would 5 boys have ? 4. 3 times J = t; 6 X i == t; 8 X 1 == i; 9 X \ == J-. 5. 5 times J = i; 5 X f = .r; 5 X 1 = x; 5 X | = *. 6. 7 times f = T; 7 X f ,r; 7 X f = .r; 7 X | = x. 7. 4 times lj x\ 4 X 2J = x \ 4 X 3| = x\ 4 X 2f = x. S. If a man earns $2J a day, how much will he earn in 4 days? 9. If a bushel of clover seed costs $2f, what will 5 bushels cost? 10. 6 X 31 = x\ 7 X 2f = ;r; 8 X if = x\ 9 X J = x. 102. To multiply a fraction by a whole number. WRITTEN PROBLEMS 1. If 1 hat costs | of a dollar, what will 6 hats cost? SOLUTION EXPLANATION. Since 1 hat cost 3- fourths of a dollar, 6 hats will cost 6 " = 4f = 4 times 3-fourths of a dollar or 18- fourths of a dollar, which is $4^. NOTE. Always divide the denominator when it is exactly divisible by the multiplier. 2. Multiply f by 5. 7. Multiply T V by 12. S. Multiply A by 9. 8. Multiply if by 9. 4. Multiply f by 4. 9. Multiply T \V by 27. 5. Multiply rV by 6. 10. Multiply |f by 14. 6. Multiply A by 10. H. Multiply T f,7^4r;t-T-.9=Tjr. 7. A paid $6| for 5 bushels of clover seed, what did he pay per bushel? (6f == V.) 8. I paid $5^ for 3 turkeys, find the cost of each. 9. Find the value of the following : 3J -j- 5 = x ; 16 J -f- 10 = >;5t4-6==;r;8J -r- G = x. WRITTEN PROBLEMS 1. If 3 bushels of timothy cost J of a dollar, what will 1 bushel cost? SOLUTION L^~ 3 = JL 24 NOTE. We divide the numerator when it is exactly divisible by the divisor; otherwise we multiply the denominator. FRACTIONS 65 2. Divide f by 2. 6. Divide T VV by 25. 5. Divide T 9 7 by 3. 7. Divide H by 11. 4. Divide ff by 5. 8. Divide ff by 21. 5. Divide -f f by 9. P. Divide HI by 75. .?#. If G pounds of cheese cost J of a dollar, what will 1 pound cost? 11. At $4 a yard what part of a yard of broadcloth can be bought for /T of a dollar? 12. If 7 dozen eggs cost -J-| of a dollar, what will one dozen cost? IS. If 7 bushels of wheat cost $6} what will one bushel cost? NOTE. Reduce the mixed number to an improper fraction and divide as before. 14- If 7 dozen hammers cost $23^, what will one dozen cost? 15. A farmer paid $563f for 4 horses. How much did he pay for each ? 16. If 9 men consume j of 5f pounds of meat in a day, how much does each man consume ? 107. To divide by a fraction. ORAL PROBLEMS 1. If coffee can be bought at the rate of $J per pound, how many pounds can be bought for $i? $|? $J? $J? $f ? $f ? $? $|? 2. Find the value of the following : f-^i;|-^i;f-^-4; I +*; f *!? 3. Find the value of the following : f-i-f;f-7-f;$H-; I -*;***. 4. If 2^ bushels of oats cost $1-J what is the cost of one bushel? 5. Find the value of the following: 3J-^ 2J; If -^- 14; 3| -f- 1J; 5J -f- 2J. 108. The Reciprocal of a number is 1 divided by the number ; thus the reciprocal of 3 is ^. 109. Since the reciprocal of a number is 1 divided by that number the reciprocal of a fraction is that fraction inverted. In- verting a fraction shows how many times it is contained in 1. 5 66 NEW BUSINESS ARITHMETIC WRITTEN ^PROBLEMS 1. At f of a dollar a yard, how many yards of cloth can be bought for $9 ? SOLUTION From the foregoing principles and explanation we derive the following rule : To Divide Fractions a. Reduce whole or mixed numbers to improper fractions. b. Invert the divisor, and multiply the dividend by the divisor inverted. c. Reduce the result to simplest form. 2. Divide 1 by f . 5. Divide by T \. 3. Divide J by f . 6. Divide f by ff 4. Divid,e j by f 7. Divide J by H. 5. How many times is contained in f ? P. How many times is t% contained in 2J ? .70. How many times is -J-f contained in 3y 9 T? I-/. How many times is J of f contained in 28? 12. How many times is f of f of J contained in of f ? 15. How many times is f of -J contained in f of H? 14. How many times is llf contained in of 45^? 75. What is the quotient of 18 J divided by 3|? 76. What is the quotient of f of 8{ divided by 7J? 17. What is the quotient of ^ of J divided by 4J times f ? 75. What is the quotient of f of J of f divided by f of f ofi 9 o? 19. What is the value of ~^? 5i SOLUTION >. What is the value of Hr J FRACTIONS 67" 8 21. What is the value of _5 ##. What is the value of Tjr "" 23. What is the value of o ~18 2 4. What is the value of -~ lo I off? 25. What is the value of gi I off? 26. What is the value of J o f i|" I of f of 4 ? 7. What is the value of g x | i + 3? #S. What is the value of 52 _ 31 16* + 3fo #0. What is the value of 1 ^| _j_ 4j" 30. What are the daily wages of a man who receives $14 J for 3J days work? 31. How many bushels of wheat at $f per bushel can be bought for $6f ? 2. How many tons of coal at $4 can be bought for $25^ ? S3. At $1^ per yard, how many yards can be bought for $6^j? 34. If 2J tons of hay cost $20, what will 1 ton cost? 35. I sold wheat at 90c per bushel and gained J of what it cost. Find the cost per bushel. EXPLANATION. Let % = the cost. Then % of the cost = 90c and % of the cost = 90 + 6 = 15c and % or the cost = 5 X 15 = 75c. 36. I sold a cow for $27 and lost T V of the cost. Find the cost of the cow. 37. A man bought a horse for $80, and a buggy for f as much as the horse. The buggy cost If times as much as the harness. Find the cost of the harness. ORAL REVIEW PROBLEMS 1. What is J of 14? 21? 36? 75? 125? 2. What is f of 24? 36? 48? 54? 63? 68 NEW BUSINESS ARITHMETIC 8. What is I of 28? 42? 56? 64? 81? 4. 18 is J of what number? J? i? J? J? 5. 12 is | of what number? f? f ? 6. Count by 2J to 100 ; by 3 ; by 6J ; by 6} ; by 12J ; by 16. NOTE. Practice on this daily until it can be done rapidly and accu- rately. 7. The sum of two numbers is 12J, one of the numbers is 7J, what is the other number? 8. J of 16 is J of what number? 9. | of 24 is J of what number ? 10. A has $12, B has 3 times as much as A and C has -J as much as A and B have. How maji^ dollars have all? 11. At 3 for 4 cents, how ma% pears can be bought for 20 cents? )| 12. At 5 for 2 cents, how many apples can be bought for 30 cents ? IS. If 5 bushels of oats cost $1.25, what will 7 bushels cost? 14- A boy spent f of his money and had $12| left, how many dollars had he at first ? 15. Paid $3J for a pair of shoes and had J of my money left, how much had I at first? 16. A has J of his sheep in one pasture, J in another and the balance, 60 in a third pasture, how many sheep had he in all? 17. A buys 20 apples at 2 for 4c and 30 more at 2 for 6c. He sells them all at the rate of 4 for lOc. Does he gain or lose and how much? 18. If 5 men can dig a trench in 16 days, what part can 3 men -dig in 8 days? Find the quotient of: 19. T\ -5- 3. 25. iV * 14. 81. 12 *- T V 37. 30 -^ |. 20. H -*- 6. 26. V- + 4. 82. 15 + }. S3. f -* 8. 21. H + 7. 27. if -5- 10. 33. 25 -5- 2j. 59. i -J- J. 00. TT -5- 5. 03. 6 -*- f . 84. 18 -* |. 40. f *- f. 3. 4 -*- 6. 0. 8 -f- 4. 35. f -i- 15. ^. | * A- &* - T\ -* 15. 50. 9 *- i 3 T . 36. 24 -f- 1. 40. | -f- f. FRACTIONS 69 48. f -7- 1. 47. t -7- I. 51. I - |. 55. T V * i 44. 16 -7- |. 48. f -7- f . 52. f - T V 5(5. 4-7-9. 45. 1 -5- 9. 49. 12 -T- f 53. f -5- If. 57. 15 - f. 46. j\ - 3. 50. 7-|. 54. 4 - |. 58. 24 -f- f . 59. What will 12 pounds of tea cost at f dollars per pound? 60. What will -f$ of a ton of hay cost at $18 per ton ? 61. Find the product of J, J, ^, ^ and J. 62. f is what part of ? 63. If a horse eats f bushel of oats in a day, how long will 30 bushels last him? 64. A crock of butter weighs 8J pounds, and the crock alone weighs 1J pounds. What is the value of the butter at 12 J cents per pound? ty 65. What will 9f cords of wood cost at 4-J dollars per cord? 66. At 36 bushels to the acre, what is the yield of if acres? 67. A lady bought 5| yards of silk for 8f dollars, what was the price per yard? 68. At If dollars per yard, how much cloth can be purchased for $14 ? 69. Sold a book for $2.25 and gained f . What did the book cost me? 70. At $4.50 per week, what will five days' board cost? 71. Find the cost of f of a ton of coal at $6.50 per ton. 72. Find the cost of f of a yard of silk at $.60 per yard. 73. A couch is worth $9. For how much must it be sold to gain T 3 ? 74. At 1J dollars per day of 10 hours, what will a man earn in 7-J hours? 75. If 10 bushels of apples will make 32 gallons of cider, how much cider will 7 bushels make ? 76. Find the cost of J of a piece of cloth of 36 yards at 1J dol- lars per yard. 77. A lady paid f of J of her money for a dress and ^ of f of it for a cloak. What part of her money did she spend ? 78. At 60c a dozen what is the cost of % of of a dozen of oranges ? What is the cost of one orange ? 70 NEW BUSINESS ARITHMETIC 79. How many strips of carpet f yard wide can be cut from a strip 9 yards wide? 80. John has $72 in the bank. He draws out T V of it each week for four weeks. How much has he left? 81. A farmer sold 10 doz. eggs at 16 Jc a dozen and took his pay in sugar at 5Jc a pound. How many pounds of sugar did he .get? S2. What is the cost of 16 pounds of coffee at 20Jc per pound ? '24 Ibs. of sugar at 6fc per pound? 12 Ibs. of rice at 5Jc per pound? --J barrel of flour at $6.44 per barrel? 20 pounds of oatmeal at 9^c -per pound ? a 12| pound ham at 10|c per pound ? REVIEW PROBLEMS. 110. 1. Reduce if If to its lowest terms. 2. Reduce -f to a fraction having 27 for its denominator. 3. Reduce 428| to an improper fraction. 4. Change -H} 1 - to a whole or mixed number. 5. Reduce f, ^, f and f to their least common denominator, 6. Add 4J, 1 and f 7. Add 23f, 14f, 16f and 1J. 8. Subtract 4 from 6f. 9. Find the difference between f of of and J of 2J. 10. The less of two numbers is 326f and the greater is 749^; what is their difference? 11. Find the difference between 3 X | X f X 5| and 3* X I X 4 X f . 12. Divide 2f by T V 13. Divide 125f by 4|. 14. A teacher who received $75 for a month's work, paid $17J for board, $lf for light and $9 T 7 2 for clothes. How much did he have at the end of the month? 15. Find the sum of 23f , 6, || and f of f . 16. How many days^must a boy work to receive $12J if he re- ceives $1J per day? 17. A spent f of his money and lost T 3 ^ of his money, and then had $21. How much did he have at first? FRACTIONS 71 18. John is 18 years old, and his age is f of his sister's age. How old is his sister? 19. A speculator paid $6428f for 135J acres of land. How much did it cost him per acre ? 20. I sold | of a flock of 18 sheep for $26f . What was the price per head for the sheep? 21. A has $40 which is 1 times B's money. How many dollars has B ? 22. I bought three pieces of carpet at $1J per yard. One piece contained 40J yards, another 33J yards, the other 35 T % yards. What was the entire cost? 23. A merchant bought 9 dozen eggs at $J per dozen and paid for them in cloth worth $f per yard. How many yards of cloth did it require? 24- The product of two fractions is f , and one of the fractions is {. What is the other fraction ? 25. If the dividend is {^ and the divisor is f, what is the quo- tient? 26. If 2 barrels of flour cost $26i, what will 8J barrels cost? 27. A and B worked for a certain sum. A worked 4 days and received $6j. How much did B receive if he worked 5 days at the same rate? 28. A farmer sold of his sheep to one man and J to another, when he found that he had 140 sheep left. How many had he at first? 89. A bought 150 tons of hay. He sold 35 tons at $4f per ton, 40 tons at $5J per ton and f of the remainder at $5-J per ton. How much money did he receive? 30. How many yards of cloth at $| per yard must be given for 15 tons of coal at $4J per ton? 31. In how many days will 3 horses eat 4J bushels of oats if each horse eats \- of a bushel each day? 32. How many pounds of butter at $ T 3 e per pound will pay for 48 bushels of corn at $f per bushel ? 33. A man paid $3500 for a farm and this was 2 times the cost of the house which he built upon it. Find the cost of the farm and house together. 72 NEW BUSINESS ARITHMETIC 34. With $lf I bought | of f of f of a yard of cloth. At that rate what will 3 yards cost? 85. A merchant paid $25 for 50 gallons of molasses. He lost by leakage and sold 20 gallons at $f . The remainder was sold so as to gain $5 on the whole. Find, the selling price per gallon. 36. How many yards of cloth yards wide will line 23J yards, 1 yards wide ? 37. A speculator bought 367 bushels of wheat at $f per bushel; he sold 126f bushels at $f per bushel. He afterwards bought 260 bushels at $| per bushel, and then sold all he had at $H per bushel. What did he gain ? 88. A and B own 280 horses. How many horses does each own, if B owns f as many as A ? 39. If llf bushels of apples cost $4 T 7 , what will be the cost of 19^ bushels? 40. A stone mason worked 11| days, and after paying his board and other expenses with,,| of his earnings, he had $20 left. How much did he receive a day? 41. What will 3 T 9 o acres of land cost, if 6| acres cost $807? 42. How many yards of carpet f yards wide will it require to carpet a room 7J yards long and 4 yards wide? 43. A and B together have $364. B's money is equal to f of A's. How many dollars has each? 44 Lyman can do a piece of work in 4 days and Farwell can do it in 5 days. How long will it take them, working together, to doit? 45. S. P. Bruce bought 40f acres of land at $164 per acre. He sold 25J acres to James Collins at $22J per acre, and sold the remainder to D. E. White at $15 T 7 per acre. How much did Bruce pay for the land, how much did he receive for it, and what was his gain? 46. A can do a piece of work in 10 days ; B, in 15 days ; C, in 12 days. How long will it take them all to do the work ? 47. A gentleman, having 271J acres of land, sold J of it, and gave of it to his son. What was the value of the remainder at per acre? FRACTIONS. 73- 48. A post stands J in the mud, J in the water, and 21 feet above the water ; what is its length ? 49. A and B together bought 680 sheep. A paid $9 as often as B paid $8. How many sheep should each receive? 50. Smith owning f of a mill, sold f of his share to Brown for $870. Find the value of the entire mill and Smith's share at present. 51. How many days will be required for A, B and C to do a piece of work, if A can do it in 20 days ; B in 30 days ; C in 25 days? 52. A and B together can do a piece of work in 4 days. A can do it alone in 6 days. How long will it take B to do it alone ? 53. A partnership business realized a profit of $6160. What was each partner's gain, if A invested f of the capital; B, T 6 T ; C, the remainder? 54. I sold two horses for $240. The selling price of one was f of the selling price of the other. Find the selling price of each horse. 55. A dealer sold two cows for $24 each. He lost J of the cost on one and gained -J of the cost of the other. Did he gain or lose and how much by the transaction? 56. A. C. Lamb bought a horse, buggy and harness. The cost of the horse was 1^ the cost of the buggy, and the cost of the harness was f the cost of the buggy. What was the cost of each, if the cost of the harness was $30 ? 57. A's money is of B's money; B's money is f of Cs money; C's money is If times D's money. How much money has each, if f of A's money is $64? How much have they to- gether ? 58. How many times is J of f of 27 contained in of J of 42|? 59. A and B together own 792 cows ; f of A's number equals | of B's number. How many cows does each own? 60. A father left his eldest son f of his estate, his youngest son f of the remainder, and his daughter the remainder, who re- ceived $1723f less than the youngest son ; what was the value of the estate? DECIMAL FRACTIONS 111. A Decimal Fraction is one which has for its denom- inator 10, 100, 1000, or 1 with any number of ciphers annexed, as TQ, Tinr, -rllhr- 112. Common Fractions arise from dividing a unit into any number of equal parts as halves, thirds, fifths, etc. Decimal fractions arise from dividing a unit into ten equal parts called tenths ; each of these parts may be divided again into ten equal parts called hundredths, etc. 113. Since the denominator of a decimal fraction is always 1 with ciphers annexed, it may be expressed by writing the numerator only and using the decimal point to indicate the de- nominator. 114. The Decimal Point is a period (.) which must always be placed at the left of the decimal. It is read "and." Thus 7.4 is read 7 and 4 tenths. A number containing an integer and decimal is called a mixed decimal. 115. Decimal fractions like simple numbers increase in value from right to left and decrease from left to right. The first figure on the right of the decimal point is called tenths, the second hundredths, the third thousandths, etc. Thus, jV is expressed .1 and read one tenth. T^TTT is expressed .01 and read one hundredth. Ter 1 oTT is expressed .001 and is read one thousandth. "rWir is expressed .125 and read one hundred twenty-five thousandths. lOOyffo is expressed 100.025 and is read one hundred, and twenty-five thousandths. NOTE. Decimal fractions are usually called decimals, and common fractions merely fractions. 74 DECIMAL FRACTIONS 75 The relation of the decimals and integers to each other is clearly shown by the following : , NUMERATION TABLE 1 = i S2 tn a o "2 E S rS 3 <> .2 "V ^ -3 c/j zvholc is reduced. 155. To perform reduction ascending. 2. Reduce 3307 farthings to pounds. SOLUTION 4)3307 far. 12) 826d. + 3 far. 20) 68s + lOd. 3 + 8s. 3 8s. lOd. 3 far. From the foregoing we have the following rule for Reduction Ascending a. Divide the given number by that number which will reduce it to the next higher denomination. b. Divide the quotient by the next higher number in the same manner; and so proceed to the highest denomination required* The last quotient, with the several remainders will be the answer. NOTE. Reduction descending and reduction ascending mutually prove each other. 3. Reduce -23 9s. 8d. 3 far. to farthings. 4. Reduce 7868d. to higher denominations. 5. Reduce 10 9s. 6d. 2 far. to farthings. 6. Reduce 5s. 3d. 1 far. to farthings. 7. In 17852 far. how many pounds? 8. In 83 6s. 3 far. how many farthings? 0. In 1624d. how many pounds? 10. In 1428 how many pence? 108 NEW BUSINESS ARITHMETIC WEIGHT 156. W eight is the measure of the force of gravity which draws all bodies towards the center of the earth. The standard of weight in the United States is the troy pound. 157. There are three kinds of weights used in the United States, viz. : Avoirdupois, Troy and Apothecaries. I. Avoirdupois Weight 158. Avoirdupois or Commercial Weight is used for weigh- ing ordinary articles, such as groceries, farm produce and all metals except the precious metals. TABLE 16 drams (dr.) make 1 ounce oz. 16 ounces 1 pound Ib. 100 pounds " 1 hundred-weight, cwt 20 cwt.,or20001bs. " 1 ton T. 112 Ibs. = 1 long hundred - weight. 2240 Ibs. = 1 long ton. NOTES. 1. In the United States Custom House and in wholesale transactions in coal and iron, the long ton is used. 2. The avoirdupois pound is determined from the standard troy pound, and contains 7000 troy grains. Special Avoirdupois Weights 100 pounds of Dry Fish make 1 Quintal. 100 Nails 1 Keg. 196 Flour " 1 Barrel. 200 Pork or Beef " 1 Barrel. 280 Salt at N. Y. S. Works " 1 Barrel. 240 Lime " 1 Cask. 159. Gross Weight is the weight of the goods together with the box, cask or whatever contains them. 160. Net Weight is the weight of the goods alone. Tare is the allowance made for the weight of the packing. When grain and seeds are bought and sold by weight so many pounds are considered as a bushel. The following table gives the weights in general use: REDUCTION OF DENOMINATE NUMBERS 109 TABLE OF POUNDS PER BUSHEL Commodities Lbs. Commodities Lbs. Commodities Lbs. Barley 48 Corn Shelled. 56 Potatoes 60 Beans . . . 60 Corn in Ear 70 Rve 56 Buckwheat 48 Flax Seed 56 Timothy Seed 45 Blue Grass Seed. . 14 Malt 34 Wheat 60 Coal, Bituminous. 80 Oats 32 Wheat Bran 20 NOTE. See page 352 for weights of other articles. 1. Reduce 3 cwt. 2 Ibs. to pounds. 2. Reduce 2 T. 5 cwt. to pounds. 3. Reduce 5 cwt. 15 Ibs. 13 oz. to ounces. 4. Reduce 2 cwt. 14 Ibs. 3 dr. to drams. 5. Reduce 3 T. 7 cwt. 18 Ibs. 11 oz. 14 dr. to drams. 6. In 4307 Ibs. how many cwt? 7. In 12600 Ibs. how many tons? 8. In 2048000 dr. how many tons? 9. In 64546 dr. how many cwt.? 10. Reduce 544272 dr. to T. 11. A merchant bought 4 T. 8 cwt. 42 Ibs. of castings at 12c per pound. What did the whole cost him ? 12. A coal dealer bought 176960 Ibs. of hard coal at $5.25 per long ton and sold it at $5.75 per short ton. What did he gain? 13. A grocer bought 3 hogsheads of sugar : The first weigh- ing 8 cwt. 13 Ibs. at 4Jc per pound; the second weighing 7 cwt. 82 Ibs. at 4fc per pound; the third weighing 9 cwt. 43 Ibs. at 4|c per pound. He sold the whole by retail at 5c per pound. What was his net profit? 14- Bought 5 barrels of pork at 7|c per pound and sold it at 9c per pound. What was my gain? 15. What is the weight of 250 barrels of flour? 16. A grocer bought 3 barrels of salt at $1.25 per barrel, and retailed it at f of a cent per pound. What did he gain? 17. At 45c per bushel what will be the value of 4865 Ibs. of shelled corn? 18. A farmer sold 8750 Ibs. of oats at 18c per bushel. What did they bring? 19. Find the value of 4627 Ibs. flax seed at $3.60 per bushel. 20. What cost 5180 pounds timothy seed at $1.45 per bushel? 110 NEW BUSINESS ARITHMETIC II. Troy Weight 161. Troy Weight is used in weighing gold, silver and other precious metals. TABLE 24 grains (gr.) make 1 pennyweight. . .pwt. 20 pennyweights " 1 ounce oz. 12 ounces 1 pound Ib. In addition to the above, the following, called Diamond Weight, is used in weighing diamonds and other precious stones: TABLE 16 parts make 1 carat grain = .792 troy grains. 4 carat grains " 1 carat = 3.168 " NOTE. The term carat is also used to denote the fineness of gold,, and means ^ part. Thus, gold 18 carats fine contains 18 parts pure gold and 6 parts alloy. 1. Reduce 4 Ibs. to grains. 2. Reduce 3 Ibs. 5 oz. 15 pwt. to pwt. 3. Reduce 13 Ibs. 9 oz. 16 pwt. 22 gr. to grains, 4. Reduce 146 gr. to pwt. 5. Reduce 32625 gr. to pounds. 6. A jeweler sold a gold chain weighing 2 oz. 16 pwt. 11 gr. at 4c per grain. How much did he receive ? 7. A miner dug 17 Ib. 8 oz. 9 pwt. of gold and sold it at 60c per pwt. What did it bring? 8. A goldsmith manufactured 1 Ib. 1 pwt. 16 grs. of gold into rings, each weighing 4 pwt. 20 gr. He sold the rings for $1.25 apiece; what did he receive for them? 9. Eight watch cases each 14 carats fine and weighing 60 pwt. contain how many ounces of gold? 10. What is the value of a diamond weighing T 3 6 of a carat at $75 per carat? REDUCTION OF DENOMINATE NUMBERS 111 III. Apothecaries' Weight 162. Apothecaries' Weight is used by druggists in com- pounding medicines. Druggists purchase their medicines at wholesale by avoirdu- pois weight. I M TABLE 20 grains (gr. xx) makel scruple ... sc. or 3. 3 scruples (3iij) " 1 dram dr. or 3. 8 drams (3 viij) " 1 ounce oz. or 3- 12 ounces (3 xij) 1 pound Ib. or ft>. NOTES. 1. The pound, ounce and grain of this weight are the same as those of troy weight; the pound of each contain' 12 ^z. = 5760 gr. 2. In writing quantities in apothecaries' weigHt the characters de- noting the denomination precede the quantity except in p6i|nds. In prac- tice the quantities are usually written in the Roman numerals. 1. Reduce 5 Ib. to grains. 2. Reduce 11 Ib. 33 to 3. f 3. Reduce 2 Ib. B2 32 32 gr.2 to grains. 4. In 48 how many pounds? 5. Reduce gr.3864 to ounces. 6. In gr.25941 of rhubarb how many pounds? 7. A druggist put up gr.263?6 of medicine into prescrip- tions, each prescription contained 92 gr.16. How many pre- scriptions did he make? 8. How much medicine will a druggist put up in one year of 365 days if he averages 8 prescriptions a day of gr.20 each? 9. An apothecary bought 3 pounds of medicine (apotheca- ries' weight) at $6 per pound and retailed it at 10 cents per 3. What was his total gain ? 10. What is gained by buying 4 Ibs. of quinine (apothecaries' weight) at $5.50 per Ib. and after manufacturing it into capsules of gr.2 each, selling them at 25c per dozen? 11. A case of drugs weighs 14 Ibs. 37 34. What is it worth at 5c per grain ? 112 NEW BUSINESS ARITHMETIC Comparison of Weights 163. The Standard Unit in both troy and apothecaries weights is the troy pound containing 5760 troy grains. 164. The Standard Unit in avoirdupois weight is the pound which is equal to 7000 troy grains. COMPARATIVE TABLE OF WEIGHTS Troy Apothecaries Avoirdupois 1 pound = 5760 grains = 5760 grains = 7000 grains 1 ounce = 480 " = 480 " = 437.5 " 175 pounds = 175 pounds = 144 pounds 1. Change 25 Ib. 7 oz. 15 pwt. troy to avoirdupois pounds. 2. A druggist bought at wholesale 15 Ib. quinine at $5.50 per pound avoirdupois, and after making the entire quantity up into 2 gr. pills sold the pills at 40c per dozen. What did he gain ? 3. A case of drugs weighs 76 Ibs. avoirdupois. How much is that troy ? 4. In 65 Ibs. avoirdupois, how many troy pounds? 5. Bought 16 Ib. of opium, avoirdupois weight, at 50c an ounce and sold the same by apothecaries' weight at 60c an ounce. What was my gain ? 6. In 243 oz. troy how many ounces avoirdupois ? 7. What is gained by buying 8 Ib. of quinine at $6 per Ib. avoirdupois weight, and selling same at Jc per grain apothecaries' weight ? 8. Reduce 75 oz. apothecaries' weight to ounces avoirdupois weight. 9. Reduce 36 Ib. avoirdupois weight to pounds troy weight. 10. What is gained by buying 25 Ib. avoirdupois weight at $3 per Ib., and selling at $3.20 apothecaries' weight? 11. Change 10 Ib. 9 oz. avoirdupois weight to Ib. and oz. troy weight. 12. Change 31 Ib. 11 oz. apothecaries' weight to Ib. and oz. avoirdupois weight. IS. Is a pound of feathers heavier than a pound of gold, and how much ? REDUCTION OF DENOMINATE NUMBERS 113 MEASURES 165. A Measure is a standard unit established by law or cus- tom, by which the length, surface, capacity and weight of things are estimated. Measures are of two kinds : Measures of Extension and Meas- ures of Capacity. 166. Extension is that property of matter which causes it to occupy space. It may have one or more of the three dimensions : Length, breadth and thickness. A Line has only one dimension length. A Surface has two dimensions length and breadth. A Solid has three dimensions length, breadth and thickness. MEASURES OF EXTENSION 167. Measures of Extension embrace Long or Linear Meas- ure, Square Measure and Cubic Measure. I. Long Measure 168. Long Measure, also called Linear Measure, is used in measuring distances or length. 12 3 5 40 320 5280 3 inches (in.) feet yds. or 16 } ft. rods rods, or ) feet, i geog. miles 1 league 1. NOTES. 1. The yard for common use is divided into halves, quarters, eighths and sixteenths. At the United States Custom Houses it is divided into tenths and hundredths. 2. The mile of 5280 feet is the legal mile in the United States and England and is called the statute mile. 3. The inch may be divided into halves, fourths, eighths, etc., or into tenths, hundredths, etc. 114 NEW BUSINESS ARITHMETIC Special Linear Measures Ys inch = 1 size. Used by shoemakers. 4 inches = 1 hand. Used in measuring the height of horses. 6 feet = 1 fathom. Used in measuring depths at sea. 1.152% statute mi. = 1 geographic mile. Used in measuring distances at sea. 3 geog. mi. - 1 league. Used in measuring distances at sea. 1 knot = 1 geog. mi. Used in measuring speed of vessels.* 60 geog. mi. { j 1 degree of long, on the equator, or 69.16 statute mi. ( ] 1 degree of a meridian. 360 degrees = circumference of the earth. NOTE. *The progress of sailing vessels is determined by a half -min- ute glass and a log line, which is divided into knots, bearing the same ratio to a mile that a half-minute has to an hour. 1. Reduce 2 yds. 2 ft. 7 inches to inches. 2. Reduce 7 yards 8 inches to inches. 3. Reduce 5 mi. to rods. 4- Reduce 8 mi. 225 rods to rods. 5. Reduce 16 mi. 25 rds. to rods. 6. Reduce 18 rds. 2 yds. 1 ft. 9 in. to inches. 7. Reduce 12760 in. to higher denominations. 8. Reduce 78980 ft. to higher denominations. 9. Find the cost of building a fence 1 mi. 165 rds. 4 yds. long at 18|c per yard. 10. A lake is 30 fathoms 5 ft. 10 in. deep. How many inches deep is it? 11. If a vessel travels 15 knots an hour, how many league? will she travel in 2 days of 24 hrs. each ? 12. What will it cost to fence a square field at 2Jc per ft., the sides of which are 14 rd. 2 yd. 1 ft. ? 13. I built four fences at 30c per yd. The first was 112 rd. 1 yd. long; the second 23 rd. 1 ft. long; the third 1 fur. 16 rd. 4 yd. 2 ft. long; the fourth 32 rd. long. What was the cost? 14. How many inches high is a horse which measures 16 hands ? 15. A vessel travels at the rate of 20 knots an hour. How many statute miles will she go in 96 hours? 16. The drive wheels of a locomotive are 24 ft. 6 in. in cir- cumference. How many times will they revolve in going a dis^ tance of 40 mi. 118 rd. 1 yd.? REDUCTION OF DENOMINATE NUMBERS 115 Surveyors' Long Measure 169. Surveyors' Long Measure is used by surveyors and engineers in measuring the dimensions of land, distance, etc. The Linear Unit commonly employed by surveyors is a Gun- ter's Chain, which is 4 rods or 66 feet long, and divided into 100 links. TABLE 7.92 inches (in.) make 1 link 1. 25 links 1 rod or pole..r. 4 rods or 100 links " 1 chain .... ch. 80 chains " 1 mile . . .mi. NOTE. In measuring roads, etc., engineers use a chain, or measuring tape, 100 feet long, each foot being divided into tenths and hundredth*. 1. Reduce 22 ch. 44 1. to inches. 2. Reduce 2 mi. 70 ch. 10 1. to inches. 3. Reduce 1 mi. 20 ch. to feet. 4. Reduce 4 mi. 36 ch. to yards. 5. Reduce 16384 1. to mi. 6. A farm is 45 ch. 16 1. long and 32 ch. 18 1. wide, many feet of fence will be required to enclose it? How II. Square Measure 170. Square or Surface Measure is used in measuring surfaces; as land, board, amount of painting, plastering, papering, paving, etc. 171. A Rectangle is a flat surface with four square corners. 172. A Square is a rectangle whose four sides are equal. A Square Inch is a square each side of which is 1 inch in length. A Square Foot is a square each side of which is 1 foot in length. A Square Yard is a square each side of which is 1 yard in length. FEET A RECTANGLE. FEET A SQUARE. 116 NEW BUSINESS ARITHMETIC The figure shows that 1 square yard, that is 3 feet square, con- tains 9 square feet, and from this we deduce the principle, that The area or surface of a square or rectangle may be found by multiplying the length by the breadth. TABLE 4 square inches (sq. in.) make 1 square foot . . . .sq. ft. 9 square feet 1 square yard . . . sq. yd. square yards " 1 square rod sq. rd. square rods ** 1 acre A. acres 1 square mile... sq. mi. NOTE. Paving, painting, calcimining, etc., are estimated by the square of 100 square feet. 1. Reduc.: 6 sq. yd. to square inches. 2. Reduce 10 A. to square rods. 3. Reduce 1 sq. mi. to square rods. 4. Reduce 2 sq. yd. 5 sq. ft. to square inches. 5. Reduce 5 A. 85 sq. rd. 20 sq. yd. 7 sq. ft. to square feet. 6. Reduce 65 A. 115 sq. rd. 13 sq. yd. 5 sq. ft. 120 sq. in. to square inches. 7. Reduce 960 sq. rd. to acres. 8. Reduce 2467 sq. in. to square yards. 9. Reduce 4178 sq. in. to square yards. 10. Reduce 16328 sq. in. to higher denominations. 11. How many square feet in a square measuring 7 ft. on a side? 12. What is the area in acres of a rectangular field measuring 150 rd. long by 80 rd. wide ? 13. How much greater is tne area of a lot 25 yd. square than a lot containing 25 sq. yd.? 14. How many yards of carpeting 1 yd. wide will be required to carpet a room 27 ft. long and 18 ft. wide? 15. What will it cost to paint a blackboard 46 ft. long and 4J ft. wide, at 27c per sq. yd. ? 16. Find the cost of paving a street 600 ft. long and 46 ft. wide at 85c per square. REDUCTION OF DENOMINATE NUMBERS 1 17 17. Find the cost of plowing a field 58 rods long and 34 rods wide at $2.20 per A. 18. Find the number of square feet in the walls and ceiling of a room 20 ft. long, 16*ft. wide and 9 ft. 6 in. high. 19. What will it cost at $3.14 per square to plaster a court room 48 ft. long, 36 ft. wide and 25 ft. high? 20. What will it cost at $4.40 per square to put the roof on a house 52 ft. long, the rafters being 22 ft. on each side? 21. At $23 per A. what is the cost of a field 38 rd. long and 30 rd. wide? 22. Find the cost of a farm 80 rd. long and 33 rd. wide, at $36.50 per A. 23. How many yd. of carpet J yd. wide, laid lengthwise, will it take to cover a floor 22 ft. long and 15 ft. wide? 24. What will it cost to carpet a room 30 ft. long and 25 ft. wide, with carpet 1J yd. wide, laid lengthwise, at 80c per. yard? 25. Find the cost of carpeting a room 36 ft. long, 28 ft. wide with carpet J yd. wide, laid lengthwise, at $1.15 per yard. 26. Find the number of strips of carpet 1J yd. wide run lengthwise of a floor 32 ft. long and 27 ft. wide. What does it cost at $1.10 per yd., allowing a waste of J yd. on each strip for matching ? 27. What will it cost at 60c per sq. yd. to concrete a walk 360 ft. long and 10 ft. 6 inches wide? 28. What will it cost at 4c per sq. yd. to build a walk 14 ft. wide around a block 240 ft. square ? 29. What will it cost at 12Jc per sq. yd. to paper the walls and ceiling of a room 20 ft. long, 16 ft. wide and 9 ft. high? 50. What will it cost to plaster the sides and ceiling of a room 36 ft. 9 in. long, 27 ft. 6 in. wide and 10 ft. 6 in. high, at 21c per sq. yd., if 28 sq. yd. be allowed for doors and windows? 51. The length of a rectangular fish pond is 90 ft, and its width 75 feet. Immediately surrounding this pond is a sidewalk 12 ft. wide. What is the distance around the outer edge of the sidewalk ? 32. A contractor received $247.50 for flagging a court-yard 30 feet long, at $2.75 per square yard. What was the width of the yard ? 118 KEW BUSINESS ARITHMETIC 33. What is the difference in the areas of two rectangles, one 15 rd. long and 18J ft. wide, and the other 71 yd. long and 3 rd. wide ? 34. A tinsmith covered a roof with "1152 sheets of tin, each sheet covering 40 by 20 inches. How many square feet of roof were there ? Board Measure 173. Board Measure is used by lumbermen in estimating the contents of boards, plank, joists, beams, etc. 174. A Board Foot is 1 ft. long 1 ft. wide and 1 in. thick, or a square foot 1 inch thick. Boards 1 inch or less in thickness contain as many board feet as the surface of the board in square feet. Boards more than an inch in thickness, and all squared lumber, are estimated by the number of square feet of boards one inch in thickness to which they are equivalent. Round timber such as masts, poles, etc., are estimated by cubic feet. 175. When lumber is one inch or less in thickness, to find the number of board feet, multiply the length in feet by the width in inches and divide by 12. When more than one inch in thickness, the above result must be multiplied by the number of inches thick. How many feet, board measure, in the following: 1. A board 16 ft. long, 1 ft. wide and J in. thick? 2. A board 24 ft. long, 9 in. wide and 1 in. thick ? 3. A board 14 ft. long, 1| ft. wide and 2 in. thick? 4. 25 boards 12 ft. long, 8 in. wide and 1 J in. thick ? 5. A stick of timber 6- in. by 8 in. and 18 ft. long? .16 joists 2 in. by 4 in. and 13 ft. long? 7. 40 2-inch planks 14 in. wide and 14 ft. long? 8. 36 3-inch planks 9 in. wide and 20 ft. long? 9. A stick 1 ft. by 1J ft. and 27 ft. long? 10. What will it cost at $1.60 per hundred, to build a side- walk 40 yd. long, 6 ft. wide, with planks f in. thick? REDUCTION OF DENOMINATE NUMBERS 119 11. What will it cost at $18 per thousand for lumber 1^ in. thick, to lay a floor in a room 19 by 24 ft., J being allowed for matching the lumber ? 12. At $12.50 per thousand, what will the lumber cost for siding a house 30 ft. long, 24 ft. wide and 16 ft. high, 30 sq. yd. being allowed for doors and windows and the gable ends being counted 544 sq. ft. ? 13. Find the cost of the following bill of lumber: 10 pc. 2x4- 14; 12 pc. 2x6-16; 20 pc. 2x8-18; 24 pc. 4x4-20; 20 pc. 4x8-20 @ $21 per M. ; 96 pc. 2x12-16 ; 75 pc. 2x10-18 @ $25 per M. Surveyor's Square Measure 176. Surveyors Square Measure is used in computing the area or contents of land. 177. A Principal Meridian is a true north and south line established as a basis for government surveys. There are in the United States twenty-four principal meridians. The meridians estab- lished for the purpose of government survey must not be confounded with meridians of longitude used by astronomers and navigators, as they are entirely different. The principal meridians used in surveying land are usually located with ref- erence to some natural landmark, such as the mouth of a river, and are not equi-distant apart. The first principal meridian starts from the junction of the Miami and Ohio rivers, form- ing the boundary be- tween Indiana and Ohio; the second starts from a point two and a half miles west of the junc- tion of the Little Blue CO RRECTIC 1 N T 6 i T.6N. R.4E. T.5 N. R.3W. 5 i 4 T.4H. R. 3 E. T. 3N. R.2W. Ul 3 2 BA SE 1 LI RE IV. Ill II. 1. 1 II. III. IV. * T. 2 S. R.2W. | 2 i j T. ? S. R. 3 E. T. 3S. R. 3W. 1 3 C( RRECTI )N 4 III E T. 4 S. R. 4E. i 120 NEW BUSINESS ARITHMETIC and Ohio rivers; the third starts from the mouth of the Ohio and runs north to the northern boundary of Illinois ; the fourth begins at the mouth of the Illinois river and extends north through Wisconsin and Minnesota, governing surveys in Wisconsin, Northern Minnesota and Western Illi- nois ; the fifth begins at the mouth of the Arkansas and governs surveys in Arkansas, Missouri, the greater part of Minnesota and Dakota east of the Missouri river; the sixth is the meridian of 97 deg. 22 min. west, ex- tends south to latitude 37 deg. and north to the Missouri, and controls the surveys in Kansas, Nebraska, the Dakotas south and west of the Missouri, Wyoming and all of Colorado except a portion along the Rio Grande, which is surveyed by the New Mexico meridian. Besides these there are eighteen principal meridians in the United States survey known by names instead of numbers. These are the Michigan merid- ian, governing surveys in Michigan; the Tallahassee, St. Stephens, Hunts- ville, Choctaw, Washington (Miss.), St. Helena and Louisiana meridians governing surveys in southern states ; the New Mexico meridian, longitude 106 deg., 52 min., 9 sec. ; the Great Salt Lake meridian, the Boise meridian governing surveys in Idaho; the Mount Diablo meridian, 121 deg., 5 min. west, governing surveys of Central and Northeastern California and all Nevada; the San Bernardino meridian for a part of Southern California, the Humboldt meridian for Northwestern California, the Willamette meridian for Oregon and Washington; the Montana meridian, the Gila and Salt River meridian for Arizona and the Indian meridian for Indian Territory. N 178. A Base Line is a line which crosses the principal merid- ians at right angles to them, and is used as a basis of measurements north or south. The intersections of the meridians and base lines are marked by substantial stone monuments. Across the principal meridians and base lines at right angles, other A TOWNSHIP. h'nes are run six miles apart which 6 5 4 3 2 1 7 8 9 10 11 12 18 17 16 15 14 13 19 20 21 22 23 24 30 29 28 27 26 25 31 32 33 34 35 36 E S REDUCTION OF DENOMINATE NUMBERS 121 N. *. 320 A N.W.fc of S. W.& 40 A. EH of S. E. &. S.W.J4 of S. W.& 80^. 160 A. S.W.M 40^1. divide the territory into square tracts six miles square. These tracts are called Townships. 179. Since the surface of the earth is convex, all meridians con- verge as the latitude increases; hence, the townships and sections are not exactly rectangular, which creates a necessity for occasional offsets called Correction Lines. A SECTION. The townships are numbered north or south from the base line. Thus "town 1 north," "town 1 south," etc. 180. A Range is a line of townships running north and south, and is designated by its number east or west from the principal meridian. Thus the range of townships lying next a prime meridian is known as range 1, east or west, the next range 2, etc. 181. Each township is divided into thirty-six Sections, each 1 mile square and containing 640 acres. These sections are numbered as shown in the accompanying diagram beginning at the N. E. cor. and running W. in the first tier, E. in the second, etc. All fractional sections except those due to lakes, rivers, and other natural boundaries are thrown into the northern and western rows. Sections are further divided into halves, quarters and eighths or forties. TABLE 10000 square links make 1 square chain . . . . sq. ch. 10 square chains 1 acre A. 640 acres 1 square mile sq. mi. 36 square miles (6 mi. sq.) " 1 township Tp. 1. How many acres in a township of land? 2. In 38 A. 8 sq. ch. 240 sq. 1. how many square links ? 3. Reduce 6525000 sq. links to acres. 4. A bought a farm of 8584250 sq. 1. at $65 per acre. What did the farm cost him ? 122 NEW BUSINESS ARITHMETIC 5. A sold the S. W. J of the S. E. J of section 15 in a certain township at $87.50 per acre. How much did he receive for it? Locate the land in a diagram. 6. Make a diagram and locate B's farm of 40 acres in the E. i of the S. 4 of the N. W. i of sec. 29, T. 3 N. Range 2 W. 7. I bought a half-quarter section of land at $22 per A., and sold same for $26.15 per A. How much did I gain? 8. A farmer purchased the following tracts of land : N. E. J of N. E. i, S. W. i of N. E. i at $43.50 per A. ; N. E. i of S. W. i, S. E. i of N. E. i at $37.50 per A. ; N. W. i of S. E. J, N. E. I of S. E. i at $27.50 per A., and S. E. i of N. W. i, N. W. J of N. E. at $31.25 per A. Find the cost of the farm. What will it cost to enclose the farm with a board fence five boards high each 6 inches wide and 16 ft. long at $16 per M. for lumber and $25 per C. for posts, same to be placed two to the board length? Draw a diagram of the farm. 9. H's farm contains the following pieces of land : W. -J of N. W . JL, W. i of S. W. i, E. J of N. E. , E. J of S. E. i, S. 4 of S. E. i of N. W. i, S. J of S. W. i of N. E. i, N. J of N. E. i of S. W. i, N. i of N. W. i of S. E. . How many acres of land in his farm ? Draw diagram. 10. E owns the following described property : N. W. i of N. W. i, S. W. i of N. W. i, N. W. i of S. W. i, S. W. i of S. W. i/ S. E. i of N. W. i, S. E. i of S. W. i, N. E. i of N. W. i, N. W. i of N. E. i and N. E. J of N. E. i. How many acres does he own? 11. Draw a diagram of E's land. A public highway is laid out on the N., W. and S. sides of it of the usual width (4 rods) one half on E's land. How many acres of land will the road occupy on his land ? What will it cost to fence this piece of land with a post and wire fence, posts to be p/aced one to the rod at $21 per C and 5 strands of wire, each strand weighing 3 pounds to the rod at 1 Jc per Ib. ? REDUCTION OF DENOMINATE NUMBERS 123 i CUBIC FEET A RECTANGULAR SOLID 27 CU. FT. III. Cubic Measure 182. Cubic Measure is used in estimating the contents of solid bodies, or things which have length, breadth and thickness. 183. A Rectangular Solid is a solid bounded by six rectangular sides. 184. A Cube is a rectangular solid bounded by six squares. A Cubic Inch is a cube each dimen- sion of which is 1 inch. A Cubic Foot is a cube each dimension of which is 1 foot. A Cubic Yard is a cube each di- mension of which is 1 yard. By inspecting the figure it will be readily seen that 3 cubic feet are 3 cubes of 1 foot each, and a cube 3 ft. each A CUBE dimension must contain 27 such cubes or 27 cubic feet. Hence we conclude, that The solid contents of a body may be found by multiplying its length, breadth and thickness together. TABLE 1728 cubic inches (cu. in.) make 1 cubic foot cu. ft. 27 cubic feet " 1 cubic yard cu. yd. 128 cubic feet " 1 cord of wood C. NOTES. 1. In measuring wood a pile 8 feet long, 4 feet wide and 4 feet high is called a cord. 2. A cubic yard of earth is called a load. 3. Railroad and transportation companies estimate light freight by the space it occupies in cubic feet, and heavy freight by weight. 4. A perch of stone or of masonry is \Q l / 2 feet long, \ l / 2 feet wide, and 1 foot high. 1. Reduce 5 cu. yd. 12 cu. ft. to cu. feet. 2. Reduce 3861 cu. ft. to cords. 3. Find the number of cu. ft. in a solid 26 ft. long, 2 ft. wide and iy 2 ft. thick. 4- Find the number of cu. yd. in a solid 25 yd. long, 14 ft. wide and 12 ft. thick. 124 NEW BUSINESS ARITHMETIC 5. Find the number of cu. yd. in a solid 12 yd. long, 12 ft. thick and 8 ft. wide. 6. How many cords are there in a pile of wood 28 ft. long, 6 ft. high and 4 ft. wide ? 7. At $2.20 per cord, what will be the cost of a pile of wood 18 yd. long, 6 ft. high and 2 ft. wide? 8. How many cords of wood can be put into a building 16 ft. long, 12 ft. wide and 10 ft. high? 9. How many cu. ft. of water will a cubical cistern hold, each of whose dimensions is 5 ft. ? 10. What will it cost to dig a cellar 21 ft. long, 18 ft. wide and 7 ft. 4 in. deep, at 40c per cu. yd.? 11. I bought 24 cords of wood 3 ft. long, and put it in a pile 8 ft. high. How long was the pile ? 12. My sleeping room is 12 ft. long, 10 ft. wide and 9 ft. high. If I breathe 10 cu. ft. of air in one minute, in how long a time will I breathe as much air as the room contains ? 18. A cellar wall is 112 ft. long, 6 ft. high and 1| ft. thick. What did it cost at $1.25 a perch? 14- What did it cost to dig the same cellar, its length being 32 ft., at 15 cents a cubic yard? 15. How many cubic feet in a wall 16 in. thick, 38 ft. long, and 30 ft. high? How many bricks would be required for the above wall allowing 22 to a cubic foot? W r hat would be their value at $8.50 per thousand? MEASURES OF CAPACITY 185. Measures of Capacity are those which determine the quantity of matter necessary to fill a given space. 186. Measures of Capacity embrace Liquid Measure and Dry Measure. REDUCTION OF DENOMINATE NUMBERS 125 I. Liquid Measure 187. Liquid Measure is used in measuring liquids. TABLE ... ,.. 4 gills (gi.) make 1 pint pt. 2 pints 1 quart qt. 4 quarts 1 gallon gal. 31 J : gallons 1 barrel bbl. 2 barrels, or 63 gal. 1 hogshead . . hhd. NOTES. 1. The gallon, which contains 231 cu. in., is the unit of measure in liquids. 2. Casks of various sizes are used in commerce, called tierces, pipes, butts and tuns. In practical business each cask is gauged separately and its actual contents ascertained. 1. Reduce 13 gal. to pints. 2. Reduce 8 gal. 2 qt. 1 pt. to pints. 3. Reduce 5 hhd. to gills. 4. Reduce 5 gal. 3 qt. 1 pt. 3 gi. to gills. 5. Reduce 2 bbl. 16 gal. 1 pt. to pints. 6. Reduce 1270 pt. to gallons. 7. Reduce 13725 pt. to barrels. 8. How many barrels in 10000 gallons? 9. What will be the cost of 2 hhd. of wine at 9c a gill ? 10. A merchant bought 3 barrels of cider vinegar at $5.25 per barrel and sold it at 8c a quart. What did he gain ? 11. How many cans, each holding 3 qt. 1 pt. 3 gi., can be filled from a barrel of kerosene oil containing 42f gal. ? 12. How many cubic inches in 63 gal.? 13. How many gallons in 4623 cu. in.? 14- How many gallons will a rectangular cistern hold, which is 4 ft. wide 6 ft. long and 8 ft. deep? 15. How many gal. of water will a cubical cistern hold, each of whose dimensions is 5 ft.? 16. How many gallons of water may be put into a cistern 6 ft. deep and 4 ft. square at the top? 17. A cistern 3 ft. by 4 ft. by 5J ft. is f full of water. How many gallons does it contain? 126 NEW BUSINESS ARITHMETIC Apothecaries * Fluid Measure 188. Apothecaries' Fluid Measure is used by druggists in compounding liquid medicines. TABLE 60 minims (TTL) make 1 fluid drachm, marked f3. 8 3 "1 fluid ounce " 3. 16 fS " 1 pint, " O. 8 O "1 gallon, " cong. NOTES. 1. The symbols of this measure precede the numbers to which they refer. Thus, O4 6, is 4 pints 6 fluid ounces. 2. The gallon and pint of this measure are the same as in wine measure. 1. Reduce O3 to fj.- 2. Reduce Oo fJ12 to f3. 3. Reduce cong.l O7 f9 f35 to fluid drachms. 4. Reduce cong. 3 Oo 37 111,42 to minims. 5. Reduce 1348 minims to higher denominations. 6. Reduce 142860 Til to cong. II. Dry Measure 189. Dry Measure is used in measuring dry articles ; as grain fruit, salt, etc. TABLE 2 pints (pt.) make 1 quart qt. 8 quarts 1 peck pk. 4 pecks 1 bushel bu. NOTE. The 40-quart or "heaped" bushel is used for apples, pota- toes, etc. Its dimensions are 18J4 inches inside and 8 inches deep. When heaped, the cone must not be less than 6 inches high, and it contains 2747.715 cubic inches. NOTE. The standard unit of Dry Measure is the bushel, which con tains 2150.42 cu. inches. 1. Reduce 2 bu. to pints. 2. Reduce 5 bu. 3 pk. to pints. 3. Reduce 2 bu. 2 pk. 2 qt. to pints. 4. Reduce 7 bu. 3 pk. 7 qt. 1 pt. to pints. REDUCTION OF DENOMINATE NUMBERS 127 5. Reduce 384 pt. to bushels. 6. Reduce 47 pt. to pecks. 7. Reduce 2865 pt. to bushels. 8. Reduce 11 bu. 3 pk. 7 qt. 1 pt. to pints. 9. What will 2 bu. of nuts cost at 2-Jc per pint ? 10. What will 4 bu. 3 pk. of beans cost at 6c per quart ? 11. W T hat will 2 pk. 4 qt. of cherries cost at 4fc per pint? 12. What is gained by buying 3 bu. 1 pk. of cherries at 2Jc per pint and selling same at 3Jc per pint? 13. A merchant bought 3 bu. of chestnuts at $1.20 per bu., and sold the same at 3c per pint. How much did he gain ? 14- I bought .1 bu. 1 pk. 1 qt. berries at 2^c per pint and sold same for $2.46. Find the total cost, and the selling price per quart. 15. How many cubic inches in 17 bushels? 16. How many bushels in 15590.545 cu. in.? 17. How many bu. of wheat may be placed in a bin 26 ft. long, 12 ft. high and 9 ft. wide? 18. What is the value at 23c per bu. of potatoes that fill a bin 18 ft. 5 in. long, 7 ft. 8 in. wide and 6 ft. 9 in. high ? 19. At 35c a bushel, what is the value of oats which fill a bin 16 ft. long, 6 ft. wide and 4 ft. high? 20. B wishes to build a bin that will hold 2000 bu. of corn. How long must he make the bin if it is 16 ft. wide and 8 ft. high? 21. A wagon whose box is 11 ft. long, 3 ft. 6 in. wide and 2 ft. 4 in. high is filled with barley worth 48c per bu. Find its value. 22. Wheat worth $120 at 75c per bu. fills a bin 5 ft. wide and 4 ft. high. Find the length of the bin. Comparison of Dry and Liquid Measures 190. The Standard Unit of Dry Measure is the bushel, which contains 2150.42 cubic inches. 191. The Standard Unit of Liquid Measure is the gallop which contains 231 cubic inches. 128 NEW BUSINESS ARITHMETIC COMPARATIVE TABLE OF MEASURES OF CAPACITY LIQUID MEASURE DRY MEASURE 1 gallon = 231 cu. in. 268f cu. in. 1 quart = 57j cu. in. 67i cu. in. 1 pint = 28J cu. in. 33| cu. in. 1. Reduce 2 bu. 3 pk. 6 qt. dry measure to gallons liquid measure. 2. Reduce 1 bbl. 20 gal. 1 qt. to dry measure. 3. I bought 2 bu. 1 pk. 1 qt. of nuts by dry measure, at 4c per qt. I sold same at 4|c per qt. by liquid measure. How much did I receive and what was my gain? 4' I bought 21 gal. 3 qt. of strawberries liquid measure at 5c per qt. and, sold them by dry measure at 8c per qt. Find gain. 5. A person has 15 gal. of cherries liquid measure, and can sell them at 5c per qt. liquid or 7c qt. dry measure. Which is the "better and how much ? 6. A bushel or 32 quarts dry measure contains how many .more cubic inches than 32 quarts liquid measure? TIME 192. Time is a measure of duration. The Measures of Time are fixed by the revolutions of the earth on its axis and around the sun. 193. A Day is the time required for the revolution of the earth on its axis. A Year is the time required for the revolution of the earth around the sun. 60 seconds (sec.) 60 minutes 24 hours 7 days 365 days (52 weeks 1 day) 366 days 12 calendar months 100 years TABLE make 1 minute min. " 1 hour hr. " 1 day da. " 1 week wk. 1 common year.yr. 1 leap year yr. 1 year yr. 1 century C. NOTES. 1. The exact length of the solar year is 365 days, 5 hours, 48 minutes, 48 seconds; but is usually considered to be 365 days, 6 hours. Hence, the year being regarded as 365 days, the odd 6 hours of each year REDUCTION OF DENOMINATE NUMBERS 129 make in 4 years 24 hours, 01 an additional day, which is added to the shortest month, February, and gives 3G6 days to every fourth year, called leap year. 2. All leap years are divisible by 4 and all centennial years not divisible by 400 are common years. 194. The year is divided into calendar months and seasons as follows: i January (Jan.) 31 days February (Feb.) 28 days February in leap year . . .29 days ( March (Mar.) 31 days SPRING , -j April (Apr.) 30 days ( May (May) 31 days {June (Jun.) 30 days July (July) 31 days August (Aug.) 31 days I September (Sept.) 30 days AUTUMN -J October (Oct.) 31 days ( November (Nov.) 30 days WINTER December (Dec.) 31 days The number of days in each calendar month may be easily re* membered by committing the following lines : "Thirty days hath September, April, June and November; All the rest have thirty-one, Save February, which alone Hath twenty-eight ; and one day more We add to it one year in four." .?. Reduce 2 hrs. to seconds. 2. Reduce 5 da. 8 hrs. to minutes. 3. Reduce 2 da. 7 hr. 45 min. 32 sec. to seconds. 4- Reduce 145 da. 5 hr. 27 min. 18 sec. to seconds. 5. Reduce 9 wk. 5 da. 15 hr. 25 min. to minutes. 6. Reduce 5 yr. 7 mo. 3 wk. 5 da. 16 hr. 42 min. 18 sec. to seconds. 7. Reduce 14600 sec. to hours. S. Reduce 26345 minutes to weeks. 9. -Reduce 41761 min. to months. 10. Reduce 12684500 sec. to higher denominations. 11. How many days are there from March 18 to July 1? 12. How many days are there from Nov. 26 to Feb. 22 ? 7-9. How many days are there from June 1 to Dec. 16? .I-/. How many days in winter in a leap year? 9 130 NEW BUSINESS ARITHMETIC CIRCULAR MEASURE 195. Circular Measure is used by surveyors in determining directions, by navigators in fixing the location of vessels at sea and by astronomers in making observations on the heavenly bodies. Every circle, great or small, may be said to be divided into 360 parts called degrees, consequently the length of a degree will vary according to the size of the circle. 196. A Degree is the 7 J 7 part of the circumference of a circle. TABLE 60 seconds (") make 1 minute ' 60 minutes " 1 degree 30 degrees " 1 sign S. 12 signs or 360 " 1 circumference. .C. NOTES. 1. A degree at the equator, also the average degree of lati- tude, is equal to 69.16 statute miles. 2. Minutes on the earth's surface are called geographic miles. 1. Reduce *4 15' 36" to seconds. 2. Reduce 37 48' 52" to seconds. 3. Reduce 12346" to higher denominations. 4. How many degrees are there in J of the circumference of the earth? 5. How many degrees in 5700 geographic miles? 6. How many minutes or geographic miles in a semi-circum- ference of the earth ? 7. How many statute miles in 180 or the semi-circumference of the earth ? 8. A ship was driven out of her course by a storm, 5 15' 28". How many geographic miles was this? 197. MISCELLANEOUS TABLE 12 things = 1 dozen. 12 gross = 1 great gross. 12 doze!? =r 1 gross. 20 things = 1 score. REDUCTION OF DENOMINATE NUMBERS 131 1. What cost 3 gross pencils at 4c apiece? 2. A bought 6 doz. eggs at ISc per dozen. Suppose he had paid 2c apiece for them how much more would they have cost? 3. A merchant bought 5 doz. straw hats at $5.45 per dozen and retailed them at 75c each. What was his profit? PAPER 24 sheets = 1 quire of paper. 2 reams = 1 bundle. 20 quires = 1 ream. 5 bundles = 1 bale or case. The terms folio, quarto, octavo, duodecimo, etc., indicate the number of leaves into which a sheet of paper is folded. STOCK SIZES OF FLAT OR WRITING PAPERS 14 x 17 called Cap. 18 x 23 called Medium. 16 x 21 " Demy. 19 x 24 " Royal. 17 x 22 " Folio. 17 x 28 " Double Cap. Most flat papers are now furnished 500 sheets to the ream in- stead of 480 sheets, as formerly. STOCK SIZES OF BOOK PAPERS FURNISHED 500 SHEETS TO THE REAM 24 x 36 28 x 42 36 x 48 25 x 38 32 x 44 38 x 50 The weight of papers is graded as so many pounds per ream. The more the ream weighs the heavier each individual sheet will be. Paper of a certain size and weight may have been used and it is often desirable to know the weight per ream of an equivalent sheet but of another size. 4. A stationer bought 1 bundle of note paper for $12 and sold it at the rate of 3 sheets for 5c. What did he gain ? 5. What will 408 eggs cost at 28c per dozen? 6. Find the cost of 5 great gross of lead pencils at 3c each. 7. How old is a person who is three-score and five years old? S. Find the weight per ream of the equivalent of a sheet 24 x 36 60# in 25 x 38. In 28 x 42. 9. Find the weight per ream of the equivalent of a sheet 32 x 44 80# in 24 x 36. In 25 x 38. In 28 x 42. 132 NEW BUSINESS ARITHMETIC 10. What must be the weight of a ream of Cap to make a sheet equivalent to 24# Royal ? 11. 24# Folio would be what in Double Cap? 12. 28# Royal would be what in Folio? 13. 16# Cap would be what in Royal? 14. What would be the weight of 35 sheets of 28# Double Cap? 15. What would be the weight of 16 sheets of 40# Royal? 16. An untrimmed book has 512 pages 5J x 7. Out of what may it be most advantageously run? How many sheets does it take for each book ? 17. An untrimmed book is 5 x 8. Out of what will it cut to best advantage ? How many pages to each sheet ? 18. A merchant has a catalogue 3 x 9J when trimmed. He wishes to bind it in a manila cover which can be had in 22% x 28| 90# and in 24 x 36 100#. Allowing a trim of % in. on both top and bottom and J in. trim on sides, how many covers can be cut out of each size and at 4{ cents per pound which is the most economical size to use ? REVIEW PROBLEMS 198. 1. What is the cost of 3 bu. plums at 8c a qt.? 2. What is the cost of 4 bu. 3 pk. peaches at 40c a peck? 3. At 28c per pk. how many bushels of apples can be bought for $36.96? 4- It requires 8 yd. 3J qr. to make one suit of clothes. How many suits will 143 yards make? 5. What cost 1 Ib. 15 pwt. of silver ore at 2c per grain ? 6. What cost 3660 Ibs. of wheat at 87|c per bushel? 7. How many spoons, each weighing 2 oz. 12 pwt. can be made from 3 Ib. 8 oz. 4 pwt. of silver? 8. A druggist put up 64 doz. gr.2 quinine powders. How much did he use ? 9. If one bushel of wheat will make 45 Ib. flour, how many barrels of flour can be made from 1000 bu. of wheat ? 10. How many yd. of carpet f yd. wide, will be required to cover a floor 27 ft, long and 18 ft. wide? REDUCTION OF DENOMINATE NUMBERS 133 11. At 30c per cord, what must be paid for sawing a pile of wood 22 ft. long, 7 ft. high and 4 ft. wide ? 12. I paid $10.50 for a barrel of pork. How much is that a pound ? 13. How many bu. of wheat can be put into a bin 7 ft. 4 in. long, 4 ft. 10 in. wide and 3 ft. high? 14. What must be the length of a bin that is 6 ft. wide and 5 ft. G in. high to contain 240 bu.? 15. If a family use 4 Ib. 14 oz. of sugar in a week how long will 1 cwt. 65 Ib. 12 oz. last them? 16. Find the cost of 2 hhd. wine at 12c per pint. 17. The human heart beats 70 times a minute. How many times will it beat in a day? 18. At 7Jc per cu. ft, what will be the cost of a block of stone 7 ft. 6 in. long, 5 ft. 3 in. wide and 4 ft. 8 in. thick ? 19. At 50c per oz., what is the value of a silver cup that weighs 1 Ib. 5 oz. 7 pwt. 10 gr. ? 20. At $21 per M., what is the cost of 3 sticks of timber 20 ft. long and 18 in. square at the ends? 21. A druggist paid 50c a Ib. Av. for potash and sold same in powders of 3 1 gr.5 at 5c each. How much did he gain on 10 Ib. ? 22. A cistern is 7 ft. long 5 ft. wide and 9 ft. deep. How many hogsheads of water will it contain ? 23. How many square feet are there in a walk around the outside of a rectangular garden which is 100 feet long and 65 ft. wide, the walk being 3 ft. 6 in. wide? 24. How many boards 11^ ft. long and 10 in. wide will be re- quired for the flooring of a room 17^ ft. by 23 ft? 25. How many hours longer is summer than autumn ? 26. A farmer started for market with 6 dozen dozen eggs; he broke half a dozen dozen and sold the remainder at Ic each. What did they amount to ? 27. How much time will a man gain in 60 yrs. of 365 days by rising 45 min. earlier every day than his usual time? 28. How many cu. ft. in a stone 4 ft. 8 in. long, 3 ft. 2 in. wide and 2 ft. thick ? How many sq. ft. on its surface ? 134 NEW BUSINESS ARITHMETIC 29. A room 30 ft. long and 24 ft. wide is covered with 12G yd. of carpet. What is the width of the carpet ? 30. A rectangular field containing 15 A. is 350 rd. long. How wide is the field? , 81. A cistern 7 ft. long and 5 ft. wide contains 105 cu. ft. What is the depth of the cistern, and how many gal. of water will it hold ? 82. What will be the cost of the plank, at $15 per M., that will cover a floor 13 ft. by 24 ft., if the plank is If in. thick? 83. How many dry qt. of berries may be put into a cask that contains 128J wine gallons, and what are they worth at 4c per qt? 84. Find the cost of 10 pc. 2 by 4 in., 10 pc. 2 by 6 in., 15 pc. 2 by 3J in., 12 pc. 2 by 7 in., if the pc. are 12 ft. long and the cost is $18.50 per M. 35. How many tons of hay of 320 cu. ft. each, in a mow 40 ft. 8 in. long, 20 ft. 3 in. wide and 13 ft. 10 in. high? 36. Allowing 320 sq. ft. for doors and windows, what will be the cost at 30c per sq. yd. of plastering a room the ceiling and walls 42 ft. 6 in. long, 26 ft. 3 in. wide and 14 ft. high? 37. I bought 14 bu. 3 pk. by dry measure at $4 per bu., and sold the same at 18c per qt. liquid measure. Did I gain or lose and how much ? 38. My silver weighs 3 Ib. 7 oz. by the scales of a grocer; what will it weigh by the scales of a jeweler? REDUCTION OF DENOMINATE FRACTIONS 199. Reduction of Denominate Fractions, either common or decimal, is the process of changing them to equivalent numbers of different denominations. Reduction takes place in two ways : From a higher denomina- tion to a lower by multiplication. From a lower denomination to a higher by division. 200. To reduce a denominate fraction to lower denomina- tions. 1. Reduce f of a bushel to lower denominations. REDUCTION OF DENOMINATE NUMBERS 135 SOLUTION I bu. = | of 4 pk. = 2^ pk. | pk. = i of 8 qt. = 4 qt. Ans. 2 pk. 4 qt. From this solution and explanation we have the following : To Reduce Denominate Fractions to Lower Denominations a. Multiply the fraction by that number which will reduce it to the next lower denomination, and if the result be an improper frac- tion, reduce it to a whole or mixed number. b. Proceed with the fractional part, if any, as before, until re- duced to the denominations required. c. The units of the several denominations, arranged in their order, will be the required result. NOTE. If after multiplying the fraction it is not an improper fraction, proceed to reduce it to the next lower denomination as before. 2. Reduce f of a yard to lower denominations. 3. Reduce of a month to lower denominations. 4- What is the value of .45 of a gallon ? SOLUTION .45 gal. 4 1.80 qt. 2 1.60 pt. 4 2.40 gi. 1 qt. 1 pt. 2.4 gi. Ans. 5. What is the value of .26375 of a long ton? 6. What is the value of f of 12 cwt. ? 7. What is the value of .725 of 16 acres? 8. What is the value of 3.48125 acres? P. What is the value of f of of 17 bushels? 10. What is the value of .165 ? 11. Reduce .8465 Ib. apothecaries* weight to lower denomina- tions. 12. What is the value of H of a mile? 136 NEW BUSINESS ARITHMETIC 13. Reduce f of J of 3 pounds troy to lower denominations. 14- Reduce | of f of f of 4 Ib. avoirdupois weight to lower de- nominations. 15. A grocer disposed of .75 of f of .175 of a hhd. of molas- ses. What amount was that? 201. To reduce a denominate fraction to higher denomina- tions. 1. Reduce f of a pwt. to the fraction of a pound. SOLUTION I x x = ^ lbs - 4 Therefore we have the following: To Reduce Denominate Fractions to Higher Denominations a. Divide the fraction by the numbers necessary to reduce it to the denomination required. NOTES. 1. Shorten the operation by cancellation whenever possible. 2. In case the fraction is a decimal divide as in division of decimals. 2. Reduce f pwt. to the fraction of a pound. 3. Reduce of a cent to the fraction of an eagle. 4.. Reduce J of a foot to the fraction of a mile. 5. Reduce gr.f to the fraction of a pound. 6. Reduce .25 of a pint to the fraction of a gallon. NOTE. .25 pt. = ^fo pt. ^ pt. and then proceed as before. 7. Reduce f pt. to the fraction of a peck. S. Reduce qt. to the fraction of a bushel. 9. Reduce .125 oz. to the fraction of a T. 10. Reduce .375 of a second to the fraction of a day. 11. Reduce T 7 ^ pt. to the fraction of a bushel. 12. Reduce f pt. to the fraction of a peck. 13. Reduce {f qt. to the fraction of a bushel. 14- i f an ounce troy is what fraction of 3 pounds? 15. f of .675 pt. is what fraction of 6 bushels ? 202. To reduce a compound number to a fraction of a higher denomination. 1. Reduce 5 da. 14 hr. 24 min. to the fraction of a week. REDUCTION OF DENOMINATE NUMBERS 137 SOLUTION 5 da. 14 hr. 24 min. = 8064 min. 1 week = 10080 min. Joei^JLwk. 10080 5 Therefore : To Reduce a Compound Number to a Fraction of a Higher Denomination a. Reduce the compound number given to its lowest denomina- tion and that to which it is to be reduced to the same. b. Make the former the numerator, and the latter the denomi- nator of a common fraction, which reduce to its lowest terms. 2. Reduce 10 hr. 30 min. to the fraction of a da. 3. Reduce 215 rd. 3 yd. 2 ft. 10 in. to the fraction of a mile. 4. Reduce 1 brl. 1 gal. 1 qt. 1 pt. 1 gi. to the fraction of a hogshead. * 5. What part of 11 hhd. is 4 gal. 1 qt. 1.28 pt.? 6. What fraction of 5 bushels are 3 pk. 1 pt. ? 7. What part of 6 ft. square is 6 sq. ft. ? 8. What part of 2 bu. 2 pk. 4 qt. is 3 pk. 7 qt. 1 pt.? 9. What part of 9 ft. square is 9 sq. inches? 10. What part of 3 is 25"? 203. To reduce a compound number to Q decimal of a higher denomination. 1. Reduce 2 pk. 6 qt. 1 pt. to the decimal of a bu. SOLUTION 2)1.0 pt. 8)675000 qt. 4) 2.812500 pk. .703125 bu. Therefore we may prescribe the following: To Reduce a Compound Number to a Decimal of a Higher Denomination a. Divide the lowest denomination given by that number which will reduce it to the next higher. Prefix the next higher denomi- 138 NEW BUSINESS ARITHMETIC nation to this quotient. Proceed in the same manner until the whole is reduced to the denomination required. 2. Reduce 8 oz. 15 pwt. 18 gr. to the decimal of a pound. 3. Reduce 1 hr. 12 min. 18 sec. to the decimal of a day. 4. Reduce 5 minutes to the decimal of a day. 5. What decimal of a peck is 7 qt. 1 pt. ? 6. What decimal of a bushel is 2 pk. 3 qt. 1 pt. ? 7. What decimal of a fathom is 3f feet? 8. What decimal of 3 miles is .3 feet? 9. What decimal of a barrel of flour is 18.25 Ibs.? 10. Reduce 5 sq. yd. 7 sq. ft. 80 sq. in. to the decimal of an acre. 11. Reduce 5A. 60 sq. rd. 25 sq. yd. to acres and decimals thereof. REVIEW PROBLEMS 204. 1. What will be the cost of 5 brls. 75 Ibs. of flour at $6.50 per barrel ? 2. What cost 18 bu. 3 pk. 5 qt. of corn at 45c per bushel ? 3. What will 45A. 122 sq. rd. 18 sq. yds. of land cost at $450 per acre ? 4. 8 gal. 3 qt. 1 pt. 3 gi. are what part of a hogshead ? 5. A jeweler sold 10 oz. 5 pwt. 8 gr. of plated ware at the rate of $2.40 per Ib. How much did he receive? 6. At $59.25 per acre, how much land can be bought for $1285.40? 7. It cost $267.30 to build a mile of fence. What will it cost to fence both sides of a railroad 17 mi. 135 rd. 3J yd. long? 8. Reduce 5 cwt. 68 Ib. 12 oz. 14 dr. to the decimal of a ton. 9. How much greater is the area of a lot 25 rds. square, than a lot containing 25 sq. rds. ? 10. In .5 hhd. .8 gal. .02 qt. how many pints? 11. What decimal of 6 mi. is 3 rd. 5 yd. 2 ft. 7 in.? 12. Find the cost of a farm 80 ch. long and 33 ch. 50 1. wide, at $36.50 per A. J5. Reduce 7 hr. 24 min. 18.625 sec. to the decimal of a year. REDUCTION OF DENOMINATE NUMBERS 139 14. How many times does a wheel, 14 ft. 8 in. in circumfer- ence, turn around in going a distance of 10 miles ? 15. If a person could travel a second of distance in a second of time, how long would be required to go entirely around the earth? 16. How many seconds shorter is autumn than spring? 17. At $21.75 per rod, what will it cost to grade a road 23 mi. 172 rd. long? 18. A bill of goods amounts to 46 6s. ; change to U. S. money. 19. An invoice totals 176 6s. 7d. ; change to U. S. money. 20. A purchase amounts to $271.64; change to English money. 21. An invoice totals 426 5s., tariff $145.60, freight $90.63. What is the total in U. S. money ? 22. Bought 220 yards of cloth at 1 9s. 2d. per yard. What is the cost U. S. money ? 23. A Liverpool clerk receives 960 per year, one in Boston receives $3,000. Which receives the larger salary and how much in U. S. money? 24. A Philadelphia merchant receives four invoices of goods purchased at foreign points, viz: A bill from Sheffield amounting to 245 6s. A bill from Paris amounting to 1463.7 fr. A bill from Hamburg amounting to 2164.8 m. A bill from St. Petersburg amounting to 2243.9 rubles. Find the total of the four bills in U. S. currency. ADDITION 205. The process of uniting numbers of different denomina- tions is termed Addition of Compound Numbers. 1. Add 16 bu. 2 pk. 4 qt. ; 11 bu. 3 pk. 5 qt. 1 pt. ; 8 bu. 1 pk. Ipt. SOLUTION 482 bu. pk. qt. pt. 16 2 4 11 3 5 1 8101 36 3 2 140 NEW BUSINESS ARITHMETIC From this solution and explanation we have the following: To Add Compound Numbers a. Write the numbers so that those of the same unit value will stand in the same column. b. Beginning at the right hand, add each denomination as in simple numbers, carrying to each succeeding denomination one for as many units as it takes of the denomination added to make one of the next higher denomination. NOTES. 1. Reduce denominate fractions, if any, to integers of lower denominations and then add. 2. It may be helpful to the student to write the numbers of the table above the columns before beginning the addition. Find the sum of the following : (2) (B) 20 12 4 20 100 16 16 L S. d. far. T. cwt. Ib. oz. dr. 6 14 8 3 2 12 65 10 15 5 7 9 2 3 8 42 5 16 4 1 5 15 84 11 12 11 18 2 3 2 6 32 8 38 43 19 9 12 41 223 26 35 4. A fanner sold six loads of wheat as follows : 23 bu. 3 pk. 7 qt. 1 pt. ; 26 bu. 2 pk. 5 qt. ; 18 bu. 5 qt. 1 pt; 32 bu. 3 pk. 5 qt. ; 38 bu. 3 pk. 7 qt. 1 pt. and 36 bu. 3 pk. 1 pt. What was the entire amount? 5. What is the sum of 3 mi. 180 rd. 3 yd. 1 ft. 10 in. ; .5 mi. 246 rd. 4 yd. 2 ft. 9 in. ; 16 mi. 148 rd. 2 yd. 2 ft. 8 in. and 30S rd. 4 yd. 2 ft. 1 in. ? 6. A man has three farms. The first contains 87 A. 116 sq. rd. 25 sq. yd. 4 sq. ft. 76 sq. in. ; the second 64 A. 84 sq. rd. 30 sq. yd. 8 sq. ft. 127 sq. in.; the third 128 A. 100 sq. rd. 16 sq. yd. 6 sq. ft. 42 sq. in. How much land has he in all ? 7. A ship leaving Boston sailed east the first day 3 25' 42" ; the second day 3 14' 7"; the third day 2 58' 16"; the fourth day 3 36' 14" and the fifth day 4 2' 18". How far was she then east of the port of Boston ? REDUCTION OF DENOMINATE NUMBERS 141 S. A farmer sold 5 loads of shelled corn at 42c per bushel, weighing respectively 3248, 2846, 3514, 2954 and 3015 pounds. \Yhat did he receive for all ? 9. What is the sum of 14 hhd. 28 gal. 1 qt. 1 pt. ; 23 hhd. 16 gal. 3 qt. 1 pt. ; f hhd. ; 15 hhd. 18 gal. 3 qt. ? NOTE. Reduce the hhd. to integers of lower denominations accord- ing to Art. 202 and then add as before. 10. Add f of a mile; 13J rd. and 148 rd. 7 ft. 8 in. 11. Sold four town lots. The first contained 2 A. 84 sq. rd. ; the second 3 J A. ; the third f of an acre ; and the fourth f of f of 300 sq. rds. How much land in all ? SUBTRACTION 206. The process of finding the difference between two num- bers having two or more denominations is termed Subtraction of Compound Numbers. 1. From 12 bu. 2 pk. 3 qt. subtract 8 bu. 3 pk. 5 qt. SOLUTION 4 8 bu. pk. qt. 12 2 3 835 3 2 6 We may therefore give the following : To Subtract Compound Numbers a. Write the less number under the greater and units of the same denomination in the same column. b. Subtract the lower number from the upper if possible. c. But, if the lower number of any order be greater than the upper, increase the upper number by as many units of that denom- ination as make one of the next higher; subtract as before, and carry one to the loiver number of the next higher order. Proceed in the same manner with each denomination. NOTE. In simple subtraction, when any lower figure is greater than the upper, we borrow ten, ten units of a lower order making a unit of the iic.rt higher. In Compound Numbers, when the lower number of any 142 NEW BUSINESS ARITHMETIC order is greater than that above it, borrow the number of units in that order which makes a unit of the next higher. Subtract the following : (2) (3) 12 20 24 365 24 60 6G lb. oz. pwt. gr. yr. da. hr. min. sec. 16 8 14 7 46 218 16 28 56 49 10 16 13 310 5 42 37 4. A bin contains 65 bu. of wheat. If 7 bu. 3 pk. 5 qt. 1 pt. are taken out how much will remain ? 5. From a hhd. of molasses there leaked out 7 gal. 3 qt. 1 pt. 3 gi. How much remained ? 6. A wagon loaded with hay weighed 3 T. 4 cwt. 18 lb. 13 oz. The wagon alone weighed 8 cwt. 24 lb. 7 oz. How much did the hay weigh ? 7. A New York merchant owed a London manufacturer 628 15s. 8d. 3 far. for goods bought. He paid him 265 10s. 9d. 2 far. How much did he still owe ? 8. A section of land is owned by three men. The first owns 256 A. 125 sq. rd. 15 sq. yd. ; the second 185 A. 64 sq. rd. 22 sq. yd. 6 sq. ft., and the third the remainder. How much land did the third man own? 9. How many weeks, days, hours and minutes are there from 15 min. after noon on April 1, to 48 minutes before midnight on September 26? SOLUTION 30 24 60 mo. da. hr. min. 9 26 23 12 4 1 12 15 5 25 10 57 10. Find the time from October 30, 1892, to May 21, 1895. 11. A note dated December 16, 1895, was paid on August 4, 1896. How long did it run? 12. Take 3 qr. 16 sheets of paper from 1 bundle of paper. 13. A ship starts at south latitude 12 42' 38" and sails to south latitude 60. Through what distance has she sailed? REDUCTION OF DENOMINATE NUMBERS 143 14- What length of time elapsed from 10 a. m. on September 20, 1893, to 3 p. m. on May 6, 1895? 15. From 12 cwt. 85 Ib. take -ft- of a ton. NOTE. Reduce the fractions to lower denominations. 16. From 8 T % wk. take 5| da. 17. From a cask containing 42 gal. of brandy J leaked out and J of the remainder was sold. How much still remained?- MULTIPLICATION 207. The process of taking a number consisting of different denominations a certain number of times is called Multiplication of Compound Numbers. 1. Multiply 7 bu. 2 pk. 3 qt. 1 pt. by 5. SOLUTION 4 8 bu. pk. qt. pt. 7251 3 v * 5 38 1 31 Therefore, To Multiply Compound Numbers a. Write the multiplier under the lowest denomination of the multiplicand. b. Multiply as in simple numbers and carry as in addition of compound numbers. NOTE. We multiply the lowest denomination first so as to carry from: a lower to a higher. (*) (s) 12 20 24 bu. pk. qt. pt. Ib. oz. pwt. gr. 5 3 V 1 3 8 16 20 3 7 * 9 4. A farmer owns 5 fields each containing 68 A. 86 sq. rd. sq. yd. 7 sq. ft. 65 sq. in. How much land has he in all ? 144 NEW BUSINESS ARITHMETIC 5. How many gallons in 5 casks each containing 18 gal. 3 qt. 1 pt. 3 gi. ? 6. A laborer excavates 2 cu. yd. 5 cu. ft. 41(1 cu. in. of earth in one day. How much will he excavate in 17 days at the same rate? 7. What will be the weight of 23 loads of hay, each weigh- ing 4 T. 6 cwt. 38 Ib. 14 oz. ? DIVISION 2O8. The process of finding how many times a given num- ber is contained in another number consisting of different denom- inations is called Division of Compound Numbers. 1. Divide 13 da. T hr. 25 min. 45 sec. by 5. SOLUTION 24 60 60 da. hr. min. sec. 5)13 7 25 45 2 15 53~ ~9 Therefore we have the following : To Divide Compound Numbers a. Begin at the left hand and divide the highest denomination of the dividend by the divisor, and write the quotient beneaih. b. If there be a remainder after the division of any portion of the dividend, reduce the remainder to the next lower denomina- tion, add to it the number belonging to that denomination, if any, and divide as before. c. Continue to divide in this manner until the entire dividend has been used. NOTE. We begin at the left hand in order to reduce the remainders to lower denominations and thus finally succeed in dividing them. (e) (s) 482 12 8 3 20 bu. pk. qt. pt. Ib. 3. 3. 3. gr. 7)25 3 5 1 9)17 1 2 18 4- A railroad train runs 1000 mi. in 26 hours. What rate is that per hour ? REDUCTION OF DENOMINATE NUMBERS 145 5. Seventeen barrels of sugar weigh 2 T. 6 cwt. 34 Ib. 8 oz. What is the average weight ? G. A man owning -J- a section of land left it to his 3 sons equally. How many acres should each receive? 7. A silversmith made half a dozen silver spoons weighing 2 Ib. 8 oz. 10 pwt. What was the weight of each ? 8. A farmer raised 846 bu. 3 pk. 5 qt. of wheat in a field of 16 acres. How much was that per acre ? 9. A family consumes 10 bbl. of flour in a year. What is the average amount each day? 10. A cellar 45 ft. long, 30 ft. wide and 6 ft. deep, was ex- cavated by 5 men in 6 days. How many cubic yards did each man excavate daily ? 10 LONGITUDE AND TIME 209. Longitude is the distance east or west from an estab- lished point or meridian on the earth's surface. Nations usually fix their own capital or national observatory as the point from which to measure longitude, but in the United States it is quite customary to reckon from the observatory at Greenwich, England. 210. Standard Time is the sun time of some selected meridian of longitude. Solar Time is the sun time, mid-day occurring at a given place when the sun reaches the meridian of that place, thus, there is a different time for every meridian. The standard time was adopted to avoid the necessary confusion caused to travel- ers and others by the difference of time. Railroads and many cities and towns have adopted standard time. In the United States eastern standard time is the sun time of the meridian 75 west of Greenwich; central standard time, 90 ; mountain standard time, 105 ; western (Pacific) standard time, 120. The standard time is one hour earlier in the day, in each successive belt toward the west; and one hour later in the day, in each successive belt toward the east. Thus, when it is 11 a. m. in the Eastern belt 7-J on each side of the 75th meridian it is 10 a. m. in the Central belt, 9 a. m. in the Mountain belt, 8 a. m. in the Western belt. Every circle, great or small, may be considered as divided into 360 equal parts called degrees. Since the earth turns on its axis once in 24 hours, a point on the earth's surface will describe a circumference (360) in 24 hours; in 1 hr., the point would describe % of 360 or 15 ; in 1 min., the point would describe ^V of 15 or 15'; in 1 sec., the point would describe ^V f 15'' or 15". Therefore we have the following : TABLE OF COMPARISON BETWEEN LONGITUDE AND TIME 15 of longitude = 1 hour of time. 15' of longitude = 1 min. of time. 15" of longitude = 1 sec. of time. 146 LONGITUDE AND TIME 147 The following table showing the longitude of important cities of the world east or west from Greenwich, England, will be used in the solution of the problems : TABLE OF LONGITUDES Place Longitude Place Longitude Portland Me . . o / // 70 15 18 V I St Louis Mo O i n 90 12 14 \V Boston Mass .... 71 3 40 Minneapolis Minn 93 14 8 New Haven Conn. 72 55 45 Des Moines la 93 37 16 New York City. . . 74 24 Omaha, Neb : . . . 95 56 14 Philadelphia, Pa. . 75 9 3 Austin, Tex 97 44 12 Baltimore, Md. ... 76 36 59 Denver, Colo 104 59 33 Washington, D. C. Richmond, Va. ... 77 15 77 26 4 Salt Lake City, Utah San Francisco, Cal 111 53 47 122 27 49 Charleston S C 79 55 40 Sitka Alaska. 135 19 42 Pittsburg Pa 80 2 Rio Janeiro Brazil 43 20 Savannah Ga. . . . 81 5 26 * t Honolulu Sandwich Is 157 52 Detroit Mich 83 3 ( Paris France 2 20 E Cincinnati O .... 84 29 45 t Rome, Italy 12 28 Louisville, Ky. . . . Indianapolis, Ind. 85 25 86 6 * Berlin, German Empire. Vienna, Austria 13 23 16 20 Nashville, Terin. . . Chicago, 111 86 49 87 35 ' i Constantinople, Turkey. St. Petersburg, Russia. . 28 59 30 16 M^obile Ala 88 2 28 ' Bombay India 72 48 Madison Wis 89 24 3 ' Pekin China 116 26 New Orleans, La. . 90 3 28 ' ' Sydney, Australia 151 11 1. The difference in longitude between two places is 18 ( 30". What is the difference in time ? 25' SOLUTION 60 60 15)18 25' 30" 1 13 42 EXPLANATION. By reference to the table of comparison on the previous page we see that 15 equal an hour of time, 15' equal 1 min. of time and 15" equal 1 second of time. There- fore 18 25' 30" will be equal to as many hours, minutes and seconds as 15 is contained in them, and dividing according to the rules for division of Compound Numbers we have as a result 1 hr. 13 min. 42 sec. From the foregoing we have the following: To Change Longitude to Time a. Divide the longitude by 15 according to the rule for division of Compound Numbers and the result will be time. Since the reverse of division is multplication, we may reduce time to longitude by the following : 148 NEW BUSINESS ARITHMETIC To Change Time to Longitude a. Multiply the time by 15 according to the rule for multiplica- tion of Compound Numbers and the result will be longitude. NOTE. If one place be in east, and the other in west longitude, the difference of longitude is found by adding them, and if the sum be greater than 180% it must be subtracted from 360. 2. The difference of longitude between two places is 30. What is the difference of time ? 3. The difference of longitude between two cities is 16 34'. What is the difference of time ? 4. The difference of longitude between New York and Chi- cago is 13 11'. What is the difference in time? 5. The difference of time between two places is 2 hr. 30 min. What is the difference of longitude ? 6. The difference of longitude between London and Wash- ington is 77 0' 15". What is the difference in time? 7. What is the difference in time between Portland, Me., and New Orleans? 8. What is the difference of time between Richmond, Va., and Des Moines, la. ? 9. What is the difference in time between Detroit, Mich., and San Francisco, Cal.? 10. What is the difference in time between Nashville, Tenn., and Omaha, Neb. ? 11. What is the difference in time between New Haven, Conn., and Denver, Colo.? 12. What is the difference in time between New York and Sitka, Alaska ? 13. What is the difference in time between Rio Janeiro, Bra- zil, and Honolulu, Sandwich Islands ? 14. What is the difference in time between Rome, Italy, and Boston, Mass. ? 15. When it is noon at Charleston, S. C, what is the time at Indianapolis, Ind. ? NOTE. Since Charleston is east of Indianapolis, subtract the differ- ence of time. LONGITUDE AND TIME 149 16. When it is 2 p. m. at St. Louis, Mo., what is the time at Philadelphia, Pa. ? NOTE. Since St. 'Louis is west of Philadelphia, add the difference of time to 2 p. m. 17. When it is noon at Chicago what is the time at Rome, Italy? NOTE. Since Chicago is west and Rome east of the prime meridian, the difference between their longitudes is found by taking the sum of their longitudes. Since Rome is east of Chicago, the difference of time is added to the time of Chicago to find the time at Rome. 18. When it is 1 p. m. at Omaha what is the time at Paris, France ? 19. What is the time of day at Berlin when it is 2 p. m. at New York? 20. When it is midnight at Boston what is the time at Austin, Texas ? 21. What is the time of day at Washington when it is 28 min. past 10 a. m. at Chicago? 22. St. Petersburg is east longitude and St. Louis is west longitude. When it is 1 a. m. at St. Petersburg, what is the time at St. Louis? 23. When it is 1 a. m. on Wednesday at Washington what is the time at Bombay? When it is 10 min. past 2 a. m. on Sun- day at Bombay what is the time at Washington ? 211. The International Date Line is an imaginary line, in crossing which navigators must either add or subtract a day in order to make their calendar correspond to that of the inhabitants of the adjacent islands. Given the time of day and longitude of one place and the longitude of another, and the time of day of the latter is easily found but to find the correct day of the month is not always so easy. For this purpose a knowledge of the "International Date Line," a cut of which is given on the following page is indispens- able. Travelers in going round the earth to the west find themselves a day behind the calendar and when going east, a day ahead, irrespective of the: time required to make the trip. 150 NEW BUSINESS ARITHMETIC Starting from somewhere in Asia the world has been peopled by some going east and some going west. These tides, as it were, of people met in the Pacific ocean, Asia and a few islands along the coast being peopled by those coming from the west and America with the islands in the eastern Pacific by those coming from the east. Each branch brought its own time and when they met they must necessarily differ by a full day. The "Inter- national Date Line" represents where they met and hence marks the division between the two kinds of time. On one side of the line it is LONGITUDE AND TIME 151 a certain time of day and on the other it is the same time of either an earlier or later day according to which side of the line it may be on. When it is 9 a. m. April 30 at Honolulu, long. 157 20' W., what is the day and hour on an island situated on the equator in the same degree of longitude ? Being in the same degree of longi- tude, by the ordinary rule they would have the same day and hour, but being on different sides of the date line they differ in time by the equivalent of 3 GO of longitude, or 24 hours, and as the point on the equator is on the west side of the date line it first had April 30, and Honolulu did not have it for twenty- four hours afterward, hence it must be 9 a. m. May 1 at the point on the equator. For such problems make use of the following rule : When the date line cuts the shortest distance between two places count the long way. 1. When it is 8 p. m. Wednesday, at Pekin, long. 116 east, what is the time at San Francisco, long. 122 west? 2. When it is 9 p. m. at San Francisco, what is the time at Pekin? 3. When it is 6 a. m. Monday, at Salt Lake City, long. 111 53' 47" west, what is the time at Sidney, long. 151 11' east? 4. When it is 9 p. m. at Omaha, long. 95 56' 14" west, what is the time at Bombay, long. 72 48' east? 5. Com. Dewey gave battle to the Spanish fleet in the harbor of Manila at 5 a. m. Sunday morning, May 1. If Manila is in longitude 120 E. and St. Louis is in longitude 90 W., what hour and day was it at St. Louis? General Review Problems 212. 1. Reduce 2 mi. 120 rd. to feet. 2. Reduce 17 T. 5 cwt. 84 Ib. 13 oz. to ounces. 3. A farmer desires to send to market 58J bu. of wheat in bags holding 1 bu. 3 pk. 6 qt. How many bags will it require? 4. What will 4 gal. 3 qt. of vinegar cost at 8c per quart? 5. 5 cents a quart for sweet potatoes is how much per bushel ? 6. A boy picked 14 qt. of cherries a day for 15 days. How many bushels did he pick? 152 NEW BUSINESS ARITHMETIC 7. In 286453 grains apothecaries' weight how many pounds? 8. At $24.50 per square foot, what is a city lot worth which is 38 J feet wide and 102J feet long? 9. John Wilson rented a house for one year for $420. He occupied it from January 1, until November 20, when the house was destroyed by fire. What rent did he pay? 10. How many bottles each holding 1 pt. 2 gi. can be filled from a barrel of vinegar ? 11. If a horse eats 1 pk. 3 qt. of oats in a day, how long will 16 bu. 3 pk. 3 qt. last him? 12. Reduce .185 of a day to lower denominations. 13. Reduce .00625 of a mi. to integers of lower denomina- tions. IJf- % of a pwt. is what part of a pound ? 15. What part of 5 T. is 4 cwt. 26 Ibs. 7 oz. ? 16. One bushel of apples makes 2 gal. 2 qt. of cider. How many gallons of cider can be made from 200 bu. 3 pk. G qt. of apples ? 17. When flour is selling at $6.75 per barrel what will a 75 Ib. sack cost at the same rate ? 18. What decimal of 3 days is 16 hrs. 24 min. 18 sec.? 19. What is the difference between 16f Ib. and 13 Ib. 8 oz. 16 pwt. 15 gr. ? 20. Reduce 9 hrs. 24 min. 18 sec. to the decimal of a day. ' 21. Reduce of a mile to integers of lower denominations. 22. What is the value of .0725 of a ton? 23. A having a farm of 84 A. 136 sq. rd. 18 sq. yd. bought at one time 24 A. 118 sq. rd. 26 sq. yd. and at another time 116 A. 32 sq. rd. 14 sq. yd. How much land did he then own ? &4. Add f of a mile, 11 f rods and T 3 c of a rod. 25. What is the sum of -J of a yard, -J of a foot and -J of an inch? 26. Change the difference between 96 Ib. 13 oz. and 14 Ib. 15 oz. to the decimal of a ton. 27. What is the cost of 3 loads of apples each containing 16 bu. 3 pk. 5 qt. at 35c per bu. ? LONGITUDE AND TIME 153 28. What is the cost of 7 bbl. of kerosene each containing 44 gal. 1 qt. 1 pt. at 12c per gal. ? 29. What is the cost of 1J A. land at 17Jc per sq. ft.? 50. George Washington was born February 22, 1732. How old was he at the time of the Declaration of Independence ? 51. The longitude of Boston is 71 3' 40" west and that of Omaha, Neb., 95 56' 14" west. What is the difference of time between the two places? 32. When it is 5 min. past 4 o'clock a. m. at Sydney, Aus- tralia, what is the time at Paris ? S3. If a note dated April 6, 1893, has 2 yr. 3 mo. 23 da. to run, when is it due? 34- How many acres of land in a field 84 rd. long and 38 rd. 3 yd,, wide ? 35. How many gallons will a cistern hold which is 6 ft. 4 in. long, 6 ft. 6 in. wide and 10 ft. 8 in. deep ? 36. How many bushels of potatoes will be contained in a bin 16 ft. 8 in. long, 14 ft. 3 in. wide and 9 ft. 6 in. deep? 37. Reduce 84 gal. to bushels. 38. Reduce 165 bu. to gallons. 39. Change 24 Ib. avoirdupois to troy weight. 40. Bought 8 bu. assorted nuts at $4.80 per bushel dry meas- ure and retailed them at 30c a quart liquid measure. How much was gained? RATIO Ratio is the quotient arising from dividing one number by another of the same kind. 214. The Terms of a ratio are the two numbers compared. 215. The Antecedent is the first term of a ratio, or dividend. The Consequent is the second term of a ratio, or divisor. Both terms of a ratio form a Couplet. 216. The Symbol of a ratio is the colon ( :) which is the sign of division with the line taken out; thus, 8 : 2 is read: the ratio of 8 to 2. Ratio may also be expressed in the form of a fraction by writing the antecedent for the numerator and the consequent for the denominator, as f . 217. A Simple Ratio is a ratio that has one antecedent and one consequent, as 6 : 4. The value of the ratio is f or 1|-. 218. A Compound Ratio is the product of two or more simple ratios, as (6 : 4) X (4 : 2) ; the value of the compound ratio is f X | or 3. From the preceding definitions we have the following: PRINCIPLES OF RATIO 1. Ratio = antecedent -=- consequent. 2. Antecedent = consequent X ratio. 3. Consequent = antecedent -f- ratio. 1. What is the ratio of 16 to 8 ? SOLUTION EXPLANATION. Since 16 is the dividend -i-o i a . o and 8 is the divisor we find the quotient or ID . o = ID -7- o = 4 , ,. . . ratio by division. From the preceding we have the following rule : To Find a Ratio a. Divide the antecedent by the consequent. NOTES. 1. Since the ratio may be expressed in the form of a fraction, the principles of fractions apply to ratio. 154 RATIO 155 2. Since only like numbers can be compared, there can be no ratio between $6 and 8 yd. or 5 men and 3 chairs. 2. What is the ratio of 32 to 8 ? 3. What is the ratio of 15 to 36 ? 4. What is the ratio of 16 ft. 8 in. to 1 ft. 10 in.? 5. What is the ratio of 16 to 82 ? 6. What is the ratio of } to f ? 7. What is the ratio of 4J to 11 J? 8. What is the ratio of 5 gal. 3 qt. to 2 gal. 2 qt. 1 pt.? 9. What is the ratio of 56 bu. 2 pk. 4 qt. to 4 bu. 2 pk. 7 qt. ? 10. The antecedent is 85 and the ratio is 5. What is the con- sequent ? 11. The consequent is 2.16 and the ratio is 14.5. What is the antecedent? 12. The consequent is J and the antecedent is T \. What is the ratio ? IS. Find the compound ratio of J jj : ^ } . ( 12 : 3 ) 14. What is the difference between the compound ratios of PROPORTION 219. Proportion is an equality of ratios and is either Simple or Compound. 220. Simple Proportion is an equality of two simple ratios. The symbol of proportion is the double colon ( : :) and signi- fies the same as =, thus, 18 : 9 : : 6 : 3 is read "18 is to 9 as 6 is to 3." 221. The Terms of a proportion are the four numbers com- pared. 222. The Extremes of a proportion are the first and fourth terms. In the above 18 and 3 are the extremes. 223. The Means of a proportion are the second and third terms. In the above 9 and 6 are the means. 224. The Couplets of the proportion are the ratios compared. In the above 18 and 9 are the first couplet, 6 and 3 the second couplet. 156 NEW BUSINESS ARITHMETIC A proportion may be written, 4 : 2 : :6 :3;4-T-2 6-=-3; | J. When written in the fractional form the antecedents are written above and the consequents below the line. f =- f, re- 4X3 6X2 duced to a common denominator - = - ; since numer- 6 6 ators of similar fractions are to each other as integral numbers, 4 X 3 = 6 X 2, but 4 and 3 are the first and last terms (ex- tremes), 6 and 2 are the second and third terms (means).. When any three terms of a proportion are given the other term may be found by the following : Principles of Proportion 1. The product of the means equals the product of the ex- tremes. 2. The product of the means divided by one extreme equals the other extreme. S. The product of the extremes divided by one mean equals the other mean. Find the unknown term in the following: 1. 6 : 2 : : 9 : . 9. 7 : } : : : 4. 2. 10 : 4 : : : 6. 10. 3J : : : 8 : 3. 3. 9: : :6 : 8. 11. : J : : 6 : 2. 4. - - : 48 : : 6 : 8. 12. $4J : $3 : : 6 Ib. : Ib. 5. $5 : $12 : : 10 ft. : ft. 13. 9 horses : 15 horses : : - 6. $21 : $7 : : ft. : 3 ft. T : 5 T. 7. 15 oz. : oz. : : 8 bu. : 10 bu. 14. 5i gal. : gal. : : $7 : $8. 8. f : 5 : : 7 : . 225. In any problem in simple proportion three terms are given, and a fourth term is required. 226. To Make a Statement in proportion is to arrange the three given terms, so that two of them form one ratio, the remain- ing term and the unknown term another ratio. 1. If 8 barrels of potatoes cost $20, what will 25 barrels cost? SOLUTION brl. brl. $. $. 8 : 25 : : 20 : 25 X 20 -f- 8 = 62J. RATIO 157 Therefore we have the following rule : To Find the Fourth Term of a Proportion a. Place for the third term that which is of the same denom- ination as required. b. If the term required be greater than the third term, place the larger of the other two numbers for the second term; if smaller, place the smaller of the two numbers for the second term. c. Multiply the third term by the second and divide by the first. NOTES. 1. If the terms of any couplet be of different denominations, they must be reduced to the same unit value. 2. If the divisor and dividend contain one or more factors common to both, they should be cancelled. 2. If 15 acres of land produce 535 bu. of oats, how many bushels will 32 acres produce ? 3. If 6 barrels of flour cost $32, what will 75 barrels cost? 4. What must be paid for 15 tons of hard coal, if 2 tons cost $15 ? 5. If 8 men earn $75 in one week, how much will 14 men earn in the same time ? 6. If $90, principal, produces $12.60, how much interest will $420 produce? 7. I paid $42.50 for 17 barrels of apples. How many barrels could I buy for $85 ? <9. I can walk 12 miles in 4 hours. How many hours will it take to walk 57 miles ? 9. If 23 trees bear 143 bu. 3 pk. of apples, how many apples will 96 trees bear? 10. If 18 barrels of flour contain 3528 lb., how many pounds will 26 bbl. contain ? 11. What is the cost of 17 gal. 1 qt. of wine, if 3 gal. cost $4.40? 12. I borrowed $320 for 3 mo. 18 da. For what time should I loan $212 to return the favor ? 13. If f of a yard of cloth cost 18c, what will 7J yd. cost? 14- 25 men built a wall 120 ft. long in a day. How many feet will 65 boys build a day, if 5 boys do as much as 4 men ? 158 NEW BUSINESS ARITHMETIC 15. If 15 men can build a bridge in 10 days, how many men will be required to erect three of the same dimensions in J the time? 16. If a man receive $4.50 for 3 days' work, how many days ought he to remain in his place for $25 ? 17. If a troy ounce of gold is worth $19.20, what is an avoir- dupois ounce worth? 18. If 3 cwt. 14 Ibs. of sugar cost $15.70, what will 42 Ibs. cost? 19. A butcher used a false weight 14| oz. , instead of 16 oz. for a pound. Of how many Ibs. did he defraud a customer who bought 112 Ibs. from him? 20. Suppose a certain pasture, in which are 20 cows, is suffi- cient to keep them 6 weeks ; how many must be turned out, that the same pasture may keep the rest 24 weeks. COMPOUND PROPORTION 221. Compound Proportion is an equality of ratios, when one or both are compound. Any problem in compound proportion may be stated and solved as in simple proportion, and all of the principles and ex- planations of simple proportion apply equally to compound pro- portion. 22S. Cause and Effect is a method of stating problems in Compound Proportion. Cause and Effect is based upon the principle that like causes produce like effects, and that effects are in proportion to their causes. 1. If 8 men will mow 24 acres of grain in 9 days of 8 hours a day, how many men will be required to mow 48 acres in 12 days working 9 hours a day ? EXPLANATION. The first cause produces the first effect and the 1st Cause. 2d Cause. 1st Effect. 2d Effect, second cause produces the sec- 8 V X ond effect. 8 men, 9 days, 8 yf: \ $$. hours constitute the cause which 3 4 effects 24 acres to be mown. An lOf . unknown number of men, X, 12 days, 9 hours constitute the . V X \ ^2 : : ( fy RATIO 159 second cause which effects 48 acres to be mown. The X or unknown quantity may appear in either of the four terms, and should be placed wherever the question of the unknown appears in the problem. Employ cancellation between any mean and any extreme. Multiply the remaining extremes together and divide by the remaining mean ; the result will be the unknown mean. From the foregoing solution and explanation we have the fol- lowing rule to find the unknown quantity by : Cause and Effect a. Write for the first term the first cause and its effect for the third term. Write for the second term the second cause and its effect for the fourth term. b. Place the X in whichever cause or effect the question occurs in the problem. c. Cancel from either mean to either extreme, multiply the re- maining means together and the remaining extremes together and divide one by the other. The result will be the unknown term. 2. If 12 horses eat 18 loads of hay in 8 weeks how many weeks will it take 20 horses to eat 32 loads of hay ? 3. If a stone 15 ft. long, 6 ft. thick, weighs 12 tons, how long must a stone be that weighs 20 tons, and is 5 ft. thick ? 4. If the carpet for a room 24 by 18 ft. costs $12, what will it cost to carpet a room 30 by 22 ft. ? 5. I paid $1800 for a lot 125 by 188 ft. What will a lot cost whose dimensions are 320 by 400 ft. ? 6. If 6 men in 18 days of 10 hours each, earn $220, how much can 9 men earn in 24 days of 9 hours each ? 7. If a box 12 ft. long, 8 ft. high and 6 ft. wide contains 480 bushels, how high is a box 15 ft. long, 5 ft. wide that contains 500 bushels. 8. If 27 hogs, each weighing 280 Ibs., cost $960, what will 36 hogs, each weighing 350 Ibs. cost? 9. If $900 for 1 yr. 4 mo. at 6% earns $72 interest, what will $630 earn in 2 yr. 1 mo. at 9% ? 10. What will be the cost of 18 logs, 24 ft. long, 15 in. wide and 9 in. thick, if 4 logs, 16 ft. long, 10 in. wide and 8 in. thick, cost $45 ? 165 NEW BUSINESS ARITHMETIC 11. If 120 men in 9 days of 8 hours each, build a wall 80 rods long, 6 ft. high and 4 ft. wide, how many hours per day must 90 men work to build a wall 65 rods long, 5 ft. high, 4 ft. wide in 12 days? 12. What will a pile of brick 33 ft. long, 18 ft. high and 15 ft. wide cost if a pile 24 ft. long, 15 ft. high and 11 ft. wide, cost $325? 13. What will it cost to paper the walls of a room 25 ft. long, 18 ft. wide and 12 ft. high, if it cost $44.20 to paper the walls of a room 36 ft. long, 28 ft. wide and 10 ft. high? 14- If 12 pieces of cloth, each containing 34 yd., J yd. wide, cost $204, what will 8 pieces cost, each containing 42 yd., f yd. wide ? 15. If 4 men, working 8 hours a day, can reap a field of grain of 20 acres in 8 days, in how many days can 9 men, working 10 hours a day, reap a field containing 35 acres? 16. If 25 men can build a wall 4800 ft. long, 7 ft. high, and 1J ft. thick in 42 days of 8 hours each, in how many days of 10 hours each will 200 men build a similar wall 1 mile long, 8 ft. high and 2 ft. thick? '17. If the interest on $540 for 1 year (360 days) at 5% in- terest is $27, what is the interest on $925 for 284 days at 7% ? 18. If a person can read a book containing 380 pages, each page containing 42 lines, each line 12 words, in 17^ hours, how many hours will be required to read 2 books, each containing 480 pages, each page 50 lines, and each line 15 words? 19. If a bin 8 ft. long, 4J ft. wide, and 2J ft. deep holds 67^ bu., how deep must another bin be made that is 24 ft. long and 6J ft. wide to hold 625 bu.? 20. How many men will be required to excavate a cellar 40 ft. wide, 172 ft. long, and 16 ft. deep, in 12 days of 8 hours each, if 6 men can dig a similar one 14 ft. long, 12J ft. wide and 8 ft. deep in 5 days of 10 J hours each? 21. If 4 compositors in 18 days of 8 hours each, set up 165 pages of a book, each page containing 34 lines, each line contain- ing 10 words, and each word containing on an average 8 letters, in how many days of 9J hours each, can 6 compositors set up a book of 340 pages, each page 48 lines, each line 11 words, and each word 9 letters ? MEASUREMENTS USED IN BUSINESS 229. In estimating labor and materials, contractors use the following : TABLE OF STANDARD UNITS 1 square foot = 144 sq. inches. 1 square yard = 9 sq. feet. 1 square = 100 sq. feet. 1 cubic foot = 1728 cu. inches. 1 cubic yard = 27 cu. feet". NOTE. In writing dimensions, the accent mark (') is used to indicate feet and the double accent (") ; to represent inches. Thus 4 ft. 3 in. are written 4' 3". 230. Excavating is estimated by the cubic yard of the actual amount of material displaced. A cubic yard of earth in its natural position will occupy from 1J to H cu. yds. when dug. On public works a cu. yd. of earth is a standard load. 231. Foundations are estimated by the cubic foot, in either concrete or stone. Foundations are generally composed of either concrete or large flat stones, called dimension stones. In estimating foundations of either, the concrete, dimension, or rubble stone, the actual contents are measured. "\Yhen foundations are composed of rubble stone they are esti- mated by the perch at 24-2 cu. ft. 232. Rubble Stone Work. Stone is estimated by the perch. All of the outside walls of buildings below the surface of the ground are usually composed pf rough stone or rubble stone work. In estimating rubble stone work a perch of 24f cu. ft. is used 11 lei 162 NEW BUSINESS ARITHMETIC extensively by contractors. In the western states the cord con- sisting of 100 cu. ft. is sometimes used. T ^ is allowed for mortar. In measuring for the amount of stone or brick required in a building, girt the building and subtract four times the thickness of the wall for the corners. Openings less than 4' 0" are not deducted. Cut Stone Work is estimated by the cubic foot. The stone used for the facing and trimming of buildings above the surface of the ground is called cut stone, and is esti- mated by the cubic foot for the bulk of such material. This stone is usually 4" thick. Mouldings, sills and string courses are generally estimated by the linear foot. * 233. Brick Work is estimated by the cubic foot and also by the thousand. Brick are of two kinds : Common and pressed. Pressed brick are used mostly for the facing of walls of buildings, exposed to the street. Pressed brick work is seldom more than one brick or 4" in thickness and is estimated by the superficial foot. Common brick of standard dimensions are 8" x 4" x 2". The bricks of different localities may vary slightly from this. 7J bricks laid in a wall one brick thick are usually estimated as a square foot, and this multiplied by the number of bricks in the thickness will give the number of bricks in 1 sq. ft. of the face of the wall. In measuring for the amount of material required, girt the building and subtract four times the thickness of the wall. For each corner of wall greater or less than 90 add 1' 6" to length of girt. Chimneys and hollow walls are measured as solid. Circular walls add J. Openings, if 2' 6" wide or less are not deducted. Greater than this deduct -J. 234. Estimating Work. In estimating the amount of work done in laying stone and brick, the length of the wall is found by measuring around the wall on the outside, or by measuring on the MEASUREMENTS USED IN BUSINESS 163 inside and adding 8 times the thickness of the wall. The corners are thus counted twice because more difficult to lay. 235. Roofing is estimated either by the square or by the thousand shingles. A shingle is estimated to average 4" wide by 16" to 18" long and is usually laid 4" to the weather. 900 shingles laid 4" to the weather cover 1 square of 100 sq. ft. 1000 shingles laid 4" to the weather will cover 111 sq. ft. Allowing for waste 1000 shingles are estimated to cover 1 square. Slating, gravel roofing, tinning, etc., are estimated by the square. 236. Concrete Floors are estimated by the superficial foot or yard. No deductions are made for piers, chimneys or other projec- tions of walls unless they amount to 10 sq. ft. in area. 237. Plastering is estimated by the square yard from floor to ceiling for walls, and from wall to wall for ceiling. Usually in measuring the plastering in a room, ^ of the open- ings are taken out. Plaster mouldings, cornices and the like are estimated by the linear foot. These are measured on their longest dimension and 1' 0" is added for each angle or corner around which the cornice is to break. A bunch of lath contains 50 pieces, each 4' long, and will cover 3' of surface. Openings in lathing and plastering are not deducted unless 2' 0" wide. One-half of contents is to be deducted for openings from 2' 0" to 6' 0" wide. 238. Painting and Glazing is estimated by the square yard or by the square of 100 sq. ft. In measuring a building for painting, the tape is carried around and into all projections or corners. In measuring doors take the actual superficial measurement, carrying the tape into mouldings. Windows are measured with- out allowance for glass. 239. Carpenter work is estimated by the board foot. Doors and windows are estimated by the piece. 164 NEW BUSINESS ARITHMETIC PROBLEMS 240. 1. What will be the expense of excavating a cellar 28' 6" wide, 42' 3" long and 4' 8" deep at $1.30 per cu. yard? 2. A cellar floor to be concreted is 27' 3" long and 13' 8" widu at 8 Jc per sq. foot. What will be the cost ? 3. How many bricks 8" x 4" will it take to pave a yard which is!6'0"x25'0"?' 4- The plans of a house show that it is to contain five rooms : The first 12' 0" x 10' 8", the second 15' 0" x 9' 6", the third 14' 0" x 9' 10", the fourth 11' 3" x 8' 6", and the fifth 7" 2" x 5' 9". What amount of lumber will be required to floor these rooms after allowing J for waste ? 5. A man having the contract for excavating a cellar 6' 0" deep for a house 35' 4" wide by 62' 8" long at $1.15 per cu. yd. finds on beginning the job that the digging and hauling will cost him $1.30 per cu. yd. but he can sell the dirt for $.50 a yard. In determining the amount of earth sold, assume that its volume increases one-fourth by swelling when it is loosened in digging. How much will he make on his contract? 6. The walls of a building are V thick and the building is 30' long 20' wide 32' high. How many bricks of standard size do they contain, and what will be the cost at $11 per M. bricks? 7. Suppose in the preceding example the walls are faced with pressed brick worth $40 per M. when laid in the wall, the thickness of the walls remaining the same, what are the walls worth ? 8. Three piers of a bridge are of rubble stone 8' 0" wide, 24' 0" long and 28' G" high. What will they cost at 40c per cubic foot, making no allowance for excavating? 9. How many perch of stone are contained in the walls of a cellar 30' 0" wide, 50' 8" long, 9' 6" high and 1' 3" thick? 10. There are three rooms in the basement of a house. The first is 1G' 0" x 9' G"; the second is 12' 4" x 8' 0", and the third is 10' 8" x 8' 6". What will it cost to concrete the floors of these three rooms at 8c per square foot ? 11. How much will it cost to plaster a room if the length is MEASUREMENTS USED IN BUSINESS 165 25' 0", the width 16' 0", and the height 17' 5" at 15c per square yard ? 12. How many feet of 2x4 studding will be required for a partition 23' 9" in length, 10' 0" high, if they stand 15" to cen- ters (one stud at each end), making no allowance for waste? What will be the cost of the studding at $17 per M. ? 13. The joists in a house are 16' long and are 2 x 6's laid 1' 4" to centers for a distance of 48' 0". What will they cost at $18 per M. ? 14- How many bricks are required for a building, the walls of which are 58' long, 25' wide, 44' high, and 1' thick, making no allowance for windows, doors, or corners. 15. At $3.75 per M. for bricks, and $4.25 per M. for laying them, what will the walls of such a building cost? 1<>. I wish to saw a square yard from a plank .15" wide and 2" thick. How far from the end must I cut ? 17. What is the difference in area between 2 rectangles, the first being 4' 5" x (>' 8" and the second 5' 4" x 8' 6". 18. How many ordinary bricks required for the walls of a house, 60' deep, 36' high, 24' wide, if 240 sq. feet be allowed for windows and doors, the walls being 3bricks thick? 19. In the walls of a cellar, the thickness of which is 1' 6", the height 8', each side wall 52' and each end wall 25' how many perch of stone ? At $4.87 J a perch, what will it cost to build the walls of this cellar ? 20. What will it cost to wainscot both sides of a hall 48' 9" long, to the height of 5' at 75c per sq. ft. ? 21. A skylight is 42' long and the rafters are 16' 4" long on each side to the ridge. What will be the cost of glazing the same at 60c per square foot, the gables not being glazed? 22. What will be the cost of a gravel roof on a building 50' x 150', deducting for a court 25' x 40', at $3.50 per square? 23. It is desired to shingle a roof: the following dimensions are given : Length 100 ft., width 24 ft. ; shingles to be exposed 4 inches and average 4 in. in width, the shingles on the lower course being doubled. The shingles will cost $3.25 per M. and 166 NEW BUSINESS ARITHMETIC it will cost $2 per M. to lay them. What will it cost to put on the roof? @4- The roof of a barn is 50 ft. long, and the width of each side is 25 ft. from the ridge to the eaves. Shingles are to be laid exposed 5 in. to the weather and average 4 in. in width. If the first course is doubled on each side, how many shingles will be required for the roof? PERCENTAGE 241. Percentage is the department of arithmetic, which treats of all operations in which 100 is the basis of computation. 24:2. The term Per Cent, from the Latin, per centum, means by, or on the hundred. 2 per cent, is 2 of every hundred or two hundredths. $3 gain on $100 is a gain of 3 per cent, or three hundredths on each dollar. 243. The Sign % is generally used for the words per cent.; 4% means 4 per cent., 8J% means 8-J per cent. 244. Since any Per Cent, is a number of hundredths, it may be written as a decimal or a fraction. Thus 6 per cent. = 6% = .06 = jib. Since hundredths occupy two places, every per cent, requires at least two decimal figures, and if the per cent, is less than 10 a cipher must be prefixed to the figure denoting the per cent. When the decimal point is used in expressing any per cent., the words per cent, and the sign % are omitted ; when the words per cent, or the sign % is used, the decimal point is omitted. 245. In solving problems in Percentage, five quantities are considered: Base, Rate, Percentage, Amount and Difference. 246. The Base is that on which Percentage is computed. 247. The Rate is the number of hundredths to be taken of each unit of the Base. 248. The Percentage is the number of hundredths of the whole Base as indicated by the Rate. 249. The Amount is the sum of the Base and the Percentage. 250. The Difference is the difference between the Base and the Percentage. In all departments of Arithmetic, except Percentage, we use one as the basis of computation, while in Percentage, we use one hundred as the basis of computation ; in this only does the work differ. The principal applications of Percentage are to the computa- tion of Commission, Brokerage, Insurance, Profit and Loss, Duties or Customs, Interest, Discount and Exchange. 167 168 NEW BUSINESS ARITHMETIC In Percentage and all its applications 1. The Base is represented by 100%. 2. The Amount is represented by 100% plus the given rate. 3. The Difference is represented by 100% minus the given rate. 4' The Percentage is represented b\ the given Rate. 251. Given Base and Rate to find Percentage. ORAL PROBLEMS 1. If 100% = the whole of a thing, what part of it is 50% ? 25% ? 20% ? 10% ? 5% ? 4% ? 2% ? 2. How would you get 50% of a thing? 2S% ? 20%? S. What is 25% of a bushel of apples? 50%? 75%? 4* What is 25% of 4 bushels of apples? 50%? 75%? 5. What is 33^% of 6 bu.? 12 bu.? 24 bu.? 75 bu.? 6. What is 50% of 18 qt. ? 37 qt. ? 45 qt. ? 63 qt. ? 7. What part of a thing is 121'% ? 37-J% ? 62J% ? 87J% ? 8. What is 37 J% of $40? $56? $64? $72? $88? $96? 9. A man has $120 and lost 12J% of it, how much did he lose, and how much has he left? 10. A mzn having $150 spent 10% for board, 20% for a suit of clothes and 5% for books. How much did he spend for each and how much has he left? WRITTEN PROBLEMS 1. What is 20% of $840? SOLUTION Or 1. 100% = $840. $840 Base. 2. 1% == $8.40. _^o Rate. 3. 20% = $168. $168X)0~ Percentage. From this solution and explanation we have the following method of solution : To Find the Percentage a. Let 100% equal the given number or Base. b. Find the value of 1% by pointing off two decimal places. c. Find the value of the given Rate by multiplication. Or, Multiply the Base by the Rate expressed decimally. PERCENTAGE 169 2. What is 6% of $400? s 3. What is 12% of $950? 4. What is 18% of $1-440? 5. What is 24% of $2160? 6. What is 35% of $1750? 7. What is 45% of 1800 bushels? 8. What is 52% of 20500 men? 9. What is 115% of 3462 feet? 10. What is 165% of 2450 pounds? / 11. Whatis8f% of $480? J. What is 6|% of 24360 bushels? , 13. What is 14% of J? 14. What is 2i% of 7J? 15. What is 33 J% of T V 16. What is |% of $28.30? 17. What is J% of $420? 18. A man had $2460 and gained in business 28% of this amount. What was his gain ? 19. A merchant having $5640 worth of goods in store, re- duced his stock 25% by an auction sale. What amount of goods was sold, and what amount still remained? 20. Bought a house and lot for $6450 and sold it for 92% of its cost. What was the loss? 21. What is the difference between 19% of $2635, and 15% of $3267? 22. A library was sold for $4500. A bought 30% of it; B 25% ; C 20%, and D the remainder. What per cent, of the whole was D's purchase and what did it cost him ? 28. A banker failed but afterwards paid 34% of his indebted- ness. He owed Jones $2475 and Brown $1432. How much will each receive ? 24. A man owning J of a store building sold 60% of his share. What part of the building did he sell and what part did he still own 25. Find 10% of 20% of $265. 26. Find 40% of 20% of 15% of $450. 170 NEW BUSINESS ARITHMETIC 27. A owed B a sum of money. At one time he paid him 4:0% of it; at another time he paid 25% of what was still owing. How much then remained unpaid? 28. A grain dealer bought 16240 bushels of grain, of which 36% was wheat, 27% was oats, 18% was rye and the balance was corn. How many bushels of corn did he buy ? 29. A newspaper publisher having 4560 subscribers, lost 12%% of them; 20% of the remainder failed to pay. How many paying subscribers had he ? 30. I had $1600 deposited in a bank. On July 1st I drew out 20% of it; on August 15, 16f% of the remainder and on Septem- ber 10; an amount equal to 75% of the amounts previously drawn. How much still remained in the bank ? 252. When the given per cent, is an aliquot part of 100, in- stead of multiplying by the rate, multiply by the aliquot part of 100. Thus: 2$% = A- m% = i 33J% = J. 5% = ^ 16f % = J. 50% . = 1. 8$% = T V 20% == i. 66f% = f. 10% = T V. 25% = 1. 75% = J. Find the percentage in the following problems : 1. 20% of $560. 7. 10% of 286 doz. 2. 25% of 1280 bu. 8. 12$% of 1432. 3. 33J% of 3645 yd. 9. 2$% of $3600. 4. 16f % of 1428 Ib. 10. 50% of 2436. 5. 6i% of $2860. 11. 8J% of 168 bbl. 6. 5% of 4532 yd. 12. 25% of $1472. 253. Given Base and Rate to find Amount or Difference. ORAL PROBLEMS i 1. What is 25% more than a whole thing? 50% ? 37% ? 2. What is $40 plus 25% of itself? 20% ? 50% ? 75% ? 3. What is 60 bu. less 10% of itself? 20% ? 25% ? 75% ? 4. A has $100, he spends 20% for a fishing outfit, 10% of the remainder for a pair of shoes and 75% of the remainder for rail- road fare. How much did he spend for each and how much has he left? PERCENTAGE 171 5. A merchant starts in business with $500; the first year he increased his capital 20% and the second year he increased this sum 25%. How much had he at the end of the second year? WRITTEN PROBLEMS 1. A man bought a horse for $108, and sold it for 25% more than the cost. What did he receive for the horse ? SOLUTION 1. 100% + 25% = 125%, the amount. 2. 100% = $108. 3. l% = $1.08. 4. 125% = $135. $135.00 From the foregoing solution we have the following: To Find the Amount or Difference a. Add the given Rate to 100% if the Amount is required, or subtract the given Rate from 100% if the Difference is required. b. Let 100% equal the given number or Base. c. Find the value of 1% by pointing off. d. Find the value of the Amount or Difference per cent, by multiplication. Or, Multiply the Base by the Amount or Difference per cent, expressed decimally. 2. The Base is $240, the Rate is 35%, find the Amount. 3. The Base is $7.20, the Rate is 20%, find the Difference. 4. The Base is 130 gals., the Rate is 40%, find the Amount. 5. The Base is 225 feet, the Rate is 33J%, find the Differ- ence. 6. The Base is 2500 yds., the Rate is 12 J%, find the Amount. 7. What is received for a lot that cost $450, and is sold for 20% less than cost? 8. A man invested $4850 and gained 22% during the year. How much was his capital at closing ? 9. A dealer bought 26 hogs at $5.50 each, and sold them at a 172 NEW BUSINESS ARITHMETIC gain of 18%. What did he receive for them? If he had sold at a loss of 26%, what would he have received? 10. A field produced last year 405 bushels of wheat. It pro- duced 65% more this year. How many bushels did it produce this year ? 11. I bought 400 sheep and lost 10% of them, after which I sold 45% of what I had left. How many did I have left? 12. A hatter bought a hat for $5 and sold it so as to gain 25%. What did the hat sell for? IS. A speculator having $4273, lost 10% of his money by a venture. How much did he lose, and how much had he left? 14. A merchant lost 12J% of his sales by bad debts. His sales amounted to $5428 ; what was the amount of his collections ? 15. In a school 20% of the pupils are absent and there are 685 enrolled. How many pupils are present in the school ? 16. A merchant invested in business $12500. The first year he increase^ his capital 18%, the second year he increased the capital at the close of the first year 24%. What was he worth at the end of the second' year ? 17. A stock of goods which cost $6820, decreased in value 33-J% and then again 20% of its lessened value when it was sold. What did it bring ? 18. A man dying left an estate worth $45000. He gave 30% of it to his wife; 20% of the remainder to his elder son; 25% of the remainder to his younger son, and the remainder to his daugh- ter. What was the share of each ? 19. A firm began business with a capital of $27800. The first year they gained 12% which was added to the capital ; the second year they gained 18% which was added to the capital; the third year they lost 15%. What was the firm worth at the end of the third year ? 20. A watch cost $134, and another cost 25% more than the first. What was the cost of both ? 254. Given Rate and Percentage to find Base. PERCENTAGE 17B ORAL PROBLEMS 1. 25 is \ of what number? J? i? J? 2. 36 is i of what number? i? J? f? f? 3. 50% of a thing is what part of it? 25% ? 66f % ? 75% ? 4. 48 is 50% of what number? 75% ? 66f % ? 5. One boy has $2.50; this is 25% of another boy's money. How many dollars has this boy ? 0. $25 is 10% of what number? 20% ? 30% ? 40% ? 50% ? 7. 10% of $75 is -J of what number? i ? J ? 8. 25% of 48 bu. is 50% of how many bushels? 9. 37J% of 72 quarts is 33J% of how many quarts? 10. 33-J-% of A's money equals 37J% of B's money. How much money has B if A has $72 ? WRITTEN PROBLEMS 1. $840 is 20% of what sum? SOLUTION 1. 20% of the required sun, == $840. ' = $ $4200 3. 100% (the required sum) =$4200. From the foregoing- solution and explanation we have the fol- lowing : Rate and Percentage Being Given to Find the Base a. Let the given Rate equal the Percentage or number given. b. Find the value of 1% by dividing. c. Find the value of 100%. Or, Divide the Percentage by the Rate expressed decimally. 2. 420 is 8% of what number? 3. 252 is 18% of what number? 4. 720 is 32% of what number? 5. 75 is 40% of what number? 6. Of what sum of money is $987, 47% ? 7. Of what number of dollars is $45, 2% ? S. I paid $150 for a horse, and found it had cost me of mv monev. How much had I at first? 174 NEW BUSINESS ARITHMETIC 9. A farmer sold 90 sheep which was 22%% of his flock. How many sheep did he have at first and how many left? 10. A retail merchant bought from a jobber 225 yards of cloth, which was 37J% of all the jobber had. How much had he before he sold this ? 11. By selling- a house for $288 more than it cost, the owner gained 8%. What was the cost and selling price of the house? 12. Jones has $280 which is 35% of Smith's money and 9J% of Brown's money. How much has each? 13. A farmer paid $62.40 for a wagon. The cost of the wagon was 80% of the cost of his horse. How much did he pay for both? 14- A field produced 1470 bushels of oats last year and this was 4:2% of what it produced this year. This year's crop was sold for 34 cents per bushel. Find the amount received. 15. A collector collected $2925, which was 75% of the claim. What was the claim and what was the collector's commission if he received 3J% on the amount collected? 16. The assets of a firm consist of cash $3250, notes $1870, and real estate $2740. The assets are 39-^% of the liabilities. What are the liabilities of the firm ? 17. The expenses of a clerk are as follows: $180 for board, $72 for lodging, $68 for clothes, $25 for books, $37 for incidentals. His total expenses are 32% of his salary. What is his salary? 18. A man bought 66f% of a flock of 240 sheep ; the number he bought was 53 \% of what he already had. How many sheep did he buy, and how many did he then have? 19. A boy bought a pair of boots for $2.80, a cap for $.65, a knife for $.45, and a pair of skates for $1.60; he had 45% of his money left. How much had he at first, and how much did he have remaining? 20. Brown gave his son $37.50, which was 60% of what he gave his daughter and 25% of what he gave his wife; he had 87 \% of his money left. How much had he at first, how much did he give his wife and how much did he give his daughter? 255. Given Amount or Difference and Rate to Find Base. PERCENTAGE 175 ORAL PROBLEMS 1. What number plus 25% of itself equals 30? 2. What number plus 33J% of itself equals 50? 3. What number minus 25% of itself equals 75? 4. What number minus 66f % of itself equals $45 ? 5. What number increased by 25% of itself equals $25? 45 bu.? 60 qt? $120? 2400 min.? 6. What number diminished by 12%% of itself equals 21 bu. ? 42 hr.? 84 sec.? $140? $91? 7. A man spent 12% of his money, he then finds that he has $176. How much had he at first? 8. A has a certain number of horses, he buys 25% of his pres- ent number. He now has 250 horses. How many had he at first ? WRITTEN PROBLEMS 1. I gained 20% by selling my house for $840. How much did the house cost me ? SOLUTION 1. 100% + 20% = 120%, the amount. Or, 2. 120% = $840. 1.20) $840.00 3. 1% = $7. $700 4. 100% = $700. From the foregoing solution and explanation we have the fol- lowing : Amount or Difference and Rate Being Given, to Find the Base a. Let 100% plus the given Rate equal the Amount, or 100% minus the given Rate equal the Difference. p_ b. Find the value of 1%. ' l-t 3. c. Find the value of 100%. ^ -_ jC-^ Or, Divide the Amount or Difference by the Amount or Differ- ence per cent, expressed decimal! y. 2. $560 is 12% more than what sum? 3. 375 is 25% more than what number? 4- 280 is 40% more than what number? o. $440 is 12% less than what sum? 176 NEW BUSINESS ARITHMETIC 6. A's fence is 4029 feet long which is 18% longer than B's. How long is B's fence? 7. Smith raised 2535 bushels of corn. Smith had 15% less than Brown. How many bushels did Brown have? 8. A man owes $960 which is 40% less than the money he has on hand. How much has he? 9. The weight of two hogs is 591 pounds, which is 1^% ^ ess than the weight of three others. Find the weight of the five hogs. 10. A blacksmith sold a wagon for $270 and gained 20% on the cost. Find the cost and what he should sell for to gain 18% . 11. The amount of a note that was on interest at 8% for one year, was $756. How much was the principal, and how much was the interest? 12. I sold 5% of my sheep to A, 4% of them to B, 3% of them to C. I then had 175 sheep. Find the number I had at first and the number sold to each. ( 13. A salesman's salary is $726, which is 21% more than his salary for last year, and that was 20% more than his salary for the previous year. Find his salary for each year. 14- A house is valued at $1620, caused from a rise of 35% in real estate, and its value before the rise was 20% more than its first cost. Find the cost. 15. A farmer sold one horse for $175 and thereby lost 25%. Had he sold the horse for $215 would he have gained or lost and how much? 1G. A man dying left 25% of his property to his wife, 50% of the remainder to his son, 75% of the remainder to his daughter, and the balance $500 to a servant. What was the value of his estate ? 17. 1642 is 6% of 50% of 87^% more than what number? 18. In a company of 87 the children are 37J% of the women, who are 44i% of the men. How many of each? 19. A dry goods merchant increased his sales 20% the sec- ond year over the first; 30% the third year over the second, and the fourth year over the third. He then found that his PERCENTAGE 177 total sales for the first four years had been $45552. What were his sales for the first year? 256. Given Base and Percentage to find Rate. ORAL PROBLEMS 1. 15 is what part of 30? of 45? of 75? of 105? 2. 15 is what per cent, of 30? of 45? of 75? of 105? 3. 25 is what per cent, of 25? 50? 100? 7500? 4. 1 hr. 20 min, is what per cent, of 4 hrs. ? 5. What per cent, of 75 is 15? 25? 50? 150? 225? 6. A has $50 and B has $75. A's money is what per cent, of B's money? B's money is what per cent, of A's money? A's money is what per cent, of what both have? B's money is what per cent, of what both have ? WRITTEN PROBLEM^ 1. A house cost $960 and was sold at a profit of $240. What per cent, of profit was this ? SOLUTION Or, 1. $960 = 100%. $960) $240.00 (.25 or 25% 2- $1 = &%. 1920 3. $240 = 25%. 4800 4800 From the foregoing solution and explanation we have the fol- lowing : Base and Percentage Being Given to Find the Rate a. The Base equals 100%. b. Find the value of a unit of the Base. c. Find the value of the Percentage. Or, Divide the Percentage by 1% of the Base. 2. 18 is what % of 360 ? 5. $48 are what % of $400? 4. 35 sheep are what % of 500 sheep? 5. 75 yards are what % of 300 yards? 6. 448 bushels are what % of 1120 bushels? 7. 250 Ibs. are what % of 750 Ibs. ? 12 178 NEW BUSINESS ARITHMETIC 8. 115 feet are what per cent, of 920 feet? 9. 72 gallons are what % of 864 gallons? 10. 2 bushels 2 pecks are what % of 10 bushels? 11. A dealer bought a wagon for $72 and sold it for $21.60 more than it cost. What % did he gain? 12. A farmer sold 36 bushels from a bin containing 160 bush- els of oats. What % of the oats did he sell ? 13. The rent of a house worth $3600, is $720. The rent is what % of its value? 14' A farmer harvested 420 bushels of wheat from 21 bushels of seed. The seed was what % of the amount harvested ? 15. $768 profit was received from an investment of $4800. Find the rate of profit. 16. Jones paid his attorney $32.50 for collecting a debt of $520. What per cent, of the debt was paid for collecting it? 17. A banker's assets are $4260, and his liabilities $7100. What % can he pay his creditors? How much will A receive, whose account is $860? 18. I received $1904 for a farm that cost $1700. How much % did I gain, and what % would I have lost by selling for $1445 ? 19. A father divided his estate of $2540 among his three sons: to the oldest, he gave $1016; to the next oldest, he gave $889 ; to the youngest he gave $635. What % of the estate did he give each? 20. A farmer who had 650 sheep, sold 182 to West; 169 to Packard ; 156 to Young. What % of the flock did he retain and what % did each buy ? 21. A merchant bought an invoice of goods for $365.60 and sold them for $406.73. The gain is what % of the cost? 22. A capitalist owns a house worth $7500, the income from which is $540 a year. What % does his investment bring him ? 23. A Wyoming cattle dealer lost 137 head of cattle during a blizzard out of a herd of 548 head. What per ce.nt. of the herd was left? 24. A man owned i interest in a mill and sold 25% of his interest for $2860. His income from remainder was $858. What was the entire income from the mill and what % does the mill pay? PERCENTAGE 179 REVIEW PROBLEMS 257. 1. Jones had 275 horses and lost 24% of them. What number did he lose? 2. A bought a drove of hogs for $2895, and sold them at a profit of 8$%. Find his gain; 3. How much above cost must goods, that cost $9.80 per yard, be marked to gain 15%? 4. The invoice price of a lot of merchandise was $710. A discount of 19% was allowed. Find the amount of discount. 5. I sold 92 bbls. of flour at $8.25 per bbl, and received 3J% for selling same. What amount did I receive ? 6. Lyman sold 90 shares of bank stock of $100 each at a premium of llf %. How much was the premium? 7. A farmer harvested 780 bushels of oats last year, and 35% more this year. Find the number of bushels harvested this year. 8. Davis invested $4368 in business and gained 26J% on the investment. Find his present capital. 9. Find the selling price of cloth that cost $1.46 per yard, and sold at a gain of 45%. 10. West purchased goods that were marked $18.40, at a dis- count of 19 J%. How much did he pay for the goods? 11. An agent purchased 1240 yards of cloth at 95 cents per yard. He charged 4J% for buying. How much did he receive ? 12. B bought $6400 worth of stock at a discount of 14%. Find what the stock cost him. 13. A farmer bought 72f acres of land, which was 16% of what he already had. Find the number of acres he had before buying. 14- A manufacturer sold a carriage for $246.50, thereby gain- ing 25%. Find the cost of the carriage.* 15. Goods costing $76, were sold at 12J% gain. What was received for them, and what would have been received by selling them at 6J% loss? 16. Goods were sold at $384, at a loss of 14|%. What was the cost, and what % would have been gained by selling them for $492.80 ? 180 NEW BUSINESS ARITHMETIC 17. An agent's charges for buying were $22.50 and his rate of charges was 4J%. What was the amount of the purchase? 18. The dividend on stock was $837, the rate of dividend was 9%. Find the value of the stock and the number of shares at $-100 each. 19. B had $620. He paid $24 for a desk, $122 for a safe, and $71 for books. What % of his money did he pay out, and what % remained? 20. The invoice price of goods was $288. The discount al- lowed by the seller was $43.20. Find the rate of discount. 21. A horse dealer sold two teams for $240 each. On one, he gained 20% ; on the other, he lost 20%. Did he gain or lose by the transaction, and how much ? 22. A sold 3432 bushels of corn, which was 12% less than B sold and 16% more than C sold. How many bushels did B and Csell? 23. The entire cost of goods was $207. The charges were $17.68 for freight, $2.12 for cartage and 1% of first cost for insurance. Find the first cost of the goods and what % of the first cost the charges were. 24.. A speculator invested $4280 in railroad stocks. He lost 10% the first year; gained 15% the second year; gained 25% the third year; lost 5% the fourth year. Find the value of the investment at the end of the fourth year. 25. A debtor paid me 66f % of his account. With 75% of the money received I bought a horse for $150. How much was the account? 26. A farmer sold 20% of 70% of 800 bushels of wheat at $f per bushel. How much money did he receive ? 27. If $1260 are gained by selling property at a profit of 16f %, what would be received by selling it at a loss of 16f % ? j 28. How much more % is gained on an article bought at $9 and sold for $12, than on one bought at $8 and sold for $10? 29. 35% of a piece of land, 40 chains long and 35 chains wide, was sold at $22 per acre; and 25% of the remainder was sold at $19.50 per acre; what now remained was sold at $17 per acre. Find the total amount received. PERCENTAGE 181 SO. Smith owned 46% of a farm worth $7250. He sold 30% of his share to Preston, and 22% of his share to Walker. Find the value of the land he now owns. 31. 19% of a merchant's stock of goods was destroyed by fire. He sold 60% of the remainder at 25% profit, and sold what now remained at 12% profit. How much did he receive, his stock at first being worth $4400? 32. I bought 100 yards of carpet at $.80 per yard. I sold 52 yards at $.92 per yard, and the remainder at 15% profit. How * many % did I gain on the whole lot? 33. Davis raised 1003 bushels of potatoes, which were 18% more than 80% of the number of bushels King raised. Find the number of bushels King raised. 34. Equal quantities of coffee that cost 19| cents, 22 \ cents, 24J cents, and 29 cents are mixed and sold at 30 cents. What is the gain % ? 35. In a sum of money containing $1300, $585 is currency, $455 is gold, and $260 is silver. What % of the sum is in cur- rency; what % in gold; what % in silver? 36. A merchant who began business with $1500, gained 35% the first year. 80% of the gain was left in the business. The second year he gained 30% on what he had. Find his capital at the close of the second year. 37. A farmer paid $720 for a horse, a wagon and a reaper. He paid 60% more for the wagon than for the horse; and 25% more for the reaper than for the wagon. How much did he pay for each ? 38. A manufacturer owning 60% of a factory, sold 12J% of his share at 20% profit and received $1440. Find the value of the factory. 39. Brown deposited 65% of his money in a bank. He paid 40% of the remainder to Myer on a debt, and 30% of what yet remained for a suit of clothes; when he found he had but $14.70 left How much did he have at first? 40. The value of my farm increased 20%, and again 25% ; then it decreased 10%, and again 20%. I now sold for $2160. 182 NEW BUSINESS ARITHMETIC Find the original value of the farm and the amount I would have received if I had sold after the second increase. 41. A capitalist has 7-|% of his money invested in U. S. bonds; 12% in real estate; 33J% in bank stock; 15% in mort- gages; 4%% in city bonds; $40000 in telegraph stock. He has on deposit $3500. Find the value of his property. 42. A paid $4800 for two houses. 20% of the brick house was equal to 30% of the frame house. Find the cost of each. 43. 25% of A's money is equal to 30% of B's money, and 40% of B's money is equal to 32% of Cs money. How much money has each, if 35% of Cs money is $252? 44' A dealer purchased a quantity of oysters, fish and clams, and paid for the entire quantity $166.75. The cost of the fish was 45% of that of the oysters, and the cost of the clams 25% of that of the oysters and fish together. What was the cost of each? 45. The sales of a firm were increased 25% the second year, 20 % t the third year, and 16|.% the fourth year. What was the amount of sales during the first year, if the fourth year's sales were $64442 ? 46. The amount is $361.10, the percentage $47.10. What is the rate of percentage? PROFIT AND LOSS 258. Profit and Loss are commercial terms used to express the gain or loss in business transactions. 259. The Cost of goods is the sum paid for them, or the ex- pense of producing them. The Prime Cost of an article is its original or first cost. The Gross Cost is the original cost of an article increased by all expenses such as freight, duty, packing, commissions, cartage, etc. 260. The Selling Price of goods is the sum received for them. 261. Profit is the sum above cost for which goods are sold. 262. Loss is the sum below cost for which goods are sold. The gain or loss is usually estimated in business transactions at a certain % on the gross cost. 263. In computations in profit and loss 1. Cost = Base. 2. Gain or Loss = Percentage. 3. Selling price at a profit = Amount. 4. Selling price at a loss = Difference. The subjects of Profit and Loss, Marking Goods, Trade Discount, Commission, Insurance, and Taxes are but applications of Percentage. Their problems may be classified the same as in Percentage but as these classifications have been duly considered in the study of Percentage they will not be repeated in these subjects. The pupil should endeavor to clearly understand the relations of the parts of a problem that are given and from these by a process of reasoning determine the unknown or re- quired part. He should learn as rapidly as possible to become independent of either formula, rule or classification, for in business problems are not presented tabbed with a rule nor classified by a case. ORAL PROBLEMS 1. I paid $4 for a hat and sold it at a gain of 25%. How much did I gain? 183 184 NEW BUSINESS ARITHMETIC 2. Find the gain : Cost $84, sold at a gain of 10% ? 20% ? 3. Find the loss : Cost $60, sold at a loss of 20 % ? 25% ? 4. Find the gain in the following : Cost $120, sold at a gain of 12% ? 20% ? 25% ? 33J% ? Cost $75, sold at a gain of 10% ? 30%? 66f%? 25%? Cost 36 cents, sold at a gain of 12|%? 33J%? 125%? 5. Find the loss in the following : Cost $64, sold at a loss of 12J% ? 37% ? 87|% ? Cost $72, sold at a loss of 100% ? 66f% ? 75% ? Cost 50 cents, sold at a loss of 25% ? 66f % ? 90% ? 6. 25 = iof what number? ? J?i?i? 7. 25 = 50% of what number? 33% ? 25% ? 20% ? 8. $40 = 20% of what number? 30% ? 40% ? 60% ? 9. In the sale of a horse $25 was gained. Find the cost if the sale was made at a profit of 10%? 20%?? 25%? 33^%? 50%? 40% ? 30% ? 10. A dealer gained $x20 on a sale, which was at a gain of 16|%. What was the cost? 11. 24 is J more than what number? 12. 24 is 20% more than what number? 13. $36 is 12 J% more than what number? 14. A horse was sold for $150 thereby gaming 20%. What did the horse cost ? 15. By selling berries at lOc per quart a grocer gains 25%. Find the cost of the berries. 16. A merchant sold potatoes at 84 cents per bushel thereby losing 12J%. What did the potatoes cost per bushel? 17. An article cost $36 and sells for $48. How much was gained ? What part is the gain of the cost price ? What per cent. ? 18. I paid $6 for each of 5 chairs and, sold them for the fol- lowing sums: $7, $8, $9, $10 and $11. What was the gain in each case and what was the per cent, gain? 19. A dealer paid $25 for each of 4 cows and sold them for the following amounts: $30, $35, $40 and $45. What was his gain per cent, in each case? 20. Find the gain or loss per cent, in the following : PROFIT AND LOSS 185 Cost. Selling price. Cost. H $5. $20. $6. $8. $25. $7.50 $10. $12.50 $12. $18. $50. $ .63 $ .72 $27.50 21. Find the selling price in the following Cost. Gain. Cost. $1000. 50 % $960. $50. 10% $40. $'2.50 20% $24. $30. wy*% $1600. $240. 6s^% $80. $10. 25% $62.50 Selling price. $15. $20. $24.75 Loss* 5% 1% 4% WRITTEN PROBLEMS 264. 1. A bill of goods cost $280 and was sold at a profit of 25%. What was the gain? SOLUTION 1. 100% = 2. 1% = $2.80. 3. 25% = $70. Or, $280 .25 1400 560 $70.00 2. A merchant sold goods that cost $185 at a gain of 12%. Find his gain. 3. What is the loss on goods that cost $140, and sold at a loss of 18% ? 4- I bought 170 yards of cloth at 80 cents per yard, and sold it at a gain of 35%. Find my total gain. 5. A commission merchant bought 210 bbls. of apples at $2J per bbl., and sold them for 9% less than cost. How much did he lose? 6. The loss on a bill of goods was $21.20, which was 4% of the cost. Find the cost. 186 NEW BUSINESS ARITHMETIC 7. Lyman gained $58.38 by selling at a profit of 14%. What did the goods cost him? 8. A jeweler sold a ring for $2.25 less than it cost, and lost 7|%. How much did he pay for the ring? 9. A stock dealer bought 26 hogs that averaged 285 Ibs., at 7 cents per lb., and sold them at 1H% profit. Find his gain. 10. Miller bought two horses for $80 each, and sold one at a gain of 27%, the other at a loss of 19%. Find his net gain. 11. A quantity of tea was sold for $414, which was 10% below cost. Find the cost. 12. The selling price is $360, the rate of gain is 20%. Find cost. 13. The selling price is $189, the rate of gain is 5%. Find cost. 14. The selling price is $140, the rate of gain is 16%. Find cost. 15. A firm gained 12% of its capital. The amount of gain was $1410. Find the firm's capital. 16. A real estate dealer gained 21^% by selling a house for $344 more than it cost him. Find the cost of the house. 17. A stock dealer bought a lot of cattle for $1200, and sold them at a gain of 15%. What were they sold for? 18. A broker bought a bond for $920, and sold it at a gain of 17f %. Find his selling price. 19. The selling price is $224, the rate of loss is 20%. Find cost. 20. The selling price is $387.20, the rate of loss is 12%. Find cost. 21. How much is received for goods, bought for $355 and sold at 12|% less than cost? 22. What is gained by selling real estate that cost $1272, at a gain of 8J% ? 23. Hall sold a house and lot to Miller for $650 more than cost, and gained 20%. Miller sold it to Davis at a gain of 16%. What did the house cost each ? #4. A grain dealer sold corn at 33 cents per bushel, thereby PROFIT AND LOSS 187 losing 25%. If the entire loss was $825, how many bushels did he sell? 25. The selling price is $21, the rate of loss is 12 \%. Find, cost. 26. I sold 10 acres of land at 27% gain, and received $825.50 for it. What was the cost per acre? 27. A sold 65 yards of cloth for $89.10, and gained 15%. Find the cost of the cloth per yard. 28. Ward sold his property for $1080, which was 33J% more than it cost him. How much did he pay for the property? 29. I sold a coat at a loss of 16f % and lost $4.50. How much did I pay for the coat, and what would I have gained by selling it at a profit of 33 J%? 30. If 28 yards of cloth are bought at $5.50, for how much must it be sold to gain 32%? 31. A purchased a bill of goods amounting to $430. He paid 3%% for freight and cartage. For how much must he sell them to gain 13% on the entire cost? 32. Amos Libby paid $30 for a cow, and sold it for $37.50. Find the rate of gain. 33. Hill lost $6 on a watch that cost him $75. What was his rate % of loss? 34. B bought a lot of books for $60, and sold them for $70. What % did he gain? 35. I sold an acre lot that cost $90, for $75.60. Find my % of loss. 36. C. W. Carey paid $750 for a hall. He rented it nine eve- nings at $5 per evening, and then sold it for $825. What was his gain %? 37. A dealer sold 125 hogs at a loss of 8%. He received $1150 for them. How much did he pay per head for the hogs? 38. A partner's loss was $2250, which was 25% of his investment; his investment was 80% of the firm's loss. Find the loss of the firm. 39. A load of coal, costing $46.50, was sold at 9f% below cost. Find the selling price. 188 NEW BUSINESS ARITHMETIC 40. Snyder bought a house for $1370, and sold it to Byrne at a gain of 19%. Byrne sold it to Fuller at a loss of 8%. How much did Fuller pay for the house ? 41. John Adams bought 72 yards of cloth at $8 per yard and sold it at a gain of $158.40. Find the rate % of gain. 42. A speculator sold a quantity of flour for $828. He paid $920 for it. Find his rate % of loss. 43. B bought 6 bushels of chestnuts at $4.50 per bushel, and sold 4 bushels of same at $8.50 per bushel, and the remainder at $5.25 per bushel. What was his rate of gain ? 44- How much does a carriage dealer lose by selling a car- riage that cost $210 at a loss of 17% ? 45. B bought a bond for $1280 and sold it for 42% more than he paid. Find his gain. 46. Jones gained 25% by selling a cow for $30 and lost 18% by selling another for $20.50. Did he gain or lose and how much on the two cows? 47. Johnson bought 45 sheep at $2.50 each. He sold 10 at a gain of 12% ; 12 at a gain of 15% ; 14 at a gain of 20% ; the re- mainder at a loss of 34|%. How much did he gain and what % did he gain? 48. A grocer bought eggs at 27 cents a dozen and sold them at the rate of 8 for 25 cents. What % profit did he make ? 49. White sold a horse to Ellis at a gain of 25%. Ellis sold the horse for $75, which was 16|% less than the sum he paid. How much did the horse cost White ? 50. A stock of goods were bought for $1840 ; } of the stock was sold at 21% profit; -J of the remainder at 24% profit; the remainder at 12% loss. Find the total amount received for the stock. 51. 25 yards of cloth were bought for $187.50. At how much per yard must it be sold to gain 20% ; at how much per yard to lose 12% ? 52. A and B each lost $500 which was 12%% of A's and 13 J% of B's money. Which had the more money and how much? 53. How much is gained by purchasing 5 carloads of wheat, PROFIT AND LOSS 189 of 940 bushels each, at 62Jc per bushel and selling 40% of it at a gain of 12 J% and the remainder at a gain of 7-|% ? 54. I sold a bill of goods for $360 and lost 20%. Had I sold 60% at 20% profit and the remainder at 12|% profit, what would 1 have gained? 55. A merchant sold a bill of goods for $750 and lost 6J%. What ought they to have been sold for to gain 8% ? 56. A stationer bought 3 gross of penholders at $5 per gross and retailed them at 5 cents apiece. What % profit did he make ? 57. A contractor received 25 cents a yard for excavating a cellar. He paid his laborers 21 cents a yard. What % profit did he make? 58. Sold a horse at a gain of 33 J% and with the proceeds bought another horse, which I sold for $120 at a loss of 20%. What did the first horse cost me? 59. A merchant's asking price is 25% above the cost. If he allows a customer a discount of 12% from the asking price, what per cent, profit does he make? 60. A merchant gained this year $1800 which was 120% of his gain last year and that was 44 -f% of his gain the year before. What were his profits for the three years? 61. Sold pork at an advance of 1^|% ; invested the proceeds in pork again, and sold this lot at a profit of 16%, receiving $4627.50. How much did each lot of pork cost? 62. A broker bought a quantity of wheat at $1.12 per bushel and sold the entire lot at $1.19J per bushel. What % profit did he make? 63. A drover bought 15 .horses at $125 per head; and sold 2 of them at $127.75 per head, 8 at $140 per head, and the re- mainder at $150 per head. If his expenses in taking them to mar- ket were $5 per head, what was his gain per cent. ? MASKING GOODS In Marking Goods, merchants usually resort to some device or characters to conceal the cost and selling price from the customer. The common method in marking goods is to use a word, phrase or sentence of ten different letters, to represent the nine digits and cipher, as a private mark. Characters other than let- ters are also frequently used. 266. The Key is the word, phrase or sentence used to rep- resent the nine figures and zero. An extra letter is used to pre- vent the repetition of a letter, and this is called a repeater. The cost price is usually written above a horizontal line and the selling price below. Fractions may be represented the same as whole numbers. 267. Suppose our key is : 1234567890 repeater, chri stopenx cost $3.18 r. cp. Goods which and r- would be marked sell for $4.46 i. xt. In the following problems the quantities considered and meth- ods of solution are the same as those in Profit and Loss. 1. My key is "He saw it run." If I pay $4-.80 per yard for cloth, how must I mark it to gain 20% ? 2. Mark the cost and selling price from the key "Now be sharp," the cost being $1.40, and selling price at a gain of 30%. Mark the cost and selling price of the following from the key "You mark his." 3. Cost $40, sold at a gain of 35%. 4. Cost $1.25, sold at a loss of 20%. 5. Cost $2.60, sold at a gain of 15%. 6. Cost $90, sold at a gain of 190 MARKING GOODS 191 7. Cost $9.50, sold at a gain of 60%. 8. Cost $13.50, sold at a gain of 52%. 9. Knives bought at $4.50 per dozen, are sold at 35% profit. From the key "Charleston" mark the cost and selling price of each knife. 10. A merchant bought boots at $37.50 per dozen pairs. He sold them at retail at 40% profit. Mark the selling price from the key "Importance." 11. Caps bought at $18.75 per dozen, are sold at retail for 40% more than cost. Mark the cost and selling price from the key "Market sign." 12. Mark the selling price of collars, bought for $2.70 per dozen and sold at 60% gain, from the key "The big four." IS. Mark the selling price of goods that cost $1.46, and sold at a gain of 45%. Use the key "He saw it run." 14. Goods marked from the key "Cash profit," were sold at a gain of 40%. The gain was a.st. What was the cost and sell- ing price? 15. I sold goods, marked from the key "Charleston," for o.cn, and gained h.en. What was my rate of gain? '16. I sold goods marked from the key "Hard moneys" for d.he, and gained 10%. Find the cost and gain. 17. Broadcloth cost $2.40 per yard, and is sold at a gain of 25%. Mark the cost and selling price from the key "Impor- tance." 18. Goods marked from the key "Importance" were sold at a profit of 25%. The gain was p. re. What was the cost and selling price ? 19. Mark the selling price of shoes, bought at $4.25 and sold at 33J% profit, from the key "Gambolines." 20. A merchant bought caps at auction at $10 per dozen. How will he mark the selling price to gain 20%, from the key "Blackhorse?" 21. By selling an article at $15 per dozen I gain 20%. How should I mark the cost of each article from the key "Cash profit?" 192 NEW BUSINESS ARITHMETIC 22. A dealer bought 12 chairs for $12,50 and sold them at 20% profit. How will he mark the selling price, by the key "God help us?" 23. A merchant buys boots at auction at $37.50 per dozen pairs. How shall he mark each pair by the key "Market sign" in order to gain 25% ? TKADE DISCOUNT 268. Trade Discount is an allowance or deduction made by merchants or manufacturers from their list or marked price. In issuing price lists and catalogues it is customary with man- ufacturers and large dealers to establish a fixed price, above the usual market price, and then meet the fluctuations in the market price by giving discounts, greater or less, from this established price. 269. The List Price or Invoice Price is the face of the bill before the discount has been deducted. 270. The Net Price is the selling price or the list price less the discount. 271. Cash Discount is a certain per cent, deducted for pay- ment of a bill immediately, or within a limited number of days. Thus upon the bills of a wholesale merchant may be seen the follow- ing : Terms : "4 months, 30 days less 5%" or "30 days, 2% off 10 days," which means that purchasers are entitled to a credit of 4 months but will be allowed 5% discount if bills are paid within 30 days, etc. 272. The bill from the jobber or manufacturer frequently bears two dates ; a shipping date and a date from which sales com- mence. The jobbing and manufacturing business is from six months to a year ahead of the wholesale and retail trade. Goods so sold and billed are frequently paid for before the arrival of the selling date and if paid for before that date an additional discount is deducted. This is called anticipating a bill, the rate is usually the current rate of interest. 273. When more than one discount is given, the first is reck- oned upon and deducted from the list price, the others are deducted from the successive remainders. The order in which the discounts are deducted does not affect the result. Thus a discount of 25%, 10% and 5% is the same as 10%, 5% and 25%. 274. It must not be supposed that several separate discounts are equal to their sum. This is not the case beca.use they are not 13 J93 194 NEW BUSINESS ARITHMETIC computed upon the same base. Thus 25% and 10% is not the same as 35%. In computations in Trade Discounts list price = Base. 275. To find the net amount of a bill when discounts are allowed. ORAL PROBLEMS 1. Find the net in the following single discounts: 90%, 85%, 75%, 66f%, 50%, 874%. 2. Find the net in the following double discounts : 10 and 10%, 25 and 20%, 20 and 20%, 20 and 10%, 33J and 10%. 3. What is the net price of a piano listed at $300 subject to a discount of 10% ? 25% ? 30% ? 12$% ? 20 and 25% ? 10 and 10% ? 33J and 10% ? 50 and 10% ? 25 and 20 and 10% ? 4. I bought a bill of hardware amounting to $120, subject to a discount of 33J% and 10%. What is the net? 5. A merchant paid $36 for an article which he sells at an advance of 33^%. What must be the asking price if he allows a discount of 25% ? WRITTEN PROBLEMS 1. A bought a bill of goods amounting to $125. He is al- lowed 20% and 10% off, and 5% off for cash. What amount of cash will pay the bill ? SOLUTION Or, 1. 100% - - 20% = 80% $125 2. 90% of 80% = 72% 25 = 20% discount. 3. 95% of 72% = 68% $100" after first discount. 4. 100% = $125. 10 = 10% discount. 5. 1% = $1.25. $90 after second account. 6. 68f% = $85.50. 4.50 = 5% discount. $85.50 net. From the foregoing solution and explanation we have the fol- lowing : TRADE DISCOUNT 195 To Find the Net Amount of a Bill a. Find the net amount of 100%. b. Let 100% equal the face of the bill. c. Find the ralue of 1%. d. Find the value of the net amount of 100%. NOTE. The net amount of a bill may also be found by computing each: discount separately and subtracting. 2. I was allowed 35% discount on a bill of $780. Find the net amount of the bill. 3: J. W. West sold a bill for $112.50 on 30 days time. He accepted cash payment at a discount of 14%. Find the discount allowed. 4. A. M. White bought a reaper for $218.40 on 6 months time, or 12J% off for cash. He paid cash. What discount was allowed ? 5. Find the net cost of a bill of $187.26 at a discount of 16%. 6. Smith bought an overcoat, marked at $19.20, at a discount of Yt\%. What did it cost him? 7. Shoes, which were marked $6.40, were sold at 12 \% less than the marked price. How much was received for them? 8. A merchant allowed me 4J% discount on a hat, marked at $2.65. How much did the hat cost me? 9. A dealer bought a lot of coffee for $360, at a discount of 20 and 10%. What was the net cost of the coffee? 10. What single ctfscount is equal to a discount of 25%, 10% and 5%? NOTE. Find the net amount of 100% and subtract this from 100%. 11. A discount of 10 and 5% is allowed on a bill of $450, Find the net cost. 12. Owens sold Moore clothing amounting to $234.50, at a discount of 20 and 12^%. What was the net cost? 13. Find the net cost of an invoice of $312.90, at a discount of 15 and 5%. IJt. B bought dry goods at a discount of 15, 10 and 6%. The amount of the bill was $520. Find the net cost. 196 NEW BUSINESS ARITHMETIC 15. I was allowed a discount of 30, 20 and 10% on an invoice of books amounting to $84. How much did I pay for the books ? 16. Howard sold a bill of notions for $760, with 25, 13 J and 8% off for cash. How much cash did he receive? 17. How much must I ask for goods that cost $20, that I may gain 20% and allow 20% off from marked price? Let 100% = the cost $20, 1% = $.20, 120% = $24 = selling price, or 80% of marked price. If 80% of marked price = $24, 1% of marked price = $.30 and 100% or marked price = 100 X .30 = $30. 18. Find the marking price of goods that cost me $30, that I may gain 20% and allow 25% discount from the marking price. 1$. A gained 25% on goods that he sold for 40% discount. The goods cost him $12. How much did he ask for the goods? 20. B sold me a bill of goods that cost him $8.40, at a discount of 19$%. He gained 15%. How much did he ask for the goods ? 21. What must be the marked price of goods that cost $5.80, that the seller may allow 5J% off and still make a gain of 30%? 22. The cost of a pair of shoes was $1.12. The seller gained 45%, and allowed a discount of 20%. What was his marked price from the key "Christopen ?" BILLS 276. A Bill is a written statement of merchandise sold, or services rendered. It should contain the date and place of pur- chase, names of the buyer and seller, and each article with the prices, terms and total cost. 277. An Item is a single article with price and amount, as given in a bill or statement. 278. An Invoice is a statement rendered by a wholesale dealer, or an account of goods imported. The term invoice usu- ally refers to larger quantities of goods than the term bill, but the terms are often used interchangeably. 279. A Statement is a copy of an account showing the date and amount of each bill and also the balance carried down from the last preceding statement. 280. A Duplicate Bill or Invoice is a copy of the original bill. It should always be marked Duplicate across its face. To receipt a bill the seller writes below the items the words Re- ceived Payment and signs his name. If this bill is receipted by a clerk,, who may be authorized to perform such duties, he should sign Per his own name or initials immediately beneath that of his principal. No. 1 CHICAGO, JUNE 18, 1905. GEORGE ADAMS, Bought of AMOS BROWN & Co. 3 5 25 10 2 bbl. Minn. Flour $7.00 bu. Potatoes .80 Ib. Granulated Sugar .05 " Japan Tea .65 box Florida Oranges 4.00 i Received Payment, AMOS BROWN & Co. Per Davis. 281. Signs and Abbreviations Used in Bills, Statements, Etc, a\c or acct. account. C. O. D. collect on de- prox. next month. @ at or to. livery. ult. last month. 197 198 NEW BUSINESS ARITHMETIC Ami. amount. bal. balance. Bo't bought B\L bill of lading. Co. Company. ctg. cartage. int. interest. .contra, contrary or op- in*t. present month. posite. No. 2 Cr. creditor. Mdse. merchandise. Dr. debtor. Pd. paid. E. and O. E. errors and Rec'd Paym't, received omissions excepted. payment. F. O. B. free on board. Sunds. sundries or sev- eral. #number or pounds. Folio 172. WORCESTER, MASS., May 1, 1005. Sales Book 345. RICHMOND BROS. Bought of A. B. DICKINSON & Co. Terms Interest after 00 days; 2% discount, 30 days. Case No. Yd. Price Items Amount #23 12 Pieces Bleached Cotton, 40 1 43 2 41 1 42 3 46 47 1 45 s 46 2 441 40 s 41 a 433 .061 #5 15 Pieces Muslin, 33 1 322 31 a 30 i 33 2 32i 31 2 34 - 33 3 31 2 34 s 33 35 1 323 351 .07 #7 21 Pieces Windsor Prints, 23 3 20 1 21 2 22* 24 23 2 21 3 22-' 24 2 25 24 1 23 1 20 2 21 2 25 1 24 3 20 3 23 2 21 25 3 26 .05 #32 16 Pieces Merrimac Prints, 30 31 1 322 333 29 1 27 8 28 2 30 1 29 2 24 2 27 2 26 1 29 s 30 2 31 2 33 .04| #11 6 Pieces Delaine, 39 1 40 39 s 42 41i 40-". .15 Extend all amounts. What was the cost if paid in 60 days ; if paid in 30 days; if paid in cash with 2 and 2% off? (The small figures at the right represent fourths 40 1 is 40*4 yd.) BILLS iyy No. 3 Folio 123. NEW YORK, JAN. 1, 1905. Sales Book 291. MR. M. I. PETERSON, Bought of CLARK BROS. Terms Cash 380 yd. Body Brussels @ $1.20 710 yd. Tapestry i .92 1% yd. Moquette " @ 1.45 500 yd. 3-ply Ingrain @ .65 310 220 yd. yd. 2-ply " Matting @ @ .48 .22 250 yd. Lining @ .iii Find what will pay the bill with 4 and 4% off. No. 4 ST. Louis, Mo., MARCH 11, 1905. Folio 367, MR. G. H. BROWN, Bought of JACKSON BROS. Terms 30 days, 10 days 3% discount, Cash 3 and 2 l / 2 % discount. 2 Bbl. 25 Prunes 240-20 220 270-20 250 470 @ .06 28 70 3 212-19*** Bbl. 2 5 Rice 219-20 ****** @ .08f 220-20 * * * 4 Bbl. 20 "A" Sugar 311 300 297 288 @ .08* 5 Bbl. 20 "G" Sugar 300 287 310 303 295 @ .07 2 Bbls. 25 Cut 260-18 *** Loaf Sugar *** @ .10 252-17*** 3 Bbl. 25 "C" 310-18*** Sugar 320-20****** @ .09 212-19*** Cartage 2 What sum will pay this bill at the end of 30 days; at the end of 10 days , in cash when purchased ? (The small figures at the right of "Bbl./' are the price of the same. 1st item 240-20, means that the gross weight was 240lb., allowance (tare) 20tb., net Weight 220 tb. The 2d, -">th and 6th items are same as 1st.) 200 NEW BUSINESS ARITHMETIC No. 5 Book 4, Page 411. SOUTH OMAHA, NEB., MAY 2, 1905. MESSRS. J. C. OLIVER & SON, Bought of L. B. SMITH, Terms, 60 days, 5% off 10 days, 4 and 2% for cash. No. Lb. Price Items Amount 6 Basket Pork Loins 310 313 308 296 301 299 . .07 4 Tubs Lard 68 71 69 70 -08| 3 Casks Shoulders 420 429 427 07J 7 Bbl. Mess Pork $17.40 11 Casks Hams 389 387 2 40P 403 392 397 3 400 2 398 397 402 400 .11 Find what sum will pay the bill on July 1 ; on May 12 ; on date of pur- chase. No. 6 LYNN, MASS., JUNE 2, 1905. MR. C. B. ACKERS, Bought of P. T. BUTLER & Co. Terms 60 days. # 271 H doz. pr. Buff Oxford Shoes @ $1.30 #2710 6 doz. pr. Ladies' L. B. @ 1.40 #4231 4 doz. pr. Ladies' K. S. B. @ 2.25 #1161 #3210 5 3 doz. pr. Farmers' K. Boots. @ 3.20 4% off doz. pr. Farmers' C. P. Boots @ 3.00 # 769 4 doz. pr. Boys' Stoga Boots @ 1.90 #1279 2i doz. pr. Kid Brogans @ 2.25 #2128 #3670 2 3 doz. pr. Kip Plow Shoes @ 1.85 5^ off doz. pr. Custom Kip Boots @ 2.10 #2737 2 doz. pr. Men's Thick Boots @ 3.10 3^ off How much cash will pay this bill with 3 and 5% off? BILLS 201 No. 7 SAGINAW, MICH., JAN. 23, 1905. MESSRS. D. C. WILSON & Co. Bought of L. B. WRIGHT & Co. Terms, Sight Draft after 60 days ; 5% off if paid within 10 days. 128640 ft. 33245 ft. 76898 ft. 23840 29300 33400 49800 ft. 96384 79860 ft. 29200 ft. Pine Plank Clear Pine Clapboards Cedar Posts Shingles "A" Shingles "B" Pine Timber Cedar R. R. Ties Flooring Barn Boards $21.60 26.80 24.20 7.00 3.80 3.00 19.00 27.00 24.91 12.60 per M. per M. per M. per C. per M. per M. per M. per C. per M. per M. What is the amount of the above bill, if paid March 10, 1905; if paid Feb. 1, 1905? (M. means by the 1000; C. by the 100.) No. 8 CHICAGO, ILL., SEPT. 26, 1905. MESSRS. BRUNER & SON, Bought of H. B. SILVER & Co. Terms, 90 days, 4% off, 10 days. 15 F. Base Burners @ $27.50 12 K. Ranges @ 30.00 18 Cook Stoves @ 23.50 12 Cook Stoves @ 14.00 8 Kegs Nails "10's" 100# each @ .05 6 Kegs Nails "8's" 100# each @ .05* 2 doz. Sets Knives & Forks @ 1.20 3 doz. Sets Silver Spoons @ 3.60 4 doz. Tack Hammers @ 1.10 What is the amount of the bill? What if paid within 10 days? W r hat if paid Oct. 4, 1905, and 4 and 3# are allowed? 202 NEW BUSINESS ARITHMETIC No. 9 NEW YORK, JULY 6, 1905. MR. D. B. WARD, Bought of AMERICAN BOOK Co. Terms, 30 days. 18 24 30 12 36 18 12 12 12 12 24 18 6 12 12 12 24 New Practical Arithmetic @ $ .68 " Primary @ .42 Lessons in Grammar (Welsh) (g> .60 Eclectic Geography @ 1.20 Wright's Spellers @ .26 Word Analysis (Swinton) @ .35 Wright's Alternate Reader @ .80 First @ .20 Second @ .28 Third " @ .40 Less 10# Loomis' E. Algebra @ .55 C. " @ .85 Wentworth's Geometry @ 1.12 Harkness Latin Grammar @ 1.12 " Reader @ .60 Rice's Book-keeping @ 1.60 Barnes' Brief History, U. S. @ .90 Less 20# Cartage 1 70 What will the above cost at 4% discount? Folio 828. MR. J. B. HINMAN, Terms, 30 days. No. 10 GRAND RAPIDS, MICH., FEB. 14, 1905. Bought of B. M. WESTON & Co. 1 12 Bedroom Sets @ $31.50 6^ off 20 Parlor Sets @ 42.00 H)# off 6 Walnut Sideboards @ 16.00 4 off 15 Walnut Dining Tables @ 12.00 5# off ' 12 Round Tables @ 8.00 2^ off 10 Cherry Book Cases @ 13.50 3^ off 18 Easy Chairs @ 3.20 12 Patent Rockers @ 5.00 4% off 22 Baby Carriages ( 6.00 5> off Find the cost of the above at 10 and 2 l />% off. BILLS 203 No. 11 DETROIT, MICH., OCT. 1, 1905. MR. A. B. CUM MINGS, Bought of R. K. MEYERS & Co. Terms, April 1, 1906, 60 days, 2% off 10 days. #47 8 Pieces Merrimac D. Prints, 32 31 2 33 1 29 8 30 1 31 30 3 32 1 No. Yd. Price Items Amount .05 #30 11 Pieces Gingham, 34 1 33 2 32 3 31 31 8 34 33 1 30 3 3 I 2 32 33 .10 #26 14 Pieces Cotton Flannel, 36 35 2 37 1 36 37 38 37 3 36 2 35 3 36 1 37 2 35 1 34 3 35 .14 #9 10 Pieces Cottonade, 33 32 1 31 2 33 3 30 1 34 29 3 33 2 32 2 32 3 .19 #13 6 Pieces Irish Linen, 37 37 1 36 2 36 37 2 35 3 .32 #7 3 Pieces Brown Duck, 35 34 3 35 1 .12 How much will pay the bill April 20, 1906? How much will pay the bill on April 6, 1906? MESSRS. CLARK & CHIDESTER, Terms, net cash 30 days. No. 12 GLOUCESTER, MASS., SEPT. 15, 1905. Bought of A. BOOTH & Co. 2 3 10 10 2 15 8 7 Qtl. New Geo. Cod $ 5.75 bbl. Ex. #1 Mackerel 22.00 Kits 15 Ibs. Ex. #1 " 1.80 " 20 " Bay #1 " 1.80 bbl. #2 Shore " " lg. 11.75 Kits 20 Ibs. #2 shore 1.55 Halfs New Labrador Herring 3.67 " Round Shore " 3.12i Box .25, Ctg. .80 204 NEW BUSINESS ARITHMETIC No. 13 MEYER VALVE CO. Steam, Brass and Iron Goods. CHICAGO, July 29, 1905. Your Order No. 1463. Our Order No. 9463. Terms : 10 da. 2% ; Net 15 da. 2 i Pt. SC Zero Lub. Net $3.05 *** 2 1 " " " " " 4.25 *** 12 Filling Plugs for Pt. SC Zero Lub. .35 *** 20* ** *** 12 i Coil Pipe Syphon .50 # 63-10-10* *** *** 13 1| Eng. Tav Flue Cleaners 2.00 ** 80-10-10* ##** *** 1 2" Roller Tube Expanders 10 **. 70-7i-10* **** *** 2 2" Spring Tube Expanders 12.00 ** 50-5* **** **** COMMISSION 282. Commission is a compensation allowed a person who buys or sells goods or other property for another. 283. An Agent is a person authorized to transact business for, and in the name of another. 284. The Principal is the person for whom an agent trans- acts business. 285. A Commission Merchant is a merchant who buys or sells goods, produce, live stock or other property, as an agent for others. 286. A Consignment is a quantity of goods sent to a commis- sion merchant to be sold on commission. 287. The Consignor is the person who sends the goods. 288. The Consignee is the commission merchant or person to 3vhom the goods are sent. Commission is commonly estimated at a certain per cent, of the amount of the sale or purchase. This rate per cent, varies according to the agreement of the parties or the customs of busi- ness, and is not fixed by law. Commission merchants are by the customs of business respon- sible to their principals, for the value of goods sold by them on credit. Xo separate rate per cent, is charged for assuming this liability, but the rate of commission is made large enough to cover it. In this respect commission merchants differ from other agents. 289. The Xct Proceeds of a sale or collection is the amount remaining after th^ commission and other charges have been de- ducted. 290. An Account Sales is a statement rendered by the com- mission merchant to his principal after the property has been sold, showing the amount of sale, commission and other charges, and the net proceeds. 291. A Remittance is a term applied to the money (usually 205 206 NEW BUSINESS ARITHMETIC a draft) , sent by the commission merchant to the principal in pay- ment of the net proceeds. 292. An Account Purchase is a statement rendered by a com- mission merchant after goods have been bought, showing the cost, charges and commission, and the total or entire cost. 293. The Entire Cost is the sum of the purchase and charges. The commission is computed on the amount of purchase or the amount of sale. When money is received, to be invested, the amount received includes the commission. 294. In computations in Commission. 1. Amount of sale or amount of purchase = Base. 2. Commission = Percentage. 3. Entire cost = Amount. 4. Net Proceeds = Difference. ORAL PROBLEMS 1. Find the commission at 2% on the following sales: $75, $64, $375, $120, $320 and $525. 2. Find the commission at 2%% on the following sales : $80, $240, $280, $3.60, $4.80, $1200 and $150. 3. After a commission of 3% is deducted from the following sales, what will be the net receipts: $75? $120? $24? $60? and $160? 4. A commission merchant receives a commission of $40 for selling some wheat. What did the sales amount to if the rate of commission was 2% ? 2$% ? 4% ? 5% ? 5. Find the net proceeds in the following, sales $200, rate of commission 5% and various charges $15. C>. A commission dealer reports the following sales, $300. Find net proceeds, rate of commission 2% and $10 charges ; 24% and $12; 3% and $18? 295. WRITTEN PROBLEMS 1. What commission is received for selling $1250 worth of goods at a commission of 1% ? COMMISSION 207 SOLUTION Or, 1. 100% = $1250. $1250 2. \% = $12.50. .07 3. 7% = $87.50. $87.50 From this solution we deduce the following : To Find the Commission a. Let 100% equal the amount of sale or purchase. b. Find the value of 1%. c. Find the value of the given rate. Or, Multiply the amount of sale or purchase by the rate per cent, expressed decimally. NOTES. To find the net proceeds subtract the commission from the amount of sale. 2. To find the entire cost add the commission to the amount of sale. 2. My agent charged 5% commission for buying merchandise worth $370. Find his commission. 3. I bought goods amounting to $640 for A, and received 4f% commission. How much did I receive? 4. B paid his agent 6%% for buying goods. What was the agent's commission on a bill of $39.50? 5. The amount of sale was $172.50. Find the agent's com- mission at 3J%. 6. White sold goods to the amount of $28.72 for me. I al- lowed a commission of $\%. Find the commission. 7. How much commission at 7J% is received on a sale of $1282.40? 8. A commission merchant sold 185 bbls. of apples at $5.20 per bbl., at a commission of 4J%. Find the amount of commis- sion. 9. An agent received ?>\% commission for selling 90 boxes of shoes at $12.70 per box. What was his commission ? 10. My agent bought 170 boxes of Jdd gloves at $8.40 per box. How much is due him if he charges 2f % for buying? 11. A's agent in New York paid $1460 for goods and charged 3% for buying and 2$% for insurance. How much did the goods cost A ? 208 NEW BUSINESS ARITHMETIC NOTE. Since he charged 3% for buying and 2^% for insurance, the goods must have cost 105^% of the original cost. 1% of the original cost is one hundredth of $1460, or $14.60, and W5 2 / 5 % of the original cost is times $14.60 or $1538.84, the entire cost. 12. I sold $1820 worth of goods for Brown, and charged him 3| % for selling. Find the amount which was due him. IS. The invoice price of goods was $470, the agent's charges for buying were \%. Find the entire cost. 14- A commission merchant bought eggs to the amount of $128.50 for Brown at a commission of 7f %. What did the eggs cost Brown? 15. An agent sold 610 bushels of corn at 30 cents per bushel. He charged a commission of 4%. Find the net proceeds of the sale. 16. A grain dealer sold through a commission merchant 1000 bushels of wheat at 84 T ^ cents per bushel. He allowed 2f % commission. Find the net proceeds. $ 17. I paid an agent $24.60 for selling a quantity of flour, at a commission of 4. Find the amount of the sale. NOTE. Since 4% of the amount of the sale is $24.60, 1% of the amount of the sale is one-fourth of $24.60 or $6.15 and 100% (the amount of the sale) is 100 times $6.15 or $615. 18. A received $36.48 commission for buying goods for Gra- ham. How much did the goods cost, if the commission was 3% ? 19. An agent's commission at 2%% was $27.50. Find the amount of the bill purchased. 20. Jones paid me $18.56 for buying wheat. How many bushels did I buy at 80 cents per bushel, if my rate for buying was 2f% ? , 21. A commission merchant received 7f% for selling. He received $73.20 commission on a sale. Find the amount of the sale. 22. My agent sold 40 cases of boots at $21.20 per case, and charged 3% for selling. Find the amount the agent should re- mit to me. 23. What is the selling price, if the commission is $11.48, the rate being If % ? COMMISSION 209 24. I charged 4% for selling some sheep, and received $37.80. How many sheep did I sell at $3.78 per head? 25. I shipped to a commission merchant 140 bbls. of potatoes and 95 bbls. of flour. He sold the potatoes at $2.25 per bbl., and the flour at $8.50 per bbl. He charged 4% for selling and 2% for storage. Find net proceeds. 26. Find the amount of purchase, if the entire cost including 3% commission is $309. NOTE. Since $309 is 3% more than the amount of purchase, it is 103% of the purchase, 1% of the purchase is -^ s of $309 or $3, and 100% (the purchase) is 100 X $3 or $300. 27. An agent remits $380, after deducting his commission of 5%. What was the amount of sales ? 28. The entire cost was $676, the rate of commission 4%. Find the amount of purchase. 29. I sent my agent $341.25 to invest in hogs at a commission of 5%. How many hogs can he buy at $3.25 per head? 30. B received $186.30 to invest in oats at 30 cents per bu. He deducts his commission of 3J%. How many bushels did he buy? 31. A farmer received $164.90 as the proceeds of the sale of 85 bbls. of apples. For how much per bbl. did the apples sell, the commission being 3% ? 32. A commission merchant sold 115 bu. of wheat at 90 cents per bu., 240 bu. of oats at 32 cents per bu., and 665 bu. of rye at 80 cents per bu. His charges were 3% for selling, $24 for stor- age, $9.65 for drayage, $15.80 for demurrage. What amount should he remit to the consignor ? 33. A commission merchant received $16.74 for selling 465 bu. of wheat. For how much per bu. did he sell the wheat if his rate for selling was 3% ? 34. A commission merchant charged 2f % for selling and $6.35 storage. He remitted $500 to the consignor. Find the amount of the sale. 35. What is the selling price of a house, if the rate for sell- ing is 8%% and the proceeds are $880? 14 210 NEW BUSINESS ARITHMETIC 36. White remitted his agent $624, with instructions to buy potatoes at 40 cents per bu., after deducting his commission of 4%. How many bushels can he buy ? 37. An agent charged $14.40 for buying an invoice of goods amounting to $320. What was his rate of commission ? NOTE. Since the cost $320 is 100%, $1 is ^ of 100% or i 5 c% and $14.40 is 14.4 times &% or 4 l / 2 %. 38. A commission merchant charged $20.50 including $7 for storage, for selling a bill of $450. Find his rate of commission. 39. Lyman purchased through an agent $218.75 worth of silk. The agent charged $8.75 for buying. What rate % did he charge for buying ? 40. The entire cost was $981.82^, and the commission was $55.57. Find the rate of commission. 41. B's agent in Boston bought for him 220 pairs of boots at $2.60 per pair, and 72 pairs of slippers at $1.15 per pair. His commission was 5J% ; he paid 2% for insurance, $33.25 for freight, $7.80 for drayage. How much did the goods cost B ? 42. An agent's charges including $35 for freight, were $78.50, and his rate for buying was 5%%. Find the amount of purchase and the entire cost. 43. B collected 60% of a debt. His charges were $9^30. What was the whole debt, if he charged 1J% f r collecting? i ' j (/ 44- The entire cost of an invoice of clothing was $298.75 in- cluding $8.25 for freight and 3f% for buying. Find the net cost of the invoice. 4-5. A commission merchant remitted $358 to .the consignor after he had deducted the following charges: 5% for selling, 2% for insurance, $4.70 for cooperage. What was the selling price of the goods ? COMMISSION Account Sales 211 CHICAGO, OCT. 10, 1905. Sold for account of J. C. SAMPSON & Co. By THOMAS W. BANNING. 190 Oct. 3 50bbl. XX Flour 6.25 312 50 100 " Minn. Flour 5.75 575 M 10 100 " XX Flour . 6.30 630 100 " Minn. Flour 5.80 580 Charges. Oct 1 Freight $67 50 and Cartage $15 60 10 Storage 350 bbl @ 3c a 10 Insurance -fa% u 10 Commission 5$ Net Proceeds Put the following narratives in the form of Account Sales : 47. William C. Davidson, Kansas City, Mo., sold for account of Marshall Field & Co., Chicago, the following goods: 1905 Aug. 4, 8 pc. Summer Silk, 294 yds. @ $.72 ; Aug. 13, 5 pc. Black Silk, 216 yds., @ $1.48; Aug. 17. 16 pc. Calico, 876 yds., @ $.07 ; Sept. 3, 19 pc. Alpaca 548 yds. @ $.34 ; Sept. 10, 25 pc. Diag- onals, 587 yds., @ $.65. The charges are: Aug. 1, Freight and Cartage, $67.38; Insurance, \% ; Commission, 5%. Find the net proceeds. 4S. E. P. Ellwood & Co., Chicago, sold for account of Thomas Mason the following: 1905, Xov. 1, 300 bu. Potatoes, @ 48c: Nov. 3, 100 bu., @ 52c ; Nov. 10, 60 bu., @ 58c ; Nov. 16, 200 bu. at 56c; Dec. 1, 230 bu. at 57c. The charges are: Nov. 1, Freight, $86.35 ; Cartage at 2c per bushel ; Storage at 3c per bu. ; Commission, 5%. Find the net proceeds. 212 NEW BUSINESS ARITHMETIC 49. Account Purchase NEW YORK, AUG. 16, 1905. Bought for account of DAVID ANDERSON & Co., By HENRY HAMMOND. yd. Fancy Prints Colored Silk doz. Ladies' Felt Hats yd. Black Cassimere suits Boys' Clothes Charges. Packing and Cartage Commission 5 .12 $1.38 $24.00 $1.40 9.00 Entire Cost Put the following narrative into the proper form of Account Purchase : 50. A. B. Duncan, St. Louis, bought for account of Davis & Norse the following: 1905, March 18, 150 bbl. Dakota Flour @ $5.80; 80 bbl. Buckwheat Flour @ $12.30; 480 bu. Ground Feed @ 30c ; 500 bu. Bran @ 8c ; 20 bbl. Superfine Flour @ $7.30 : Cartage, $7.80; Commission, 5%. What is the entire cost? 51. A merchant in Peoria shipped to his broker in Chicago a car lot of potatoes, 967 bu., which were sold at 64c per bushel. What was realized on the sale if the broker charged 5% for selling and freight cost 4c per 100 Ibs. ? How many pounds of Golden Rio coffee could be purchased with the proceeds of the sale of potatoes if coffee is worth 12c per pound and the broker charges a commission of 3% for buying? INSURANCE 296. Insurance is a security guaranteed by one person or company to another, against loss or damage. The several kinds of insurance derive their names from the kinds of risks assumed ; thus we have Fire Insurance, Marine In- surance, Life Insurance, Health Insurance, etc. There are several other minor forms of property insurance, such as Live Stock Insurance, Tornado Insurance, Steam Boiler Insurance, Plate Glass Insurance, etc., the nature of which is indicated by their names. 297. Accident Insurance is security against loss or damage by accident in traveling. 298. Life Insurance secures a certain sum to a person's heirs in case of death. 299. Health Insurance secures an allowance during sickness. 300. The Insurer or Underwriter is the party who agrees to make good the loss or damage. 301. The Insured is the person secured against loss or damage. Insurance is usually conducted by companies organized for the purpose and these may be classified as Stock Companies and Mutual Companies. 302. A Stock Company is one, the capital of which is owned by individuals called stockholders, who alone share the profits and losses. 303. A Mutual Company is one in which the insured becomes a sharer in the losses and gains of the company. Some companies combine the principles of Stock and Mutual Com- panies and are termed Mixed Companies. 304.. The Policy is the written contract between the insurer and the insured. It describes the property insured, the conditions, time, rate, etc. 305. A Valued Policy is one in which the value of the prop- erty insured is specified. 213 214 NEW BUSINESS ARITHMETIC 306. An Open Policy is one in which the value of the prop- erty insured is to be determined after loss. This arises usually in cases of merchandise in transit, and enables merchants to in- sure property shipped at different times and places. 307. The Premium is the sum paid for insurance and is usually a certain rate per cent, on the amount insured. The rates of premium depend upon the character of the risk, and the length of time it has to run. The rate for three years in fire companies is usually twice the rate for one year. FIRE INSURANCE 308. Fire Insurance is a security against loss or damage by fire. Fire insurance covers not only loss by fire, but also from smoke, water used in putting out a fire in an adjoining building and breakage or dam- age done by firemen while arresting the progress of a fire, such as blow- ing up a building. Whoever owns or has an interest in property, may insure it to the full amount of his interest or ownership. No more than the actual loss can be recovered by the insured, whether there be one or several insurers. Usually property is insured for about thr.ee-fourths of its actual value. 309. Adjustment of Losses. Fire insurance companies, as a rule, pay the full amount of the loss, provided this does not exceed the valuation named in the policy. Some policies contain the ''average clause" which requires the payment of only such a portion of the loss as the amount insured bears to the whole value of the property. Thus, under the "average clause/' if property worth $10000 is insured for Y-2. its value or $5000, the company will in case of loss, pay but y* of the loss whereas without the "average clause" the company would pay the entire loss up to the limit of $5000, or the face of the policy. In Chicago the board of underwriters have inserted an "80% clause" in policies, which exempts the policy from the "average clause" in case the insured shall carry insurance equal to 80% of the value of the property. 31 0.. In computations in Fire Insurance, J. Valuation = Base. 2. Premium = Percentage. 311. To find the premium when the valuation and rate of in- surance arc giren. INSURANCE 215 ORAL PROBLEMS 1. What is the premium at 2% on the following: $1200, $350, $750, $3000? 2. What is the premium at 2% on the following : $400, $T50, $600, $1500, $900? 3. A's house cost $6000. What is the premium at \\% on a three-fourths valuation ? 4- I paid $4 premium for insuring household goods at 1%. What was the face of the policy ? 5. What is the insurance on a building if the premium at 2% is $75? 6. A house valued at $3200 was insured at a three-fourths valuation for a term of 3 years. What was the premium, the rate being 1J% per year? 7. If $72 is paid for insurance for 4 years, what is the policy if the rate is 2% ? WRITTEN PROBLEMS 1. A insured a house for $8400 at \% premium. What was the premium? SOLUTION Or, 1. 100% = $8400. $8400 2. 1% = $84. .OOf 3. \% = $63, the premium. $63.00 We therefore have the following rule : To Find the Premium a. Let 100% equal the valuation. b. Find the value of 1%. c. Find the value of the given rate. Or, Multiply the valnation by the rate per cent, expressed deci- mally. 2. A house is insured for $6400 at 2$%. What is the pre- mium ? 3. A insured a house for $2400 and its contents for $800 at 35&. What was the premium? 216 NEW BUSINESS ARITHMETIC 4- A merchant insured a stock of good,s worth $4500 for of their value at 2%%. What was the premium? 5. A building worth $28400 is insured for f of its value at '3%. What is the premium ? 6. What will it cost to insure a barn worth $4200 for f its value at \%1 7. A has $1240 worth of live stock insurance at % ; store worth $5200 insured at \\% ; stock of merchandise worth $2700 insured at|%. How much premium does he pay? 8. A house valued at $2640 was insured for f its value at &%, and furniture valued at $1650 for f its value at \\%. If the property is burned and the company pays the loss, what will be the net loss to the company ? 9. I paid a premium of $72 for insuring merchandise at What was the amount insured ? NOTE. Since the premium is 1^4% and amounts to $72, 1J4% ~ $72, and 1% equals as many dollars as l l /4 is contained times in $72 or $57.60 and 100%, the amount insured, equals 100 times $57.60 or $5760. 10. Smith paid $51.75 premium for insurance on his property for f its value at -f^%. What was the value of the property? 11. If a company charges $60 for insuring a building for f its value at If %, what is the amount of the policy and the value of the property? 12. A barn insured for $2850 for 5 years at 75c per annum was destroyed by fire. What was the actual loss of the company ? IS. A stock of goods worth $9500 is insured for $6500, and is damaged by water while extinguishing a fire in an adjoining building to the amount of $1.320. The policy contains an "average clause." What amount will the company pay? 14. A insured his stock of goods as follows: $2000 in the ytna Insurance Company, $2800 in the Home Insurance Com- pany, $3500 in the Essex Company, $4200 in the Phcenix Com- pany. His loss by fire was $4375. How much will each company pay? NOTE. Find the total insurance. Find what per cent, the loss is of the total insurance. Multiply each risk by the per cent, of loss. INSURANCE 217 15. A building was insured in the Mutual Company for $2700, in the Springfield Company for $3600, in the Local Company for $4000, in the Commercial Company for $5400. A loss of $3611 was caused by fire and water. What loss was paid by each com- pany? 16. The loss by fire and water on the Union National Bank building was $68340. It was insured as follows: Metropolitan Company $18000; Great Western Company $22000; American Company $13000; United States Company $15000; Lancaster Company $25000; Orleans Company $9000. How much of the loss is paid by each company ? 17. I paid a premium of $102 for insurance on my house for f its worth at 2J%. What was the house worth and what would be the company's net loss, if the property was destroyed ? 18. I paid $124.80 for having a building worth $6800 insured at f its value and its contents valued at $8200 insured at f their value. What rate did the company charge for insuring ? 19. A's house worth $2500 was insured for f its worth, and furniture worth $3690 for f its worth. The premium was $70.40. What was the rate of insurance? 20. A farmer had his horses worth $960 insured for their full value ; his cows worth $1260 insured for f their value ; his hogs worth $822 insured for % their value. What was the rate of insurance if he paid a premium of $89.46? MARINE INSURANCE 312. Marine Insurance is a security against loss or damage to vessels and their cargoes by the perils of navigation. Transit Insurance is security against loss or damage to prop- erty while in transit by railroad or water route and is a kind of marine insurance. 313. An Insurance Certificate is a document issued by marine insurance companies similar in nature to a policy. Insurance certificates are negotiable and are, together with bills of lading, used by shippers as security for money advanced by banks. 218 NEW BUSINESS ARITHMETIC 314. Policies on cargoes are issued for a certain voyage and on vessels for a specified time. 315. Adjustment of Losses. In Marine Insurance the com- pany pays in case of loss, such proportion of the loss as the amount of the policy bears to the value of the property. Thus if the property is insured at ^ its value, the company pays \ of the loss. This is upon the principle of the "average clause." Merchants are usually provided with open policy books, which are used under the terms of an open policy and in which they enter each ship- ment as soon as the invoice is received. At the end of the month these books are collected by the company or its agent, the entries transferred to their books and a bill rendered the merchant for the premium. Computations in Marine Insurance are based upon the princi- ples of Percentage the same as in Fire Insurance. 1. A ship is insured for $85000 at 2J%. What is the premium ? 2. A ship is insured for $35000 at \\% and her cargo is in- sured at $55000 at Z\%. What is the total premium? 3. A cargo of good,s was insured for $10200, at 1%. What was the premium? 4. A shipment of merchandise from New York to Chicago worth $20000 is insured for $15000 at \%. It is damaged to the amount of $4200. What is the company's net loss ? 5. What amount must be paid for insuring a cargo of mer- chandise for $2500 at $1.15 and another cargo of $3700 at $1.20, less 15% discount on both premiums? 6. A vessel worth $37500 was insured for $10000 in one com- pany at 3% premium, and for $17500 in another at \% premium. She was afterwards damaged by a storm to the extent of $3000. Find the owner's loss including premium paid. 7. A New York merchant sent goods worth $1186 by water to Chicago. He insured them for $800 at 1J%>. They are dam- aged to the extent of $235. What amount does the owner lose including premium paid? 8. A vessel and cargo worth $48640 were insured in the fol- lowing companies, as follows : $4500 in the Paoli ; $7200 in the INSURANCE 219 Leipsic; $8600 in the West Baden; $3350 in the Custer ; $6750 in the Litchfield. The vessel and cargo sustained a loss of $17936. What amount was paid by each company ? LIFE INSURANCE 31G. Life Insurance secures a certain sum of money to be paid to a person's heirs in case of his death, or to himself, should he survive a certain number of years. 317. The Policy is the written contract between the parties, and sets forth the conditions of the agreement. 318. The Ordinary Life Policy requires payments of pre- mium during life, and the policy is payable only upon the death of the insured. 319. The Limited Payment Life Policy requires premium to be paid for only a specified number of years, as five years or ten years, policy payable at death. 320. The Endowment Policy is payable at the end of a specified number of years or before if insured should die. 321. The Annuity Policy secures by a single payment of premium, the payment to the insured of a certain sum annually during his lifetime. 322. The Beneficiary is the person to whom the policy is made payable. 323. The Insured is the person whose life forms the subject matter of the policy. A person may insure his own life or that of any person in whom he has a pecuniary interest, or upon whom he depends for support, as that of a near relative, or debtor to the amount of the debt existing. But a person cannot insure the life of a stranger or one in whom no pecuniary interest exists. 324. The Surrender Value of a policy is the amount of cash which the company will pay the holder at any time upon the sur- render of the policy. 325. The Expectation of Life is the number of years that a person of a given age will probably live, based upon the records of. mortality. 220 NEW BUSINESS ARITHMETIC TABLE OF RATES. Annual Premium for an Insurance of $1,000. LIFE POLICIES ENDOWMENT POLICIES u < Annual Premium 10 Annual Payments 15 Annual Payments 20 Annual Payments 10-Year Endowment 15-Year Endowment ' 20- Year Endowment 25-Year Endowment 30-Year Endowment ~25~ $20 50 $43 50 $33 10 $28 10 $105 90 $67 40 $48 70 $38 00 $31 40 26 21 00 44 30 33 80 28 60 106 00 67 50 48 90 38 20 3? 60 27 21 50 45 20 34 40 29 20 106 10 67 60 49 00 38 40 31 80 28 22 10 46 10 35 10 29 80 106 30 67 80 49 20 38 60 3? 00 29 22 70 47 00 35 90 30 50 106 40 68 00 49 40 38 80 32 30 30 23 30 48 00 36 60 31 10 106 60 68 20 49 60 39 10 32 60 31 24 00 49 10 37 40 31 80 106 80 68 30 49 80 39 30 32 90 32 24 70 50 10 38 30 32 60 107 00 68 60 50 10 39 60 33 20 33 25 50 51 20 39 10 33 30 107 20 68 80 50 30 39 90 33 60 34 26 30 52 40 40 00 34 10 107 40 69 00 50 60 40 30 34 00 35 27 10 53 60 41 00 35 00 107 60 69 30 50 90 40 60 34 50 36 28 00 54 80 42 00 35 80 107 80 69 60 51 30 41 10 35 00 37 29 00 56 20 43 00 36 80 108 10 69 90 51 70 41 50 35 60 38 30 00 57 50 44 10 37 70 108 40 70 20 52 10 42 00 36 20 39 31 10 59 00 45 30 38 80 108 70 70 60 52 50 42 60 36 80 40 32 20 60 40 46 50 39 80 109 10 71 00 53 00 43 20 37 60 41 33 40 62 00 47 70 41 00 109 40 71 50 53 60 43 90 38 40 42 34 70 63 60 49 00 42 20 109 80 72 00 54 20 44 60 39 30 43 36 10 65 30 50 40 43 50 110 30 72 50 54 80 45 40 40 30 44 37 50 67 10 51 90 44 80 110 80 73 10 55 60 46 30 41 30 45 39 10 69 00 53 40 46 20 111 30 73 80 56 40 47 30 42 50 46 40 70 70 90 55 10 47 80 112 00 74 60 57 30 48 40 43 80 47 42 50 72 90 56 80 49 40 112 60 75 40 58 30 49 60 45 20 48 44 40 75 10 58 60 51 10 113 40 76 30 59 40 51 00 46 80 49 46 40 77 30 60 50 52 90 114 20 77 30 60 70 52 40 48 50 50 48 50 79 60 62 50 54 80 115 10 78 40 62 00 54 00 50 30 To find the annual premium which must be paid on a policy of $1000, look in the left hand column under Age and find the age of the insured, then opposite this look in the column descriptive of the policy and the amount will be the premium on $1,000, which multiplied by the thousands and decimals of thousands of dollars in the policy will give the premium required. 1. A man at the age of 40 desires to take out an ordinary life policy for $5000. What is the premium ? INSURANCE 221 2. What is the premium on a policy for $4250, the insured being 33 years of age, by the 15 payment life plan? 3. What will be the annual premium for $2500 on a person's life at the age of 26, for 15 years, under the endowment plan? 4. A. B. Smith, 35 years of age, desires to take out an en- dowment policy payable in 25 years for $1500. What will it cost him annually? 5. A teacher at the age of 32 years had his life insured for $3000 by the ordinary life plan and died after making 13 pay- ments. How much did his family receive more than he had paid the company? 6. A person aged 29 years takes out an endowment policy for $8000 payable in 20 years. He lived past the endowment period. What did he gain, having paid his premium regularly, making no allowance for risk or interest on payments ? 7. A gentleman in Chicago, 32 years of age, wishing to pro- vide for his family in case of his death, obtains a life policy for ten years for $3090. What amount of annual premium must he pay? S. If I take an endowment policy of $3000 at the. age of 28, payable to myself in 20 years, and the dividends increase the policy $912.25, how much more will I receive from the company than I have paid? 9. A gentleman, 45 years of age, gets his life insured for $5000, by the 20 year endowment plan, and dies at the age of 50 years. How much more has his insurance cost him than it would have cost by the ordinary life plan? 10. John Davidson, age 32, takes out a 25 year endowment policy for $5000. At 37 years of age he takes out a 10 year endowment for $5000. At 42 years he takes out a 15 year life policy for $5000. What are his total annual premiums after taking out his last policy? 11. A man aged 38 years secured a life policy for $8000. After making 7 annual payments he died. How much more than the amount of premium paid was received by the heirs of the per- son insured? 222 NEW BUSINESS ARITHMETIC 12. Amos Duncan, aged 25 years, takes out a 20 year endow- ment for $2500. Assuming that he will live to receive the policy how much more will he receive than he pays the company? REVIEW PROBLEMS IN PERCENTAGE 326. 1. What % is gained by selling f of a barrel of flour for g- of what the barrel cost ? 2. If B loses 25% by selling his horse for $80, for how much must he sell it to gain 40% ? 3. I lost $62.40 by selling 60 bbls. of flour at 24% less than cost. What was the cost per bbl.? 4. A has $1600. 75% of his money is equal to 62% of B's money. How much have both together? 5. What is the cost of an article on which 25% is gained, after deducting 40% from the marked price, which is $10? 6. B sold his horse for $105, which was of its cost. What '% would he have gained by selling it at $109.80? 7. By selling shoes at $2.30 per pair, 8%, is lost. At what price per pair must they be sold to gain 12% ? S. What % does a merchant gain by selling hats at $1.40, that were bought at $18 per dozen less 20 and 12J% ? 9. A clothier reduced the price of an overcoat 90 cents, and thereby reduced his profit from 15% to 10-|%. How much did it cost him? 10. Lyman paid 30% of his debt, and then found that $?OS would pay 65% of the remainder. What was the amount of the debt? 11. I bought goods at J of their value and sold same at 18% more than their value, and received $3776. What did I pay? 12. From the key "Have it snow," mark goods that cost $1.52, that I may gain 25% and allow 5% from the marked price. IS. What is my rate of annual income on $1905 invested in real estate which. rents for $15 per month, allowing $27.60 taxes and repairs? 14. What must be the marked price of hats that cost $2.10, that 10% may be deducted from the price, and yet a profit of 20% be made ? REVIEW PROBLEMS 228 15. What % is gained by buying goods at a discount of 20 and 25%, and selling same at a discount of 10 and 5% ? 16. A merchant sold goods at 5% less than marked price and yet made a profit of 25%. The marked price was what % ad- vance on cost ? 17. I sold wheat at a profit of 15% ; invested the amount re- ceived in wheat again, and sold it at a profit of 18%, receiving $1709.82. How much did each lot cost me? IS. An agent sold real estate on his own account for $2780, and gained 15%. For how much should he have sold it to gain 25%? 19. A merchant whose average profits were 12%, sold his business and loaned his money at 7-|%. His annual income is re- duced $427.50. Find his investment. 20. A clothing merchant paid $4.80 for a coat and marked it so that he could allow 25 and 20% discount and yet gain 30%. What was the marked price ? 21. A wholesale merchant sells goods at retail at 40% above cost and at wholesale at 15% less than retail price. What is his gain % on goods sold at wholesale ? 22. I received $5.80 less for goods sold at 12% loss, than I would have received had I sold at 17% profit. How much would be received for the goods at 30% profit? 23. An agent sold corn at 4% commission and invested the proceeds in coffee at 5% commission; his total commission was $312. Find the selling price of the corn and the cost of the coffee. 24. My room is 30 feet wide, and its length is 40% longer than the width. I carpet it with carpet of a yard wide. What is the cost at 60c a yd., laid lengthwise? Laid crosswise? 25. Wilson sold a piano to Davis at a gain of 25%. Davis sold the piano for $350, which was 12|% less than the sum he paid. How much did the piano cost Wilson? 26. I sold 36% of a purchase at 15% profit, 75% of the re- mainder at 12% profit, and what then remained at 10% profit: and gained $25.52. What was the amount of the purchase? . 21. An agent sold a quantity of sugar at 5% commission and 224 NEW BUSINESS ARITHMETIC invested the proceeds in corn, commission 3% for buying, at cents per bushel. Find the selling price of the sugar if he bought 5000 bushels of corn. 28. An agent sold 200 bbls. of apples at $2 per bbl. and charged 4% commission. He invested the proceeds after de- ducting 6f% for buying, in wheat at 90 cents per bu. How many bushels did he buy? 29. A merchant sold J of his stock at 12% gain ; J of it at 15% gain; | of it at 20% gain; the remainder which cost $295 at 25%. What was his whole gain and rate of gain? SO. A merchant bought 40 gallons of molasses at 60 cents per gallon, and lost 15% by leakage. At what price per gallon must he sell the remainder to gain 13-J% on the total cost? 31. A wholesale merchant sold goods to Davis at 40% profit. Davis failed and was able to pay but 75% of his account. Did the merchant gain or lose and how much on a bill of $1800 ? 32. The price of goods was marked down 10% or to $22.50. The dealer in order to make a sale allowed another discount of 12% and then sold at a gain of 23|%. At what % above cost were the goods marked? S3. A merchant bought 6 dozen pairs of gloves at $12.90 per dozen. He sold 2 dozen at $1.40 per pair ; 1| dozen at $1.60 per pair; and 2^ dozen at $1.20 per pair. What was his gain % on the whole lot? 34. Williams gained 20% on his investment the first year, and 25% the second year. He lost 10% the third year, and gained 12% the fourth year. His capital was then $5292. How much did he invest ? 35. My agent sold a lot of grain for me at 2% commission, and invested the proceeds in dry goods at 2% for buying. His whole commission was $200. Find the cost of the dry goods and the selling price of the grain. 36. A bought two houses for $1400; 15% of the cost of the first was equal to 20% of the cost of the second. He sold the first at 13% profit and the second at 7f % loss. How much did he .gain by the transaction? INTEREST 327. Interest is the compensation allowed for the use of money. 328. The Principal is the money for the use of which in- terest is paid. 329. The Amount is the sum of principal and interest. 330. The Time is the period during which the principal bears interest. 331. The Rate of Interest is the rate per cent, paid for one year. 332. Simple Interest is the interest on the principal only. 333. Legal Interest is the interest or the rate fixed by law if no rate is specified in the contract. 334. Usury is the interest at a higher rate than allowed by law. 335. Common Interest is the simple interest in which 360 days are considered a year; 30 days a month; a month T ^ of a year. This is used in finding the interest on notes and debts that bear interest for long periods of time generally when the time is more than a year. 336. Bankers Interest is the simple interest in which the exact number of days of each month are reckoned, and called 360ths of a year. This is used by banks, and by business men in finding the in- terest on short time notes and debts. 337. Exact Interest is the simple interest in which the exact number of days of each month are reckoned, and called 365ths of a year. This is used by the U. S. Government ; also in finding- the in- terest on foreign money. Exact interest for any time expressed in days may be obtained by subtracting^ from the amount of common interest. Or common 15 225 226 NEW BUSINESS ARITHMETIC interest may be obtained from exact interest by adding thereto fa of the exact interest. 338. Interest is allowed on all notes, debts and contracts when it is agreed upon by the parties ; on all notes, debts and contracts after they become due. When interest is allowed, though no rate of interest is expressed, the legal rate of the State is understood. The following table shows the rates of interest and penalties for usury in the several states and territories compiled from the latest official sources. The first column shows the legal rate of interest when no rate is specified ; the second column shows the maximum rate allowed by law. STATES AND TERRI- TORIES. 1 LEGAL RATE. HIGHEST RATE ALLOWED. PENALTY FOR USURY. Alabama 8* 8* Forfeiture of all interest. Alaska 8* 12* Arizona 6* any* None. Arkansas 6* 10* Forfeiture of principal and interest. California 1% any* None. Colorado 8* any* None. Connecticut 6* 6* None. Delaware 6* 6* Forfeiture of double amount of loan. Dist. of Columbia 6* 10* Forfeiture of all interest. Florida 8* 10* Forfeiture of all interest. Georgia 1% 8* Forfeiture of all interest. Hawaii 6* 12* Idaho 1% 12* Forfeiture of three times the excess of in- terest over 12 *. Illinois 5* 7* Forfeiture of all interest. Indian Territory 6* 8* Indiana 6* 8* Forfeiture of excess of interest over 6 *. Iowa 6* 8* Forfeiture of all interest and costs. Kansas 6* 10* Forf. of double the excess of int. over In . Kentucky 6% 6* Forfeiture of excess of interest Louisiana 5* 8* Forfeiture of all interest. Maine 6* any* None. Maryland 6* 6* Forfeiture of excess of interest. Massachusetts 6* any* None. Michigan 5* 7* Forfeiture of all interest. Minnesota 6* 10* Forfeiture of contract. Mississippi Missouri 6* 6% 10* 8* Forfeiture of interest. Forfeiture of all interest. Montana 8$ any* None. Nebraska 1% 10* Forfeiture of all interests and costs. Nevada 1% any* None. New Hampshire 6* 6* Forfeiture of three times the excess of in- terest. INTEREST 227 STATES AND TERRI- TORIES. J o w a HIGHEST RATE ALLOWED. PENALTY FOR USURY. New Jersey 6* 6* Forfeiture of all interest and costs. New Mexico 6* 12* None. New York 6* 6* Forfeiture of principal and interest. North Carolina 6* 6* Forfeiture of double the amount of interest. North Dakota 1% 12* Forfeiture of all interest. Ohio 6* 8* Forfeiture of excess of interest over 8 *. Oklahoma 1% 12* Oregon Pennsylvania 6* 6% 10* 6* Forfeiture of interest, principal and costs. Forfeiture of excess of interest Philippine Islands 6* any Porto Rico 12* 12* Rhode Island 6* any* None. South Carolina 1% 8* Forfeiture of all interest. South Dakota 1% 12* Forfeiture of all interest. Tennessee 6* 6* Forfeiture of excess of interest. Texas 6* 10* Forfeiture of all interest Utah 8* any* None. Vermont 6* 6* Forfeiture of excess of interest. Virginia 6* 6* Forfeiture of excess of interest over 8 %. Washington 10* 12* Forfeiture of double illegal interest. West Virginia 6* 6* Forfeiture of excess of interest Wisconsin 6* 10* Forfeiture of all the interest. Wyoming 8* 12* None. Interest differs from other applications of Percentage in hav- -ing the element of time introduced. In computations in Interest five quantities are considered, viz. : Principal, Rate, Time, Interest and Amount. In the following problems, interest will mean common interest unless otherwise stated. 339. To find the interest for any number of years and months. ORAL PROBLEMS 1. What is the interest on $150 for 1 year at 3% ? at 4% ? at 5% ? at 6% ? at % ? 2. What is the interest for 1 year at 6% on the following amounts : $250, $300, $40, $96, $2000, $800, and $640. 3. Find the interest on $250 for 2 years at 3u^ The interest on $1 for 6 days = .001. / The interest on $1 for 1 day = .000^. '/ 1. What is the interest on $120 for 2 yr. 4 mo. 24 da. at 6% ? SOLUTION 1. 2 X $-06 = $.12 interest for 2 years. 2. 4 X $-005 = .02 interest for 4 months. 3. 24 X $.000i = .004 interest for 24 days. 4. Int. on $1 = $.144 5. 120 X $.l-4 = $17.28. From the foregoing solution and explanation we have the 234 NEW BUSINESS ARITHMETIC Rule for Six Per Cent. Method a. Take as many cents as sLv times the years, one cent for every two months, one mill for every six days and one-sixth of a mill for every additional day. b. Add together these results and we have the interest upon $1 for the time and rate, which multiply by the given principal. c. To obtain the interest for a greater or less rate than 6% add to, or subtract from, the result at 6%. 2. Find the interest on $360 for 1 yr. 8 mo. 18 da. at 6%. 3. Find the interest on $500 for 3 yr. 10 mo. 15 da. at 6%. 4. Find the interest on $1360 for 4 yr. 7 mo. 24 da. at 6%. 5. Find the interest on $3200 for 2 yr. 5 mo. 15 da. at 1%. 6. Find the interest on $1270 for 10 mo. 12 da. at 8%. 7. Find the 'interest on $768 for 5 yr. 4 mo. 7 da. at 9%. S. Find the interest on $940 for 11 mo. 27 da. at 5%. 9. Find the interest on $660 for 9 mo. 9 da. at %. 10. Find the interest on $475 for 5 mo. 3 da. at ty%. 11. Find the amount of $540 for 1 yr. 10 mo. 12 da. at 8%. 12. Find the amount of $2400 for 24 da. at 7^%. 13. Find the amount of $1287.40 for 1 mo. 11 da. at t'%. 14. Find the amount of $847.80 for 3 mo. 26 da. at 6$%. 15. Find the amount of $126.10 for 2 mo. 16 da. at &%. 16. Find the amount of a note for $218.30 for 2 mo. 20 da. at 5-|%. 17. Find the amount of a note for $1625.30 at 7% for 1 yr. 2 mo. 18 da. IS. Find the amount of $735.40 at 10% interest for 3 mo. 25 da. 19. Find the amount of a note for $1420 at ty% for 3 > T - 5 mo. 15 da. '20. Find the amount of a note for $234.60 at S$% for 5 yr. 7 mo. 4 da. 21. Find the amount of a note at 1% for $185.60 dated Oct. 10, 1903, and paid June 8, 1905. 22. S. B. Davis borrowed $750 on Aug. 10, 1903, at 5% in- terest. He paid both principal and interest June 18, 1905. What amount did he pay ? INTEREST 235 CANCELLATION METHOD 343. To find the interest zvhen the operation is shortened by the use of cancellation. 1. Find the interest on $350 for 9 mo. at 8%. SOLUTION 350 .0 .02 $350 X 3 X .02 $21.00 int. We therefore have the following : Rule for Cancellation Method a. Upon the right of a perpendicular line write the principal, time in months or days and the rate. b. If the time is in months place 12 upon the left of the line, or if in days place 360 upon the left of the line (unless the accurate interest is required, in which case place 365). c. Cancel and multiply the remaining factors together for the required result. NOTE. The time must be all in months or days, and not in both. Com- mon interest is understood unless otherwise stated. 2. Find the interest on $480 at 6% for 8 mo. 3. Find the interest on $720 at 5% for 9 mo. 10 da. 4. Find the interest on $1250 at 6% for 2 yr. 6 mo. 6 da. 5. Find the interest on $160 at 6% for 1 yr. 9 mo. 18 da. I 6. Find the interest on $320 at 5% for 2 yr. 4 mo. 20 da. { 7. Find the interest on $440 at 7% for 3 yr. 1 mo. 15 da. 8. Find the interest on $400 at 9% for 1 yr. 2 mo. 28 da. 9. Find the interest on $750 at 8% for 11 mo. 16 da. 10. Find the interest on $1264.80 at 6% for 42 da. 11. Find the interest on $225 at 7% for 108 da. 12. Find the interest on $1140 at 7% for 11 mo. 20 da. 13. Find the amount of a note for $1600 drawing 8% interest for 25 da. 14- Find the amount of a note for $1080 at 5% for 3 mo. 15 da. 1-1. A note for $2500 dated April 3, 1905, draws 1% interest until Nov. 19, 1905. What will it then amount to? 236 NEW BUSINESS ARITHMETIC COMMON, BANKER'S AND EXACT INTEREST COMPARED 344. 1. Find the common, banker's and exact interest on a note of $600 at S%> dated January 15, 1905, and due August 24, 1905. COMMON INTEREST SIX PER CENT. METHOD 1905 8 24. 1905 1 15 $ 6 - 00 ~ int for 60 da. 12.00 = int. for 120 da. 7 9 - 3.00 = int. for 30 da. 7 mo. 9 da. - 219 da. 60 = int for 6 da . NOTE. In common interest we -30 int. for 3 da. reckon 30 days as a month and $21 90 int at 6% find the time by compound sub- 7 30 = int at 2% traction. In Banker's and Exact interest we find the exact number of days. BANKER'S INTEREST SIX PER CENT. METHOD 16 days in January. $6.00 = int. for 60 da. 28 days in February. 12.00 = int. for 120 da. 31 days in March. 3.00 = int. for 30 da. 30 days in April. 1.00 = int. for 10 da. 31 days in May. .10 = int. for 1 da. 30 days in June. 31 'days in July. $22.10 = int. at 6%. 24 days in August. 7 -36^ = int. at 2%. 221 days. $29.46^ = int. at 8%. EXACT INTEREST 16 days in January. 28 days in February. 31 days in March. 30 days in April. 31 days in May. 221 days = f ft yr. 30 days in June. $600 X yfa X IU = $29.07. 31 days in July. $29.07 = exact interest. 24 days in August. 221 days. 2. What is the banker's interest on $720 from May 12, 1904, to January 5, 1905, at 6% ? INTEREST 237 3. What is the exact interest on $365 from December 10, 1904, to March 15, 1905, at 6% ? 4. Find the difference between common interest and banker's interest on $98.50 from April 1, to October 30, at 5%. 5. Find the difference between common interest and exact interest on $210 from July 23, to November 28, at 10%. 6. Find the difference between banker's interest and exact interest on $190 from August 9, 1904, to March 16, 1905, at 6%. 7. Find the banker's interest on a note of $288 from January 4, to September 7, at 10%. 8. What is the exact interest on a note of $109.50, dated June ' 7 and due December 23, bearing 5% interest? 9. What is the common interest paid on a note of $178.25, at 8%, dated March 1, 1903, and due August 1, 1905? 10. What is the difference between banker's interest and exact interest on a note of $1460 bearing 10%, dated April 6, 1904, and due March 9, 1905? 11. Which is the greater, and how much greater, common in- terest or banker's interest on a note of $432 from September 16, 1904, to June 2, 1905, at 7%? 12. Which is the greater, and how much greater, common in- terest or exact interest on a debt of $182.50, from July 30, 1904, to April 14, 1905, at 9%? 13. I borrowed $2555 at exact interest and loaned same at banker's interest. Did I gain or lose, and how much from May 5, to November 22, interest at 7$% ? 14- Would I gain or lose and how much, to borrow $32850 at 8%, at common interest and loan it at exact interest from De- cember 28, 1904, to July 13, 1905? 15. How much is gained, money worth 6J%, by borrowing $4800 at common, interest and loaning it at banker's interest from July 23, 1904, to June 26, 1905? 16. Find the interest on 7 U. S. bonds of $1000 each from November 6 to March 28, at 4J% NOTE. Exact interest is used in computing interest on U. S. securities and foreign money. 238 NEW BUSINESS ARITHMETIC 17. Find the interest on a $500 U. S. bond, bearing \% inter- est from April 1 to July 25. IS. What is the interest on 240 9s. 3d. for 90 days at 8%? NOTE. Reduce shilling and pence to decimal of a pound, then find the interest as in U. S. money, after which reduce the decimal of pounds back to lower denominations. 19. What is the interest on 920 7s. 6d. from February 5 to July 1, at 5 6 / ? 20. Find the interest on 1335 11s. 3d. at 4%, from March 4 to October 10. 21. Find the interest on a note of 270 12s. at 7%, from April 10 to September 3. 22. Find the interest on a note of 120 15s. at 6%, for 146 days. gS. Find the interest on 1999 8s. 9d. from July 8, 1905 to Oct. 24, 1907 at 10%. PROBLEMS IN INTEREST 345. To find the time, ivhcn the principal, rate and interest or amount are given. 1. I received $9 interest on $150 loaned at 4%. For how long was the money loaned ? SOLUTION $150 .04 $6.00 = interest for 1 yr. $9 -j- $6 = 1J or 1 yr. 6 mo. From this solution we have the following: To Find the Time a. Find the interest on the principal for one year. b. Divide the given interest by the interest for one year and the result will be the time in years. 2. In what time will $280 produce $49 interest at 7% ? 3. In what time will $160 produce $15.36 interest at 8% ? 4. In what time will $225 produce $72.90 interest at 9% ? INTEREST 239 5. In what time will $618.50 produce $25.14 interest at 6%? 6. In what time will $750 produce $2.25 interest at 4% ? 7. I received $33 interest on a loan of $300 at o%. For how long was the money loaned? S. A farmer borrowed $640 at 9% on June 1, 1904, and paid $801.28 for the note and interest at maturity. Find the maturity of the note. 9. On July 16, 1905, I paid $860.36 for a note of $785, bear- ing 12% interest. Find the date of the note. 10. What is the date of a note bearing 11% interest for $190 on which $52.25 interest was (lue May 30, 1905? 11. I borrowed $335 on February 4, 1905, and found the amount at maturity to be $452.92. When will the note mature, it bearing 8% interest? 12. On August 24, 1905, I borrowed $600 on my note at \% interest and at maturity paid $621 for note and interest. Find the date of maturity, allowing banker's interest. 346. To find the rate, when the principal or amount, interest and time are given. 1. At what rate of interest will $500 in 1 yr. 8 mo. 24 da. produce $52? SOLUTION $5.00 = int. 1 yr. \%. 2.50 = int. 6 mo. .83J = int. 2 mo. .2;i = = int. 20 da. .05 = int. 4 da. $8.60 J = int. at \%. $52 -r- $8.66 = 6 == 6%. From this solution and explanation we have the following: To Find the Rate a. Find the interest on the principal at 1% for the given time. b. Divide the given interest by the interest at 1%, ana the re- sult will be the rate. 240 NEW BUSINESS ARITHMETIC NOTE. If the amount is given, subtract the principal from it to find the interest. 2. At what rate of interest will $720 produce $172.80 in 2 yrs. ? S. At what rate of interest will $480 produce $84 in 2 yrs. 6 mo.? 4. At what rate of interest will $320 produce $48.96 in 3 yrs. 9 mo. 27 days? 5. At what rate of interest will $1275 produce $242.25 in 1 yr. 10 mo. 24 days ? 6. At what rate of interest will $85 produce $43.01 in 4 yrs. 7 mo. 6 days? 7. A paid $36 interest on a note of $240, that had been on interest for 1 yr. 8 mo. Find the rate of interest. 8. I loaned Smith $900 for 2 yrs. 8 mo. 12 days, and at the end of that time he paid me $1094.40 in full for his note and in- terest. What rate of interest did the note draw ? 9. A merchant received from Brown $218.96 for his note of $170 that had been at interest for 3 yrs. 7 mo. 6 days. What rate of interest was charged? 10. Snyder borrowed on his note $97.50 for 1 yr. 7 mo. 18 days. He paid $6 interest at the end of the year, and at matur- ity found the sum due was $101.055. Find the rate of interest. 11. On January 6 I loaned $144, and on December 31 re- ceived the amount due, which was $158.20. What rate of inter- est did I charge? 12. B borrowed $45 on October 30, 1905, and paid the note and interest with $47.39 on June 29, 1906. Find the rate of in- terest he paid. 347. To find the principal, when the interest, rate and time are given. 1. I received $226 interest on a sum loaned for 1 yr. 4 mo. at 6. How much was the loan? INTEREST 241 SOLUTION $.06 = int. on $1 for 1 yr. .02 = int. on $1 for 4 mo. $.08 = int. on $1 for the given time and rate. $226 -7- .08= $2825 = the principal. From the foregoing we have the following: To Find the Principal a. Find the interest on $1 for the given time at the given rate. b. Divide the given interest by the interest on $1, and the quo- tient will be the required principal. 2. What principal will produce $62.50 interest in 2 yrs. 6 mo. at 5%? 3. What principal will produce $39.78 interest in 1 yr. 4 mo. 18 days at 9% ? 4. What principal will produce $63.22 interest in 3 yrs. 7 mo. 15 days at 8% ? 5. What principal will produce $11.22 interest in 9 mo. 27 days at 10% ? 6. What principal will produce $20.235 interest in 4 mo. 20 days at 12%? 7. B paid me $154.47 interest on a note bearing 9%. What was the principal if the note was for 2 yrs. 3 mo. 3 days ? 8. James Irwin received $10.97 interest on a note bearing 7% interest. The note was dated January 6, 1905, and paid July 12, 1906. Find the principal. 9. The interest on a note bearing 6%, dated October 14, 1905, and paid August 10, 1906, was $39.43^. Find the princi- pal. 10. I paid $420 for a stock of goods and sold same to B on his note for 2 yrs. 6 mo. at 6% interest. The interest on the note was $71.19. At what % profit did I sell the goods? 11. William Graham borrowed money on his note at 4% for 3 yrs. 8 mo. 12 days. He invested the sum borrowed in potatoes at 25 cents per bushel. How many bushels did he buy, if the in- terest for the time was $18.50? 16 242 NEW BUSINESS ARITHMETIC 348. To find the principal zvhen the amount, rate and time are given. 1. What principal in 2 yrs. 1 mo. 15 days at 8% interest will amount to $421.20? SOLUTION $.17 = int. on $1 for the given time and rate. 1.00 $1.17 = amount of $1. . $421.20 -f- 1.17 = $360 principal. 2. What principal in 3 yrs. 9 mo. 21 days at 1% interest will amount to $303.98 ? 3. What principal in 5 yrs. 7 mo. 28 days at 9% interest will amount to $558.51| ? 4- What principal in. 11 mo. 10 days at 10% interest will amount to $1280.50? 5. What principal in 5 mo. 12 days at 5% interest will amount to $184.05 ? 6. I owe $780, due in 2 yrs. 6 mo. What sum will pay it now, if money is worth 8% interest? 7. A note bearing 7% interest, having run for 1 yr. 2 mo. 12 days, was paid with $596.20. Find the principcu <* 8. Adams paid $2592.60 for his note that had been on inter- est for 2 yrs. 4 mo. 24 days at 8%. What was the principal of the note ? 9. What sum is required to pay a debt of $125.78, due in .> yrs. 7 mo. 6 days, if interest is allowed at 9% ? 10. West borrowed $296.01 to pay a note that had been on interest at 4% for 10 mo. 15 days. Find the sum for which the note was given. 11 I bought goods to the amount of $757.12 on 4 mo. 24 days time. I borrowed money and paid cash for the goods. How much did I borrow if 10% interest was allowed? INTEREST 243 ANNUAL INTEREST 349. Annual Interest is interest payable annually or at other regular intervals of time. 350. If the Annual Interest is not paid when due, it draws simple interest from the time it becomes due until it is paid. Annual interest is legalized in Michigan at the same rate as secured by the contract ; in Ohio, Wisconsin, Vermont, New Hampshire, and Iowa, at 6%; and in Pennsylvania, Georgia, Illinois and Indiana, by special con- tract only. When notes are made to run for a term of years secured by real estate or collaterals, it is customary to represent the principal by one or more "Principal notes" which do not read to draw in- terest, and then the several payments of interest are evidenced by interest notes maturing at the time each interest payment is pay- able. These interest notes as well as the principal notes are en- titled to draw interest after maturity, like any other note. 1. What is due on a note of $300 at 6% for five years, inter- est payable annually, no payment having been made until the maturity of the note ? SOLUTION . $300 .06 >.00 =^nt. for 1 yr. _5 ).00 int. for 5 yr. 4 yr. + 3 yr. + 2 yr. + 1 yr. = 10 yr. Int. on $18 for 10 yr. = $10.80. $300 + $90 + $10.80 = $400.80. From the foregoing solution we have the following: To Find the Annual Interest a. Find the interest on the principal until the time of settle- ment. b. Find the interest upon the first year's interest for the sum of the times ivhich the several payments of interest have to run until maturity. c. Add together the principal, the interest thereon, and the in- 244 NEW BUSINESS ARITHMETIC terest due on each year's interest. The result will be the 'amount due at maturity. NOTE. In case the interest is payable semi-annually or quarterly it is computed in the same manner as annually, substituting a half or quarter year for year. 2. Find amount due on a note of $800 for 1 yr. 8 mo. 12 days at 8%, interest payable quarterly, no payments being made be- fore maturity of the note. NOTE. At the expiration of each quarter, $16 is due. The first quarter's interest bears interest for 1 yr. 5 mo. 12 days; the second quarter's, for 1 yr. 2 mo. 12 days, etc. Find the amount due on the following notes, no payments hav- ing been made before maturity of the note. 3. $350 for 3 years at 7%, interest payable annually. 4. $910 for 3 yrs. 7 mo. 15 days at 10%, interest payable an- nually. 5. $460 for 2 years at 5%, interest payable semi-annually. 6. $590 for 1 yr. 11 mo. 12 days at 8%, interest payable semi- annually. Find the amount due on the following notes, no payments hav- ing been made : 7. $1290 for 1 year at 4%, interest payable quarterly. 8. $180 for 1 yr. 9 mo. 18 days at 10%, interest payable quar- terly. 9. What is the interest on a debt of $680 due in 3 yrs. 4 mo. 18 da. at 1% interest payable annually and no payments having been made ? 10. On August 16, 1902, A loaned $3465 at 5%, interest pay- able quarterly. If no payments have been made, what amount was due January 1, 1904? 11. A farmer borrowed $1250 on June 1, 1903, and gave his note drawing 6% interest payable semi-annually. If no pay- ments have been made, what will be the amount of the note April 13, 1905? INTEREST 245 COMPOUND INTEREST 351. Compound Interest is the interest on the principal and its unpaid interest added to it at the end of each period of time for which the interest is made payable. 352. Interest may be compounded according to agreement, at the end of each year, half year or any other period of time. Compound interest cannot be enforced by law in most of the states, but if the debtor is willing to pay compound interest he may do so without violating the law against usury. 1. What is the compound interest on $300 at 8% for three years, interest compounded annually? SOLUTION 1. $300 X .08 = $24, interest first year. 2. $300 + $24 = $324, principal second year. 3. $324 X -08 = $25.92, interest second year. 4. $324 + $25.92 = $349.92, principal third year. 5. $349.92 X .08 = $27.994, interest third year. 6. $349.92 + $27.994 = $377.914, amount due. 7. $377.914 -- $300 = $77.914, the compound interest. From this solution and explanation we have the following : To Find the Compound Interest a. Find the amount of the principal for one year and make this the principal for the second year. b. Find the amount of this new principal for the second year and make it the principal for the third year, etc. c. Subtract the original principal from the last amount and the result will be the compound interest. NOTES. 1. When the interest is payable semi-annually or quarterly, find the amount of the given principal for the first interval, and make it the principal for the second interval, proceeding in all respects as when the interest is payable yearly. 2. When the time contains years, months and days, find the amount for the even intervals upon which compute the interest for the remaining months and days, and add it to the last amount, before subtracting. 246 NEW BUSINESS ARITHMETIC Find the compound interest of 2. $600 for 4 years at 5%, interest compounded annually. 3. $720 for 3 years at 9%, interest compounded annually. 4. $1800 for 4 yrs. 8 mo. 12 days at 10%, interest com- pounded annually. ( O I ^ tf& } "4 . \ 5. $860 for 2 years at S%, interest compounded semi-an- nually. 6. $2700 for 2 yrs. 4 mo. at 6%, interest compounded semi- annually. 7. $3350 for 3 yrs. 2 mo. 20 days at 10%, interest com- Bounded semi-annually. 8. $180 for 1 year at 5%, interest compounded quarterly. 9. $450 for 1 yr. 1 mo. at 1%, interest compounded quarterly. 10. $920 for 1 yr. 7 mo. 24 days at &%, interest compounded quarterly. Where the time is long, the labor of computing compound in- terest may be greatly shortened by using the table. To find the compound amount of $1 by the table look in the column at the left of the page for the years and under the given rate per cent, at the top of the page. If the interest is compounded semi-annually, it is equivalent to double the number of years at half the rate per cent, or quarterly, four times the years at one-fourth the rate. The amount of $1 as found by the table, multiplied by the given prin- cipal will give the compound amount of the principal. The labor of computing compound interest may be greatly shortened by the use of the following : INTEREST Compound Interest Table 247 Showing the amount of $1 at compound interest at various ^s per cent, for any number of years, from 1 year to 50 years, rates per inclusive. Years. 1 per ct. VA perct. 2 per ct. 2% per ct. 3 per ct. 3', per ct. 4 per ct. 1 2 3 4 1.0100000 1.0201 000 1.0303 010 1.0406040 1.0510 101 1.0150000 1.0302 250 1.0456 7S4 1.0613 636 1.0772 840 1.02000000 1.04040000 1.0612 0800 1.0824 3216 1.10408080 1.0250 0000 1.0506 2500 1.07689062 1.1038 1289 1.13140821 1.0300 0000 1.06090000 1.0927 2700 1.1255 0881 1.1592 7407 1.0350 0000 1.0712 2500 .1087 1787 .1475 2300 .1876 8631 1.04000000 1.08160000 1.1248 6400 1.16985856 1.2166 5290 6 7 8 9 10 1.0615 202 1.0721 354 1.0828567 1.0936 853 1.1046221 1.0934433 1.1098 450 1.1264 926 1.1433 900 1.1605 408 1.1261 6242 1.14868567 1.1716 5938 1.19509257 1.2189 9442 .15969342 .1886 8575 .2184 0290 .2488 6297 .28008454 1.1940 5230 1.2298 7387 1.2667 7008 1.3047 7318 1.3439 1638 .2292 5533 .2722 7926 .3168 0904 .3628 9735 , 1.4105 9876 1.2653 1902 1.3159 3178 1.3685 6905 1.4233 1181 1.4802 4428 11 12 13 14 15 .1156683 .1268 250 .1380 933 .1494 742 .1609690 1.1779 489 1.1956 182 1.2135 524 1.2317 557 1.2502 321 1.2433 7431 1.26824179 1.29360663 1.3194 7876 1.3458 6834 1.31208666 1.34488882 1.3785 1104 1.4129 7382 1.4482 9817 1.3842 3387 1.4257 6089 1.4685 3371 1.5125 8972 1.5579 6742 1.4599 6972 1.51106866 1.5639 5606 1.61869452 1.6753 4883 1.5394 5406 1.6010 3222 1.6650 7351 1.7316 7645 1.8009 4351 16 17 18 19 20 .1725 786 .1843044 .1961 475 .2081090 .2201900 1.2689855 1.2880203 1.3073 406 1.3269 507 1.3468 550 1.37278570 1.40024142 1.4282 4625 1.4568 1117 1.4859 4740 1.4845 0562 .5216 1826 .5596 5872 .5986 5019 .63861644 1.60470644 1.65284763 1.7024 3306 1.7535 0605 1.8061 1123 1.73398601 1.7946 7555 1.8574 8920 j 1.9225 0132 ! 1.9897 8886 1.8729 8125 1.9479 0050 2.0258 1652 2.1068 4918 2.1911 2314 21 22 23 24 25 .2323 919 .2447 159 .2571 630 .2697 346 .2824 320 1.3670 578 1.3875 637 1.4083 772 1.4295028 1.4509 454 1.51566634 1.5459 7967 1.57689926 1.60843725 1.6406 0599 .6795 8185 .7215 7140 .76461068 1.8087 2595 1.85394410 1.8602 9457 1.9161 0341 1.9735 8651 2.03279411 2.0937 7793 2.0594 3147 2.1315 1158 2.2061 1448 2.2833 2849 2.3632 4498 2.2787 CS07 2.3699 1879 2.4647 1555 2.5633 0417 2.6658 3633 26 27 28 29 30 .2952 563 .3082 089 .3212 910 .3345 039 .3478 490 1.4727 095 1.4948 002 1.5172222 1.5399 805 1.5630 802 1.6734 1811 1.70688648 1.7410 2421 1.7758 4469 1.8113 6158 1.9002 9270 1.94780002 1.99649502 2.0464 0739 2.0975 6758 2.1565 9127 2.2212 8901 2.2879 2768 2.3565 6551 2.4272 6247 2.4459 5856 2.5315 6711 2.6201 7196 2.7118 7798 2.8067 9370 2.7724 6979 2.8833 t858 2.9987 0332 3.11865145 3.2433 9751 31 32 33 34 35 .3613 274 .3749 407 .3886 901 .4025 770 .4166 028 1.5865 264 .6103 243 .6344 792 .6589 964 .6838813 1.8475 8882 1.8845 4059 1.92223140 1.96067603 1.9998 8955 2.1500 0677 2.2037 5694 2.2588 5086 2.3153 2213 2.3732 0519 2.5000 8035 2.5750 8276 2.6523 3524 2.7319 0530 2.8138 6245 2.9050 3148 3.0067 0759 3.11194235 3.2208 6033 3.3335 9045 3.3731 3341 3.5080 5875 3.64838110 3.7943 1634 3.9460 8899 36 37 38 39 40 .4307 688 .4450 765 .4595 272 .4741 225 .4888637 .7091 395 .7347 766 .7607983 .7872 103 .8140 184 2.0398 8734 2.0806 8509 2.12229879 2.16474477 2.2080 3966 2.4325 3532 2.4933 4870 2.5556 8242 2.6195 7448 2.6850 6384 2.8982 7833 2.9852 2668 3.0747 8348 3.1670 2698 3.2620 3779 3.4502 6611 3.5710 2543 3.6960 1132 3.8253 7171 3.9592 5972 4.1039 3255 4.2680 8986 4.4388 1345 4.6163 6599 4.8010 2063 41 42 43 44 45 .5037 524 .5187 899 .5339 778 .5493 176 .5648 107 .8412 287 .8688471 .8968 798 .9253 330 .954 J 130 2.7521 9043 2.8209 9520 2.8915 2008 2.9638 0808 3.0379 0328 3.3598 9893 3.4606 9589 3.5645 1677 3.6714 5227 3.7815 9584 4.0978 3381 4.2412 5799 4.3897 0202 4.5433 4160 4.7023 5855 4.9930 6145 5.1927 8391 5.4004 9527 5.6165 1508 5.8411 7568 46 47 48 49 50 .5804 589 .5962634 .6122 261 .6283483 .6446318 1.9835 262 2.0132 791 2.0434 783 2.0741 305 2.1052424 2.4866 1129 2.5363 4351 2.5870 7039 2.6388 1179 2.6915 8803 3.1138 5086 3.19169713 3.2714 8956 3.3532 7680 3.4371 0872 3.8950 4372 4.01189503 4.1322 5188 4.2562 1944 4.3839 0602 4.8669 4110 5.03728404 5.2135 8898 5.3960 6459 5.5849 2686 6.0748 2271 6.3178 1562 6.5705 2824 6.8333 4937 7.1066 8335 248 NEW BUSINESS ARITHMETIC Compound Interest Table Showing the amount of $1 at compound interest at various rates per cent, for any number of years, from 1 year to 50 years, inclusive. Years. V/ 2 per ct. 5 per ct. 6 per ct. 7 por ct. 8 per ct. 9 per ct. 10 per ct. 1 2 3 5 1.0450 0000 1.0920 2500 1.14116612 1.1925 1860 1.2461 8194 1.0500 000 .1025 000 .1576250 .2155 063 .2762 816 1.0600000 .1236 000 .1910 160 .2624 770 .3382 256 1.0700 000 .1449 000 .2250 430 .3107 960 .4025 517 .0800 000 .1664000 .2597 120 .3604 890 .4693 281 .0900 000 .1881 000 .2950 290 .4115 816 .5386 240 1.1000 000 1.2100 000 1.3310 000 1.4641000 1.6105 100 6 7 8 10 1.3022 6012 1.3608 6183 1.4221 0061 1.4860 9514 1.5529 6942 .3400956 .4071 004 .4774 554 .5513 282 .6288 946 .4185 191 .5036 303 .5938 481 .6894 790 .7908 477 .5007 304 .6057 815 .7181 862 .8384 592 .9671 514 .5668 743 .7138 243 .8509 302 .9990 046 2.1589 250 1.6771 001 1.8280 391 1.9925 626 2.1718933 2.3673 637 1.7715 610 1.9487 171 2.1435 888 2.3579 477 2.5937 425 11 12 13 14 15 1.6228 5305 1.69588143 1.7721 9610 1.8519 4492 1.9352 8244 .7103 394 .7958 563 .8856 491 .9799 316 2.0789 282 1.8982986 2.0121 965 2.1329 283 2.2609 040 2.3965 582 2.1048 520 2.2521 916 2.4098 450 2.5785 342 2.7590 315 2.3316 390 2.5181 701 2.7196 237 2.9371 936 3.1721 691 2.5804 264 2.8126 648 3.0658 046 3.3417 270 3.6424 825 2.8531 167 3.1384 284 3.4522 712 3.7974 983 4.1772 482 16 17 18 19 20 2.0223 7015 2.1133 7681 2.2084 7877 2.3078 6031 2.4117 1402 2.1828 746 2.2920 183 2.4066 192 2.5269 502 2.6532 977 2.5403 517 2.6927 728 2.8543 392 3.0255 995 3.2071 355 2.9521 638 3.1588 152 3.3799 323 3.6165 275 3.8696 845 3.4259 426 3.7000 181 3.9960 195 4.3157011 4.6609 571 3.9703 059 4.3276 334 4.7171 204 5.1416613 5.6044 108 4.5949 730 5.0544 703 5.5599 173 6.1159 390 6.7275 000 21 22 23 24 25 2.52024116 2.6336 5201 2.7521 6635 2.8760 1383 3.0054 3446 2.7859 626 2.9252 607 3.0715 238 3.2250 999 3.3863 549 3.3995 636 3.6035 374 3.8197 497 4.0489 346 4.2918 707 4.1405 624 4.4304 017 4.7405 299 5.0723 670 5.4274 326 5.0338 337 5.4365 404 5.8714 637 6.3411 807 6.8484 752 6.1088 077 6.6586 004 7.2578 745 7.9110 832 8.6230 807 7.4002 499 8.1402 749 8.9543 024 9.8497 327 10.8347 059 26 27 28 29 30 3.1406 7901 3.2820 0956 3.4296 9999 3.5840 3649 3.7453 1813 3.5556 727 3.7334 563 3.9201 291 4.1161 356 4.3219 424 4.5493 830 4.8223 459 5.1116867 5.4183 879 5.7434 912 5.8073 529 6.2138 676 6.6488 384 7.1142 571 7.6122 550 7.3963 532 7.9880 615 8.6271 064 9.3172 749 10.0626 569 9.3991 579 10.2450 821 11.1671 395 12.1721 821 13.2676 785 11.9181 765 13.1099 942 14.4209 936 15.8630 930 17.4494 023 31 32 33 34 35 3.9138 5745 4.0899 8104 4.2740 3018 4.4663 6154 4.6673 4781 6.0881 006 6.4533 867 6.8405 899 7.2510 253 7.6860 868 8.1451 129 8.7152 708 9.3253 398 9.9781 135 10.6765 815 10.8676 694 11.7370830 12.6760 496 13.6901 336 14.7853 443 14.4617 695 15.7633 288 17.1820 284 18.7284 109 20.4139 679 19.1943 425 21.1137 768 23.2251 544 25.5476 699 28.1024 369 36 37 38 39 40 4.8773 7846 5.0968 6049 5.3262 1921 5.5658 9908 5.8163 6454 5.7918 161 6.0814 069 6.3854 773 6.7047 512 7.0399 887 8.1472 520 8.6360 871 9.1542 524 9.7035 075 10.2857 179 11.4239422 12.2236 181 13.0792 714 13.9948 204 14.9744 578 15.9681 718 17.2456256 18.6252 756 20.1152977 21.7245 215 22.2512 250 24.2538 353 26.4366 805 28.8159 817 31.4094 200 30.9126 805 34.0039 486 37.4043 434 41.1447 778 45.2592 556 41 42 43 44 45 6.0781 0094 6.3516 1548 6.6374 3818 6.9361 2290 7.2482 4843 7.3919 882 7.7615 876 8.1496669 8.5571 503 8.9850 078 10.9028 610 11.5570327 12.2504 546 12.9854 819 13.7646 108 16.0226 699 17.1442 568 18 3443 548 19.6284 596 21.0024 518 23.4624 832 25.3394 819 27.3666 404 29.5559 717 31.9204 494 34.2362 679 37.3175 320 40.6761 098 44.3369 597 48.3272 861 49.7851 811 54.7636 992 60.2400 692 66.2640 761 72.8904 837 46 47 48 49 50 7.5744 1961 7.9152 6849 8.2714 5557 8.6436 7107 9.0326 3627 9.4342 582 9.9059 711 10.4012 697 10.9213 331 11.4673998 14.5904 875 15 4659 167 16.3938 717 17.3775 040 18.4201 543 22.4726 234 24.0457 070 25.7289 065 27.5299 300 29.4570 251 34.4740 853 37.2320 122 40.2105 731 43.4274 190 46.9016 125 52.6767 419 57.4176486 62.5852 370 68.2179 083 74.3575 201 80.1795 321 88.1974 853 97.0172 338 106.7189 572 117.3908 529 INTEREST 249 11. What is the amount of $216.50 at 7% compounded an- nually for 9 years? 12. What is the compound interest of $785.40 at 8% com- pounded quarterly for 11 years? -ft fO^t I. * IS. What is the compound interest of $2367.25 at 10% com- pounded semi-annually for 17 years 6 months? 14. What is the compound interest of $6532.80 at 6% com- pounded quarterly for 6 years? Find the principal that will yield at compound interest. 15. $578.81J in three years at 5%, compounded annually. NOTE. Divide the amount by amount of $1. 16. $7133.03 in 4 yrs. 3 mo. 8 days at 1%, compounded an- nually. * $ 5~3^ ffl^*^. ?0 I P-H ^i ^ t3 ?* ^ **! 5 "** ^ ** 5 ^i . s ' ^ ^ ^ ^ b. ,Q *s c 3 *9 <5 N rw ^* ^ 'H "ts ^ ^ ^ ^ Q 3 ^^ The above note was settled May 1, 1905. What was the amount due at settlement? SOLUTION Date Time Interest Amount Payment Principal May 1, 1903 6# $600 Aug. 12, 1903 3 mo. 11 da. $10.10 $610.10 $75 $535.10 July 24, 1904 11 mo. 12 da. $30.50 $565.60 $200 $365.60 May 1, 1905 9 mo. 7 da. $16.88 $382.48 Ans. The foregoing problem has been solved according to the fol- lowing rule adopted by the Supreme Court of the United States and hence called the United States Rule a. Find the amount of the given principal from the date of the note until the first payment; if the payment is greater than the interest, subtract the payment from the amount, and treat the re- mainder as a new principal. Thus continue until the date of set- tlement. b. If the interest be greater than any payment, find the interest en the principal to a time when the sum of the payments exceeds the interest, subtract the sum of the payments from the amount of the principal, and treat the remainder as a new principal. 2. On a note dated January 1, 1903, for $300 bearing 6% in- COMMERCIAL PAPER 257 terest, the following indorsement was made: January 1, 1904, $70. What was due January 1, 1905? 3. On a note of $980 for 4 years at 8%, dated July 5, 1902, the following payments are made : March 7, 1903, $170 ; Jan- uary 5, 1904, $25; April 20, 1905, $320. What is due at ma- turity, July 5, 1906? 4- The following payments were made on a mortgage of $1250 bearing 7%, dated October 20, 1903; $125 on January 29, 1904 ; $145 on April 8, 1904 ; $300 on September 20, 1904 ; $90 June 2, 1905. What was due November 6, 1905? 5. On a note dated July 15, 1903, for $1100 are the following indorsements: February 24, 1904, $200; March 30, 1905, $225; April 12, 1906, $250 ; June 6, 1907, $340. What is due .Septem- ber 1, 1907, interest at 9% ? 6. A note of $900, bearing 10% interest, dated August 1, 1902, was indorsed as follows: November 13, 1902, $115; Feb- ruary 25, 1903, $125; June 7, 1903, $20; October 28, 1903, $200; January 1, 1904, $340. What was due April 25, 1904? 7. April 1, 1902, a note was given for $7500 at 5% interest. Payments were made on September 15, 1902, of $1000 ; on July 27, 1903, of $870; on March 6, 1904, of $2400; on August 27, 1904, of $1130. What was due February 18, 1905? 8. A note of $1575, bearing 6% interest, dated January 1, 1902, for 3 yrs. 8 mo., was indorsed July 20, 1902, $250; Feb- ruary 6, 1903, $200; January 10, 1904, $450. What was due at maturity ? 9. A note of $1400, bearing 10% interest, dated May 1, 1905, for 2 yrs. 3 mo., was indorsed October 30, 1905, $300; June 22. 1906, $160; December 5, 1906, $200. How much was due at maturity ? 10. A note for $10000 dated January 1, 1900, bearing 6% in- terest was indorsed as follows : May 1, 1900, $18 ; September 4, 1900, $20; December 16, 1900, $15; April 10, 1901, $21; July 13, 1901, $125; December 23, 1901, $324. What was due at the time of settlement, November 1, 1903? 370. The following rule is used by banks and generally by 17 258 NEW BUSINESS ARITHMETIC merchants in finding the sum due on a note when partial pay- ments have been made. The banker's interest is reckoned in this rule. Merchants' Rule a. Find the amount of the note from the time it zvas given until the time of settlement. b. Find the amount of each payment from the time it zuas made until the time of settlement. c. From the amount of the principal,, subtract the amount of the payments. 1. On a note, dated Jan. 1, 190 4-, for one year, for $560, interest 6%, the following payments were made: June 1, 1904, $65, and Nov. 15, 1904, $100. Find the sum due at maturity. In computing the interest under the Merchants' Rule, find the exact time in days, and consider a year 360 days. SOLUTION Date Time Interest Payment Amount Balance Jan. 1, '04-Jan. 1, '05 June 1, '04 Jan. 1, '05 Nov. 15/04 Jan. 1/05 360 da. 214 da. 47 da. 6 $33.60 $2.32 $ .78 $65. $100. $560. $593.60 $67.32 $100.78 Ans. $593.60 $168.10 $425.50 2. Find the sum due on December 10, 1905, on a note of $900, at 6% interest, dated April 1, 1905, and indorsed July 6, 1905, for $240; September 12, 1905, for $420. 3. What sum is due November 17, 1905, on a note of $2850, at 8% interest, dated March 12, 1905, and indorsed as follows: May 30, 1905, $850; August 24, 1905, $700; October 6, 1905, $470? COMMERCIAL PAPER 259 4. On a note, dated March 1, 1905, for 9 months, of $765, at interest, the following payments were made : April 26, $140 ; June 20, $280 ; November 6, $295. Find the sum due at ma- turity. 5. A note for $1800 at 1% interest was given September 2, 1905, payments were made December 28, 1905, of $480; March 1, 1906, of $325 ; May 23, 1906, of $670. What was due at ma- turity, the time of the note being 10 mo. 12 days? 6. A note of $3500 with interest at 10%, dated October 30, 1905, was indorsed as follows: January 1, 1906, $1100; March 20, 1906, $390 ; June 2, 1906, $845. What was due September 16, 1906? 7. A note of $1780, bearing S% interest, dated August 27, 1905, for 8 months, was indorsed on November 10, 1905, $275; on February 3, 1906, $600. What was due at maturity? 8. A note of $1065, bearing 6% interest, dated January 1, 1905, for 7 mo. 15 days, was indorsed on March 4, $200 ; on May 12, $180; on May 30, -$300. What was the amount due at ma- turity? 9. What is the difference between the sum due by United States Rule and Merchants' Rule, on a note of $720, bearing 5% interest, dated February 2, for 8 mo. 10 days, and indorsed April 4, for $160; June 11, $210; August 1, $80? 10. Which is greater and how much, the sum due by United States Rule or the sum due by Merchants' Rule on a note of $810 at 10% interest, dated November 19, 1905, for 10 months, and indorsed January 1, 1906, for $230; March 16, 1906, for April 4, 1906, for $360? (11) $1248. Boston, Mass., December 11, 1905. Seven months after date, I promise to pay S. M. Mack, or bearer, Twelve Hundred Forty-eight Dollars. Value received, interest at 7% from date. Payable at Second National Bank. R. S. Wilco.v. The following indorsements were made : January 25, $100 ; March 16, $350; April 16, $50; May 10, $225. What was due at maturity? 260 NEW BUSINESS ARITHMETIC 371. Annual Interest with Partial Payments. In case interest is payable annually and partial payments have been made at irregular intervals, the following rule is the method of solution. a. Find the interest on the principal for the first interest period, and find also the amounts of the payments made during this period, from the times they were severally made until the end of the period. b. If the payments amount to more than the interest due, take their amount from the amount of the principal, and make the re- mainder a new principal. c. But if the amount of the payments does not equal the inter- est due, the principal remains unchanged; and the amount of the payments is taken from the interest, the remainder being treated as deferred interest. d. This deferred interest draws interest until it is paid, or until the note matures; and all payments apply; firstly, to interest on deferred interest; secondly, to deferred interest; and lastly, to in- terest just due, and principal. 1. What amount will be due on a note dated January 1, 1902, due in 5 years for $6000, drawing interest at 6% payable an- nually, the following payments having been made thereon : May 1, 1904, $500; September 1, 1906, $800. 2. A note for $1200, at 6% interest, payable annually, is dated June 16, 1900, and is to run five years. No interest having been paid except for the first year, and the following payments having been made, viz.: September 15, 1902, $250; March 10, 1904, $400. What amount will be due at maturity ? TRUE DISCOUNT 372. Discount is a deduction made for the payment of money before it is due. 373. The Present Worth of a debt due at a future time is its value now. The present worth of a debt is such a sum as, if put at interest, will amount to the debt at the expiration of the time. 374. True Discount is the difference between the present worth and the debt, and is called true discount because the method of computing it is in strict accordance with equity. True discount is little used owing to the difficulty in comput- ing it, and bank discount has almost become universal. 375. The Face of the Debt is the sum which will be due at the expiration of the time. The Present Worth is a Principal which at the rate of interest for the time will amount to the debt. The terms Present Worth, Face of Debt and True Discount correspond to Principal, Amount and Interest. 1. What is the present worth and true discount of a debt of $354 due in 3 yrs., money being worth 6%? SOLUTION 1. 3 X $-06 = $.18. 2. Int. on $1 = $.18. 3. $1 + $.18 = =? $1.18 amount of $1. 4. $354 -=- $1.18 = $300 present worth. 5. $354 $300 = $54 true discount. From this solution and explanation we have the following : To Find the True Discount a. Divide the face of the debt by the amount of $1 for the given time and rate, and the result will be the present worth. b. Subtract the present worth from the face of the debt and the difference will be the true discount. NOTE. In the following problems the rate per cent, is 6, unless some other rate is given. 2G1 262 NEW BUSINESS ARITHMETIC 2. I owe $191.08, due in 1 yr. 6 mo. 18 days. I am allowed true discount at 8%. Find the sum that will pay the debt now.$V 3. What sum will pay a debt of $1098.39, due in 2 yrs. 9 mo. 21 days, money being worth 6% ? 4. My note of $1035.99, due in 3 yrs. 1 mo. 6 days, was pur- chased by B at 9% true discount. What did he pay for the note? 5. L. B. Jones owes $1657.50, due in 5 yrs. 11 mo. 3 days. He borrowed the money to pay same, being allowed 4% true dis- count. How much did he borrow? 6. If Parker pays a debt of $151.27, due in 1 yr. 1 mo. 24 days, with corn at 35 cents per bushel, how many bushels will be required, money being worth 7%? 7. Brown gave his note for $470, and cash for remainder, of a debt of $1073.50, due in 2 yrs. 2 mo. How much cash did he pay, if he was allowed 6% true discount on the debt? 8. I gave Smith a horse in payment of a debt of $193.60, due in 8 mo. 12 days. I was allowed 10% true discount on the debt, and thus gained 20% on the cost of the horse. What did the horse cost me ? 9. A merchant purchased a bill of goods for $260 on 6 months' time, or $245 for cash. If money is worth 8%, will he gain or lose and how much if he pays cash ? 10. A jobber paid $274 cash for a lot of merchandise, rather than give his note for $297.30 for 1 yr. 6 mo. If money was worth 7%, what did he lose by paying cash? 11. A merchant bought a bill of goods for $760 on 1 year's time, or with a trade discount of 2 and 5% for cash. He accepted the cash offer. Did he gain or lose, money being worth 6f % ? 12. I bought $721 worth of wheat on 4 months' time, and sold it on same day at 12% advance. I paid the present worth of the debt from the proceeds, being allowed 9% true discount. How much did I gain by the transaction? 13. A wholesale merchant sold a bill of $1020 at a trade dis- count of 20 and 124%, and allowed a credit of 90 days. He ac- cepted cash payment allowing true discount at 8%. What was the cash payment? TRUE DISCOUNT 263 14- A retail merchant bought a bill of goods amounting to $360 .at a trade discount of 10 and 5%. He sold the goods at 20% profit on the invoice price and allowed a credit of 6 months. What was his net gain, money being worth W% ? 15. I sold goods for $1134, and allowed 7 mo. 15 days credit. The purchaser paid me cash at true discount of S%. I invested the proceeds in wheat at $1.20 per bushel. How many bushels did I buy? BANK DISCOUNT 376. Bank Discount is the simple interest paid in advance on a note or draft for the time the paper has to run. Bank Discount may be computed by either of the methods of reckon- ing interest, but in the case of notes discounted in banks, and call loans on Wall street banker's interest is used. 377. The Proceeds of a note or draft is the sum received from the bank for it or the face of the paper less the bank dis- count. In case the paper is drawing interest, the amount due at maturity is the face of the paper and on this the discount should be computed. 378. The Term of Discount is the time from the date of dis- count to the maturity of the paper. In finding the term of discount the usual custom is to exclude the day on which the paper is discounted, but include the day of maturity. Thus on a note discounted June 10, due June 25, the term of discount would be 15 days. This custom is not universal however, and banks in Baltimore, Philadelphia and few other cities, charge for the day of discount, also, making in the above example 16 days as the term of discount. In computations in bank discount, five quantities are consid- ered, viz. : Face of Debt, Rate of Discount, Term of Discount, Bank Discount and Net Proceeds. In the following- problems, do not use grace and count exact days for term of discount. 379. To find the bank discount and proceeds of a note or debt. 1. Find the bank discount and the proceeds of a note of $240 at 6% discount, dated January 10, 1903, for 4 mo. 27 days. SOLUTION Jan. 10 + 4 mo. 27 da. = June 6. From Jan. 10 to June 6 = 147 da. Face of note = $240. Int. on $1 for 147 da. at 6% = .0245. Bank discount = $5.88. Proceeds = $240 $5.88 = $234.12. 264 BANK DISCOUNT 265 From this solution and explanation we have the following: To Find the Bank Discount a. Find the term of discount in exact days. b. Find the interest on the face of the note for the term of discount and this ivill be the bank discount. c. Subtract the discount from the face of the note to find the net Proceeds. NOTE. If a note is on interest, find its amount at maturity, and taking this as the face of the note, cast the interest on it as above. Find the bank discount of the following notes (no interest): 2. $325, dated March 4 for 2 mo. 26 days, discounted March 18 at 5%. 3. $870, dated May 1 for 27 days, discounted May 11 at 9%. 4. $465, dated April 16, for 1 mo. 12 days, discounted April 27 at 7%. 5. $1282.50, dated February 19, 1905, for 3 mo. 4 days, discounted March 23 at 8%. 6. $1848, dated January 27, 1905, for 4 mo. 2 days, dis- counted at 10% on the day of making. Find the proceeds of the following non-interest-bearing notes : 7. $920, dated January 10, 1905, due in 30 days, discounted January 10 at 10%. 8. $465, dated March 4, 1905, due in 60 days, discounted March 15 at 9%. 9. $2725, dated November 12, 1905, due in 90 days, dis- counted November 17 at 5%. 10. $194.80, dated September 4, 1905, due in 45 days, dis- counted September 4 at 6%. Find the date of maturity, term of discount, bank discount and proceeds of the following notes. (11) $280. CHICAGO, ILL., March 12, 1905. Four months after date, I promise to pay to R. T. OWENS, or order, Two Hundred Eighty Dollars. Value received. F. S. Cox. Discounted May 20, 1905, at 7%. 266 NEW BUSINESS ARITHMETIC (12) $970. LANSING, MICH., August 25, 1905. Six months after date, I promise to pay to the order of G. H. GRAHAM, Nine Hundred Seventy Dollars. Value received. In- terest at 5% from date. C. H. SMITH. Discounted November 6, 1905, at 7%. NOTE. Find the amount due at maturity, and compute the discount on this amount from November 6, to maturity. (IS. JOINT NOTE) $1280. LOUISVILLE, KY., January 1, 1905. Nine months after date, we promised to pay E. H. DURANT, or bearer, Twelve Hundred Eighty Dollars. Value received, with interest at 8% from date. THOMAS SMAILS. J. D. PETERS. Discounted July 15, 1905, at 6%. (14- SEVERAL NOTE) $1968.40. FREMONT, NEB., June 5, 1905. One year after date, either of us promises to pay R. D. ALLEN & Co., or order, Nineteen Hundred Sixty-eight tVV Dollars. Value received, with interest at 1%. Payable at the Merchants Bank. G. H. MAHLER. O. A. PRESTON. J. B. Ross. Discounted April 1, 1906, at 10%. (15. JOINT AND SEVERAL NOTE) $292.50. CHICAGO, ILL., July 14, 1905. Nine months and twelve days after date, we or either of us, promise to pay to the order L. P. DERN, Two Hundred Ninety- two r 5 A Dollars. Value received, with interest at 9%. J. F. SOMERS. P. R. CORBIN. A. C. WILSON. Discounted January 1, 1906, at 8%. 16. Find the proceeds of a note of $275, bearing 6% interest, dated March 19, 1905, payable in 3 months; discounted April 16, at S%. BANK DISCOUNT 267 17. I held B's note of $1760, bearing 10% interest, dated February 6, 1905, for 5 months, 10 days, and discounted same May 1, 1905, at 6%. How much did I receive from the bank? 18. A merchant who had a credit of $368.72 at the bank, had the proceeds of the following note placed to his credit : $628.80, bearing 8% interest, dated January 17, 1905, for 7 months, dis- counted April 2, 1905, at S%. What was his credit then? 19. Lyman discounted a note of $1600, bearing W% interest, dated April 3, 1905, for 10 months ; discounted August 12, 1905, at 1%. How much was left after paying with the proceeds a note of $630, that had been on interest 2 years at S% ? 20. For what sum must I give my note for 60 days to receive $600 proceeds, if the note is discounted at 8% ? NOTE. Since the proceeds of $1 at 8% for 60 days is .986^ it will re- quire as many dollars to produce $600 proceeds as .986^ is contained in $600 or $608.11. 21. I received $711 from a bank on a 90 days' note, at 5% discount. What was the face of the note ? 22. What must be the face of a note for 105 days, to give $536.80 proceeds when discounted at 10% ? 28. $1186.50 was the proceeds of a note, dated January 18 for 4 months, and discounted April 3, at 9%. What was the face? 2Jf. The discount on a note, dated February 6 for 6 months, and discounted July 7 at 10% is $12.50. Find the face and the proceeds of the note. NOTE. Divide the discount by the discount on $1, to find the face of the note. 25. Smith's note, dated March 1 for 4 mo. 15 days was dis- counted May 2 at 1%. What was the face of the note, if the discount was $5.25? 26. I received $581.55 at the bank for my note due in 90 days. The bank charged me 8% discount. What was the face of the note ? 27. For what sum must I give my note at the bank for 2 mo. 9 da. to receive $1176, if the bank charges 9% discount? STOCKS AND BONDS 380. Stocks represent the capital or property of an incorpor- ated company. 381. An Incorporated Company is an association authorized by law to transact business as a single individual. 382. A Charter is a legal instrument defining the powers and duties of a corporate body. 383. The Capital Stock is the funds or capital of the cor- poration. 384. A Share is one of the equal parts of the stock. A share is usually $100, though it may be of any value agreed upon by the members of the corporation. 385. A Stock Certificate is a paper issued by a corporation stating the number of shares to which the holder is entitled, and the par value of each share. 386. The Par Value of stock is the value named in the cer- tificate. 387. The Market Value of stock is the price per share for which it sells. 388. Stock is At Par when it sells for its face value. 389. Stock is Above Par when it sells for more than its face value, and Below Par when it sells for less than its face value. 390. Preferred Stock is that which takes preference over common stock in reference to dividends. Preferred Stock is issued as a special inducement to raise money or to protect a certain class of shareholders who may have advanced money to relieve a company from embarrassment. 391. A Dividend is the sum paid to stockholders from the gains of the corporation. 392. Assessments are sums levied on stockholders to meet the expenses or losses of the corporation. 393. A Stock Broker is a person who buys and sells stock as an agent for others. 268 STOCKS AND BONDS 269 394. Brokerage is the sum paid to brokers for buying and selling stock. 395. Quotations of Stock are statements made giving the price at which stock is being bought and sold. Stock quoted at 105}- is selling at 5%% premium, at 87J is selling at 12%% dis- count. Margin is cash or other security deposited with a broker on account of either the purchase or sale of securities, and to protect him against loss in case the market price of the securities bought or sold varies so as to be against the interests of the customer. It is usually 10% of the par value of the stock. NOTE. Brokers charge interest on the sums expended and purchase commission, and allow interest on the margins deposited, or preferably they charge interest on the debit balance. A Bear is an operator who believes the market price of stocks will fall. A Bull is an operator who believes the market price of stocks will ad- vance. NOTE. Hence a bull will buy stocks in order to profit by the higher price at which he expects to sell, and a bear will sell in order to profit by the lower price at which he expects to buy. Hypothecating stocks and bonds is depositing them as collateral se- curity for money borrowed. NOTE. The securities must be greater than the loan by at least 10% of their par value, and in every case by an amount equal to 20% of the amount of the loan. This excess is called the margin of the loan. Watering Stock is increasing the number of shares of an incorporated company without a corresponding increase in their value. A Corner is produced when one or more operators owning or con- trolling all the stock of a company are able to purchase still more for either immediate or future delivery. When they demand the stock, the sellers are unable to find it in the market. 396. A Bond is a written or printed obligation of a city, county, state, government or corporation, promising to pay a cer- tain sum of money at a specified time. The object of a bond is to secure payment of borrowed money. When a city, state, etc., borrows money it gives a Bond as a certificate of the in- debtedness. 397. A Coupon Bond is one having interest certificates or coupons attached. They are transferable merely by delivery, and for this reason are preferred for purposes of investment. 270 NEW BUSINESS ARITHMETIC 398. A Registered Bond is one payable to the holder, and is registered in the books of the authority issuing it. It can be transferred by assignment only. Bonds are named from the authority that issued them, their rate of in- terest, and their date of maturity. U. S. "4's of 1907" are bonds issued by the United States, bearing 4% interest and maturing in 1907. Chicago "3's of 1900" are bonds issued by the city of Chicago, bearing 3% interest and maturing in 1900. 399. Government Bonds were issued to secure the payment of money borrowed to meet the expenses of the civil war. 400. The Interest on bonds is usually paid quarterly or semi- annually. 401. The Interest on Government (U. S.) bonds is payable in gold, and is reckoned by the method of exact interest. 402. The Interest on all bonds except U. S. bonds is payable in currency, and is reckoned by the method of common interest. 403. A Mortgage is a conveyance of real estate or other property, as a pledge to secure the payment of a certain debt. When money is borrowed to build a railroad or for other purpose, the payment of the bonds is secured by a mortgage or deed of trust upon the real estate of the road made in favor of some bank or trust company as trustee. Computations in Stocks and Bonds are based upon the princi- ples of Percentage, and embrace five quantities, viz. : Par Value = Base; Rate of Premium or Discount = Rate; Premium or Discount = Percentage; Market Value above par = Amount; Market Value below par = Difference. NOTE. The par value of all stocks and bonds in the following prob- lems is $100 unless otherwise stated. ORAL PROBLEMS 1. What is the par value of 25 shares of stock? 75 shares? 125 shares? 4 shares? 2. What is the par value of 50 half shares of stock? 25 shares? 75 shares? 125 shares? 3. What is the value of 40 quarter shares of stock? 50 shares? 75 shares? UNIVERSITY F STOCKS AND BONDS 271 4. What puts stock at a premium? at a discount? 5. What is the premium at 6J% on 100 shares of stock? 120 shares ? 40 shares ? 6. What is the discount at 12$% on 240 shares of stock? 20 shares ? 7. What is the brokerage at \% on stock, the par value being $7200? $400? 8. What will 20 shares of bank stock cost at 125 and brok- erage at \% ? 9. What is the brokerage on 40 shares of stock, market value 124 J, brokerage at \% ? What is the cost ? 10. I send my broker $5000 and instruct him to buy 40 shares of railroad stock at 150, the value increases and I direct him to sell at 175. How much has he to my credit, brokerage in each case at %? WRITTEN PROBLEMS 1. A corporation made an assessment of 9%. How much will a stockholder who holds 42 shares of stock pay? 2. I. sold 38 shares of city bank stock at 8% premium. Find the amount above par I received. 3. A sold 54 shares of stock at o% discount. For how much below par did he sell the stock ? 4. 33 shares of Rock Island stock were sold at 107J. Find the amount of premium received. 5. B received a dividend of 6f % on 27 shares of Missouri Pacific stock. What was the amount of the dividend? 6. Smith was assessed 13% on 19 shares of mining stock. Find the amount of his assessment. 7. What assessment is paid by the holder of 45 shares of Western Union stock, if the rate is 4f % ? 8. Bailey sold 78 shares of New York Central stock at 129J. Find amount above par value he received. 9. Barton sold 46 shares, par value $50, at a discount of 9J% ; and 72 shares, par value $25, at a discount of !$%. Find the total sale. 272 NEW BUSINESS ARITHMETIC NOTE. Multiply the par value by the cost of $1 worth of the stock, to find the market value. 10. Find the selling price of 75 shares of stock, sold at 8f% discount. 11. What is the selling price of 17 shares of stock at a dis- count of 3f % ? 12. A paid 14 J% premium on 66 shares of mining stock. What did the stock cost him ? IS. I sold through a broker 45 shares of Wabash stock at SJ% discount, brokerage \%. What amount did I receive? 14- B's broker bought 15 shares of railroad stock at a dis- count of 19%, and charged f% for buying. How much did the stock cost B ? 15. Lyman bought 18 shares of stock at 5%% discount and sold them at 13% premium. How much did he gain by the trans- action ? 16. I purchase 30 Chicago city 5's at%5% discount. How much less than the face did I pay for the bonds? 17. A purchased through his broker 18 U. S. 4's at 122|, brokerage \%. How much more than the face did he pay for the bonds? 18. If Cook County bonds are selling at 93, what is the dis- count and selling price of $3600 of the bonds? 19. Find the proceeds of the following bonds allowing \% brokerage; 100 U. S. 4's of 1891 at 103f ; 75 Chicago 6's of 1890 at 103; 125 P. Ft. W. R. R. ($50), bonds at 44^. 20. My broker bought for me 38 shares of bank stock at 92, and sold the same for 103. He charged \% for buying and selling. How much did I gain ? 21. Brown bought through a broker 52 shares of stock at 16% discount. He paid an assessment of 4% and then sold at 98. How much did he gain, the brokerage being \% for buying? 22. A broker bought on his own account 93 shares of I. C. R. R. stock at 95 J. He received a dividend of 5%, and then sold his stock at a premium of 6%. Find his gain. STOCKS AND BONDS 278 23. Find the cost of the following bonds allowing f % broker- age : 35 U. S. 4's of 1907 at 123f ; 80 Chicago 4J's of 1900 at 107'i; 25 Cook County 5's of 1895 at 103J; 60 Western Union Telegraph G's of 1911 at 87. 24- I bought 35 Illinois state bonds at 84, and sold them at 105 after having received 3% interest. What was my whole gain, and rate of interest on the investment? 25. How many shares of stock does a man own whose divi- dend is $4G8, the rate of dividend being 6% ? NOTE. Since 6% = $468, 1% will = $78, and 100% = $7800. 26. N. W. R. R. stock is selling at 5% above par. How many shares does a man buy, who pays $135 more than par value ? 27. The dividend was $198 and the rate of dividend was 6%, find the par value. 28. I receive^ a dividend of $348.50. The rate of dividend was 8J%. Find the number of shares I own. 29. An assessment of 3f% was $47.25, find the par value. 30. A dividend at 2$% was $210. What is the market value of the stock at a premium of 22%? 31. A speculator paid $259 premium on stock that sold at 7% above par. He sold the stock at a gain of 9%. W r hat did he receive for it? 32. A broker bought C, B. & Q. R. R. bonds at 93J, and paid $1350 less than the face of the bonds. How many bonds did he buy and what did they cost ? 33. Bought at 107J, Cook County bonds and paid, including \% brokerage, $1125 more than the face of the bonds. How many $50 bonds did I buy? 34. B paid $21593.75 for 25 $1000 U. S. 4f s. What was the quotation of the bonds ? NOTE. Divide the market value by the par value. 35. A speculator paid $4284.50, including brokerage \%, for 38 C. M. & St. P. G's of 1910. What was the quotation of the bonds ? 18 274 NEW BUSINESS ARITHMETIC 36. A paid $360 premium on 45 $100 U. S. 4J's. What was the rate of premium? 37. How many U. S. 4's of 1907 of $50 each at 97, can be bought for $2917.50, allowing i% brokerage? 38. What is the face value of U. S. 4J's, that cost $19088.75 at 103 J, brokerage % ? 39. I paid $3315 for Chicago 5's at 10% premium How many $50 bonds did I buy? 40. How many $25 bonds can be bought for $1254.50 at 3f % discount, brokerage -|% ? 41. Jones sold 15 $100 R. R. 4's at 15% above par, and in- vested proceeds in mining stock at 13f % discount. How many $50 shares of the latter did he receive ? 42. What is the rate per cent, on investment, if U. S. 4's are purchased at 125? 43. What rate will I receive on my investment, if I invest $2940 in Cook County 5's at 98 ? 44- State 5's are purchased at 124-% premium. What rate is realized on the investment? 45. I invested $2175 in city 5's at 87, I sold the same at 92J after receiving the interest for one year. What was my gain and rate of income on investment? 46. Bought U. S. 4J's at 107J. I sold same at 10% premium after receiving three quarterly payments of interest. What was the rate of income on the investment ? 47. I invested $3440 in U. S. 4f s at 107J, $2694 in U. S. 4's at 112J and $4116 in Illinois 6's at 85J. What was my annual income, and rate per cent, on investment? 48. Which is the more profitable investment, a stock at 125, paying 8% annually, or a bond at 90, paying 6% annually? 49. Three companies, A, B and C, are to be consolidated on the basis of the relative market values of their stock. Thus, A's capital $1,000,000, market value 100% ; B's capital $1,500,000, market value 50% ; C's capital $625,000, market value 40% The capital of the consolidated company is to be $2,000,000, STOCKS AND BONDS 275 in 20000 shares of $100 each. What proportion and what amount of the capital should be allotted to each of the old companies; and how much stock in the new company should the holder of 1 share of the stock of each of the old companies be entitled to ? 50. When 3% government bonds are quoted at 101, what sum must be invested to yield an income of $810 a year? 51. Bought October 12th, 400 Pacific Mail at 42 J, and 200 Michigan Central at 92J; November 10 sold the former at 42}, and the latter at 92|; what was my gain not considering interest? 52. Which would be the better investment, $12120 in N. J. Central at 80, paying 3% annual dividends, or the same invested in Chemical Bank stock at 2020, paying 15% every 2 months? 53. A customer deposited $500 margin with a broker Novem- ber 23, who purchased for him 50 shares Michigan Central at 80. He sold the same stock November 30 at 98 ; what was the gain, brokerage \%t STATEMENT Nov. 23. Nov. 30. Nov. 23. Nov. 30. Nov. 30. Dr. To 50 sh. Mich. Cen. at 80. . . $4000 Brokerage Vs % 6.25 4006 * 25 ** 51=*** ** Int. on $4006.25, 7 days at 6# ........ Cr. Bv margin deposited 500 **** *# ** **#* **_ By 50 sh. Mich. Cen. at 98. ... $**** Less Brokerage Vs% Int. on $500, 7 days Balanc Less r Gain. . e . **** 500 *** ** *# nargin NOTE. The brokerage, ^ of 1% is equal to $12.50 on 100 shares of stock at the par value of $100 each. 54. July 10 deposited with my broker $800 margin for pur- chasing 60 shares Mo. Pacific R. R. stock at 92J. The stock was sold July 28 at 95|. Allowing 6% interest on the deposit and charging 6% interest on the purchase and 1% brokerage. What was my net profit? 55. If a certain stock yields a dividend of 15% per annum, what is its value when money is worth 8% ? 276 NEW BUSINESS ARITHMETIC 56. On May 7, I deposited with my broker $2000 margin, and instructed him to buy stocks. The same day he bought for my account 300 shares N. Y. Central at 118J. He sold the stock May 26, at 122|. Interest 6%, brokerage \%. What was my gain? 57. June 14, I "margined" $2000 and sold "short" through my broker 200 shares Mich. Cen. at 90 and June 28 "covered" my "short" at 86f. Brokerage, |%. Int., 6%. Find gain.* 58. A speculator deposited with his broker $800 margin April 16, who purchased 40 shares B. & O. at 114f. He sold the stock June 5 at 118f ; find gain or loss, interest 6%, brokerage J%. 59. A capitalist received his quarterly interest on 4.%% bonds amounting to $38.2.50 and then sold the same at 105J. What were the net proceeds of the sale, brokerage %%? GO. On July 10, I deposited with my broker $1200 margin with directions to buy Western Union stocks. The same da}- he purchased for my account 200 shares Western Union at 116J. He sold the stock August 16 at 112^. Interest 1%, brokerage 1%. What was my loss ? 61. If stock actually* worth $88 per share be watered by issu- ing a stock dividend of 10%, what is the actual value of the watered stock ? 62. An investor owned the following list of securities : NATURE PAR VALUE COST RATE Bank Stock, $2500 190 8% Personal Note, 1400 Par 6% Personal Note, 500 Par 6% Real Estate Mortg., 1800 Par 6% Elec. Ry. Bonds, 1000 99} 5% Gas Bonds, 3000 100 5% What was his per cent, of income on the entire investment considered as one? What was his per cent, of income on his investment in the bank stock ? What was the total investment ? * It is not a general custom among brokers to allow interest on margins advanced for "short" sales, but it is sometimes done and problem 57 is to be solved on this basis. EXCHANGE 404. Exchange is a method of making payments between persons in different cities by means of drafts. If a party in Chicago desires to remit a sum of money to a party in New York, he buys of a Chicago bank a draft on a New York bank and sends it to the party in New York. The New York party indorses the draft and presents it for payment to the bank on which it is drawn, either di- rectly or through some other bank. 405. Domestic Exchange or Inland Exchange is the ex- change between places in the same country. 406. Foreign Exchange is the exchange between places in different countries. A foreign draft is called a Bill of Exchange. 407. Exchange is At Par when the cost of a draft equals its face ; above par or at a premium, when the cost of a draft exceeds its face ; and below par or at a discount when the cost of a draft is less than its face. Time drafts or bills of exchange are subject to bank discount on their face value for the time specified. An Acceptance is the written promise of the Drawee to pay the draft when due. A Draft is accepted by the Drawee's writing across its face the word "Accepted" followed by the date of the acceptance and his signature. 408. The Balance of Trade between two places or countries is the difference between the amounts which each owes the other. Thus if the banks of New York owe the banks of London $40,000,000 and the banks of London owe the banks of New York $35,000,000, the balance of trade is $5,000,000 against New York and in favor of London. 409. The Course of Exchange between two places is the price paid at one place for drafts on the other. The course of exchange is above or below par, according as the balance of trade is against or in favor of it. A person may properly remit money : 1. By sending a Post Office money order or express money order, for small amounts. These are in effect drafts, but are sold at schedule prices, and not on principles of percentage. 277 278 NEW BUSINESS ARITHMETIC 2. By sending the actual money by express or otherwise. 3. By remitting a draft drawn on any bank in the/ city where the money is payable or some place that is recognized as a center of ex- change. New York is the recognized center of financial transactions in the United States as London is of the world. DOMESTIC EXCHANGE 410. Domestic Exchange relates to payments between cities of the same country. Computations in exchange are based upon the principles of percentage and embrace four quantities, viz. : Face of Draft = Base; Rate of Exchange = Rate; Premium or Discount = Per- centage; Cost of a Draft = Amount or Difference. ORAL PROBLEMS 1. Find the exchange at \% premium on the following drafts: $640, $720, $400, $320. 2. Find the exchange at \% discount on the following drafts : $200, $300, $400, $3000. 3. What will the following drafts cost at a premium of \% : $200, $1500, $250. 4. Find the cost of the following drafts at a discount of \% : $80, $250, $320, $480, $75. 5. I buy a bill of goods amounting to $200, if cash is paid at once a discount of 10% will be aHowed. I at once buy a bank draft at a premium of \%. What do the goods cost me? WRITTEN PROBLEMS 1. Find the cost of a draft for $560 at \% premium. 2. Find the cost of a draft for $725 at \% premium. 3. Find the cost of a draft for $1316 at f % discount. 4. Find the cost of a draft for $1867.50 at \\% discount. 5. Find the cost of a draft for $620 at \\% premium. 6. Find the cost of a draft for $2860 at \\% discount. 7. A merchant in Boston bought a draft on Detroit at %% dis- count. If the face was $290, what was the cost of the draft? EXCHANGE 279 S. I remit a draft of $480 to B on account, the rate of ex- change being \% premium. What was the cost? 9. I owed Lyman of Hartford $250. He allowed me a dis- count of 10%, and I remitted a draft in payment. Find cost of the draft at \% discount. 10. Brown bought 20 shares stock at 93, and paid for same by draft at f% premium. How much did the draft cost him? 11. I sent a draft to my agent to buy 1200 bu. of wheat at 75 cents per bu., at 3% commission. I paid \% premium on the draft. What was the cost ? 12. A retail merchant bought a bill of $684 on 3 months' time, or 10 and 5% off for cash. He accepted the cash offer and re- mitted in payment a draft at f % premium. What did the goods cost him? IS. Find the face of a draft that cost $875 at \\% premium. NOTE. Since a draft for $1 cost $1.01*4 $875 will buy as large a draft as $1.01^4 is contained times in $875. 11+. Find the face of a draft that cost $325.60 at \% discount. 15. Find the face of a draft that cost $1275.60 at \\% pre- mium. 16. Find the face of a draft that cost $329.45 at 2%% pre- mium. 11. A merchant paid $932.40 for a draft on Nashville at %% premium. Find the face of the draft. 18. The cost of a draft at \\% discount on Albany was $364.45. What was the face of the draft? 19. A sight draft on St. Louis cost $459.42 at \\% discount. For what sum was the draft drawn? 20. What is the cost of a draft for $1200 on Omaha for 60 days at \% discount, interest at 8% ? NOTE. Proceeds of $1 for 60 da. at 8% = $.986| $.005 discount = $.981|, cost of a draft for $1. A draft for $1200 will cost 1200 times as much. 21. Find the cost of a 75-day draft drawn on Pittsburg for $1860. The rate of exchange is \% premium and interest 6%. 280 NEW BUSINESS ARITHMETIC 22. I remitted to a creditor a draft for $275 at % discount. The draft was at 15 days' sight, interest 6%. Find cost. 23. Davis remitted a 45-day draft in payment of a bill of $5760; the exchange was f% premium and interest 5%. What did he pay for the draft? 24. What is the cost of a draft for $6840, drawn at 27 days on Albany, if the exchange is %% discount and interest 6%? 25. How much must I pay for a draft of $340 on Boston for 51 days at \% discount, if money is worth 10% ? 26. B sold me a horse that cost him $120, at 13J% gain; I paid for same with a New York draft at \% discount, for 69 days at 1% interest. What was the net cost of the horse to me? 27. I bought a draft drawn on Boston for 18 days at -$% dis- count. How much did the draft cost me, the face being for $1238.40, and money loaning at 6% interest? 28. A grain dealer bought wheat at 90 cents per bushel, and remitted for same a Chicago draft bought for $1344.60 at \% dis- count. How many bushels of wheat did he buy ? 29. I paid $475.80 for a bank draft at 1% discount, to send a wholesale merchant for a bill of goods bought at a discount of 6% from the invoice price. Find the invoice price. SO. A paid $584.70 for a New Orleans draft at \\% discount for 60 days, interest 6%. Find the face of the draft. 31. A merchant bought a 15-day draft for $961.50. What was the face of the draft, if exchange was If % premium and in- terest 4% ? 32. The cost of a New York draft at \\% premium, for 105 days was $433.40. What was the face of the draft, money being worth 5%? 33. A 60-day draft at If % discount was remitted for payment of potatoes bought at a gain of 10% to the seller. What did the goods cost the seller, the draft costing $117.30 at 6% ? 34- When exchange was at \% discount, and money loaning at 8%, Lyman paid $1773.30 for a Chicago draft, drawn at 33 days' sight. What would the draft cost him, if exchange was at %% premium? EXCHANGE 281 35. I bought mining stock at 31% discount, and remitted in payment a bank draft at If % premium, that cost $1380. How many shares did I buy, the time of the draft being 72 days and interest at 7%? FOREIGN EXCHANGE 411. Foreign Drafts or Bills of Exchange are usually ex- pressed in the money of the country on which they are drawn. Drafts drawn on persons and banks located in England, Ireland and Scotland, are expressed in pounds, shillings and pence ; on France, Bel- gium or Switzerland in francs ; on Germany, in marks, etc. 412. The Par of Exchange is the value of the money of one country expressed in the denominations of another. 1. The intrinsic par of exchange is the value of the coin of one country in the coin of another, based upon the relative weight and fineness of the two coins. 2. The commercial par of exchange is the market value of the currency of one country as compared to that of another. 413. Foreign bills of exchange are usually drawn at sight or sixty days after sight. The former are known as short ex- change, and the latter as long exchange. Days of grace are usually allowed on all foreign exchange. The course of exchange on time bills is as much less than that on sight bills as the per cent, of interest for the time given plus the days of grace. 414. A Documentary Bill of Exchange is one accompanied with a Bill of Lading and Insurance Certificate, giving the title of the property represented by the Bill of Lading to the holder of the Bill of Exchange. 415. The following quotations of Foreign Exchange were taken from a newspaper. STERLING EXCHANGE SIXTY DAYS. . SIGHT Posted Rates. 4.85^ 4.89 Actual Rates 4.85 4.88^ Documentary Bills 4.82^4.83^4 4.85^@4.86}4 FRENCH EXCHANGE SIXTY DAYS SIGHT Posted Rates 5.18^ 5.16*4 282 NEW BUSINESS ARITHMETIC Documentary Bills .............. 5.22^ .................... ......... .5.20 GERMAN EXCHANGE .............. SIXTY DAYS ...................... SIGHT Posted Rates .................... 95>4 Documentary Bills .............. 94@94}4 NOTES. 1. Sterling Bills at 4.82^@4.83^ means that the lowest price paid on that day was $4.82^4 for one , and the highest $4.83^4. 2. French Exchange at 5.18^4 means that the price was 5.18^4 francs for $1. Quotations are sometimes given, showing the cost of a franc, as, 3. German Exchange at 94@94^4 means that the lowest price was $.94 for four marks; and the highest $.94*4. Quotations are sometimes given, showing the cost of a mark ; as $.237. 1. What sum must I pay for a draft of 890 on London, ex- change at $4.86}? 2. James Smith remits to a customer a draft on Paris for 4056 francs, when exchange is 5.20. Find the cost. 3. Geo. Graham bought a draft of 2740 marks, to pay for a bill of goods. What did it cost at 96f ? 4. A merchant sold to a bank a draft of 320.8s. 6d. at $4.82J. How much did he receive for it? (See footnote, page 283.) 5. A commission merchant remitted to his principal a draft of 1935 francs at 5.16. Find the net proceeds of the sale. 6. I received from my agent a draft of 1975J marks at 94. What was the amount of sale, commission being 5% ? 7. An agent received a draft of 1245. 2s. 3d. to invest in grain at 2% commission. How much can he invest, exchange at $4.84 J? 8. William Brown bought a bill of goods at a discount of 20%, and remitted for same a draft for 3209| francs at 5.12J. Find the invoice price of the goods. 9. C. H. Fuller received a draft for 8400 marks to invest in wheat at 85 cents per bu., at 5% commission. How many bush- els did he buy, exchange being 93 J ? .10. My broker drew on me for 276|f for stock bought at 110. What was the purchase price of the stock, if the brokerage was 2%, and exchange $4.86? EXCHANGE 283 11. I remitted a draft on a Paris bank for 3072 francs at 5. in payment of a lot of silk bought at a discount of 20 and Find the invoice price. 12. D. W. Graham remitted to his principal a draft for 8000 marks, bought at 96, for a lot of goods sold at 4% commission. Find the amount of his commission. 13. What is the face of a draft on a Liverpool bank, that cost $2848.09, exchange at $4.88 ? 14. What is the face of a draft on a Lyons bank, that cost $812, exchange at 5.16^ francs to $1? 15. The cost of a draft on Berlin was $156.75, when exchange was $.95 for 4 marks. Find face of the draft. 16. James Nolan paid $3439.95 for a draft on a bank of Dub- lin, exchange at $4.84J. What was the face of the draft? 17. An agent sold goods for a merchant of Berlin at 6%% commission. What is the face of the draft he must send in pay- ment, exchange at $.93 J; if the amount of the sale was $2000? 18. What is the face of a draft on London, that will pay for an invoice of $4000, bought at a discount of 25 and 14% ; when exchange is $4.86^? 19. I paid $368 for a draft on Paris, exchange at 5.17}, to re- mit in payment for cloth sold at 8% commission. Find my com- mission and the face of the draft. 20. A merchant paid $720 for a draft on Frankfort, when ex- change was 94, to remit in payment for cloth that was bought at 3 marks per yard. How many yards did he buy ? To reduce English money to the decimal of a pound (a) Write the number of pounds. (6) Place a decimal point after this. (c) Divide the number of shillings by 2 and write the result as tenths of a pound. (d) Multiply the number of pence by 4| and write the result as thousandths of a pound. BANKS AND BANKING 416. A Bank is an institution which deals in money or its representative. Banks are usually incorporated concerns, and are either National or State banks. The chief business of a bank consists in : 1. Receiving deposits of money for safe keeping and conve- nience of customers. 2. Loaning money by discounting and collecting commercial paper. 3. Issuing bills or notes as" a circulating medium. 4. Making collections. 5. Selling drafts on its correspondents. Banks make no charge for keeping deposits and pay no interest on them except in rare cases, and then at a low rate. The privilege of loaning out a large proportion of the deposits is a source of profit to the bank, sufficient to compensate it for keeping the account. NATIONAL BANKS 417. A National Bank is one which is organized under the National Banking Act of the United States. According to the National Banking Act, Banking Associa- tions may be formed of any number of persons not less than five. No association- can be organized with a capital less than $100,000, except in cities whose population does not exceed 6,000, where they may be formed, with the approval of the Secretary of the Treasury, with a capital of $50,000 ; also except that the Secretary may permit the organization of a bank with a capital of not less than $25,000 where the population does not exceed, 3,000. In cities the population of which exceeds 50,000, the capital must not be less than $200,000, the stock being divided into shares of $100. All national banks are subject to periodical visitation and examination by the National Bank Examiner, as the represent- ative of the Secretary of the Treasury. 284 BANKS AND BANKING 285 The stockholders of national banks are liable individually beyond their investment for the debts of the bank, to an amount equal to the stock which they hold. National banks are not allowed to loan money on real estate security, and real estate purchased or mortgaged to secure a previous debt must be disposed of within five years. 418. Circulation. National banks issue circulating notes by depositing as security with the United States Treasurer an amount of Registered Bonds not less than one-fourth of the capital paid in. These bonds are held as security for the circu- lating notes, and in case the bank should fail the Government will redeem the notes. Banks are allowed to issue circulating notes to the full amount of the par value of the bonds deposited, but no bank can have a circulation greater than the amount of the capital stock paid in. A bank desiring to reduce its circulating notes may deposit with the Treasurer legal tenders or specie in amounts not less than $9,000, and withdraw a proportionate amount of the bonds previously deposited. However, the amount of bonds on deposit shall not be reduced below $50,000. 419. Xational Bank Notes are redeemable by the banks issuing them or by the Treasurer of the United States. Every national bank is required to keep on deposit in the Treasury of the United States, a sum equal to 5 per cent, of its circulation for the purpose of redeeming its bills, which is counted in as part of the Reserve. 420. A Reserve Fund equal to 25 per cent, of their deposits is required to be kept by national banks in the cities of New York, Boston, Philadelphia, Albany, Baltimore, Pittsburg, Washington, New Orleans, Louisville, St. Louis, Cleveland, Detroit, Chicago, Milwaukee and San Francisco, and 15 per cent, by all other national banks. These are called Reserve Cities, and the excess above the requirements is called the Surplus Reserve. 421. A Surplus Fund, of the net earnings of the bank, is also required by law to be set aside, before the usual semi- annual dividends are declared, consisting of one-tenth of the net 28G NEW BUSINESS ARITHMETIC profits for the preceding half year, until this fund amounts to 20 per cent, of the capital. 22. A Tax of one-half of 1 per cent, each half year is paid to the United States by national banks on the average amount of their circulation. But if the redemption bonds bear but 2% the tax is one-fourth of \% each half year. The advantage to a bank under the National Bank Act is that it receives interest upon the bonds deposited with the Treasurer and also loans and uses its circulating notes, and thereby derives a profit from them thus making a double income upon the same amount of capital, while paying a tax upon the circulation and being exempt from a tax on the bonds. A bank desiring to go into liquidation must deposit with the Treasurer, six months before such liquidation, an amount of lawful money equal to its outstanding circulation. The law also requires that a- sufficient amount, thus deposited for the payment of circulating notes, must remain in the Treasury until the last outstanding note shall have been presented. Hence, it will be seen that the Government derives the benefit from notes which are lost or destroyed by fire and water. PROBLEMS 1. A bank having a paid up capital of $250000 desires to issue circulating notes. What is the smallest amount of bonds that it can deposit as security for such notes, and what amount of notes will it receive ? 2. It is desired to organize a national bank in a city whose population is 3865. How many persons and what amount of cap- ital are necessary? What amount of circulating notes may the bank issue? 3. A bank deposits bonds to the amount of $480000 with the Treasury. What will be the amount of its circulating medium? What is the amount of its redemption fund? 4. A national bank having a capital of $400000, by injudi- cious loans, impairs its capital $125000. What per cent, may each stockholder be assessed to make good the loss? What must A pay who owns 5 shares of stock ? 5. A bank located in a reserve city has deposits amounting to $850260. What is the amount of its reserve fund? 6. A national bank with a capital of $600000, and having a BANKS AND BANKING 287 surplus of less than 20% of its capital earns $22350 net profits during six months. What amount must be carried to the sur- plus fund and what amount will remain after declaring a 3% semi-annual dividend? 7. What is the redemption fund of a bank having a circula- tion of $425000? What amount of bonds were deposited to se- cure this circulation ? 8. Find the semi-annual tax on a bank having an average cir- culation of $128650 if 3% bonds were deposited to secure circu- lation. 9. A national bank having a capital of $500000 and a surplus fund of $65000, earned $32650 during six months. What amount will be carried to the surplus fund? What amount will remain after declaring a semi-annual dividend of 3%% ? 10. A bank desiring to reduce its circulation deposited with the Treasurer $51400 in specie. What was the market value of the bonds withdrawn at 108J? SAVINGS BANKS 423. A Savings Bank is an institution which receives de- posits of money for safe keeping, and allows depositors interest thereon. 424. Interest is usually credited on deposits twice each year July 1 and January 1, although some banks credit the in- terest quarterly. If the interest is not withdrawn it is allowed to draw interest, and thus the interest is compounded. Usually no interest is allowed on parts of a dollar, and that is the plan which will be followed by the student. Banks do not usually allow interest on any sum which has not been in for the full term of the interest period. Some banks allow interest on money which has been on deposit during the entire quarter previous to interest day, while others allow interest on sums which have been deposited on or before the first of any month. No interest is allowed on amounts withdrawn before interest day. Savings banks are subject to the laws of the state in which they are located. In some states they are restricted as to the size of deposits, rate of interest which they must allow, etc. 425. Since in nearly all savings banks no interest is allowed on money deposited or withdrawn during an interest term, there- 288 NEW BUSINESS ARITHMETIC fore, Interest is computed at the end of the interest term on the smallest balance on deposit at any time during the term. NOTE. If it is desired to find the interest for several terms, consider the interest at the end of each quarter the same as a deposit on the first day of the next quarter. In the following examples unless otherwise stated, deposits draw interest at 4% per annum, from the 1st of January, April, July and October. Interest days January 1 and July 1. 1. On September 10, A deposited in a savings bank $235. What amount of interest will be credited to his account on Jan- uary 1 ? NOTE The deposit will /rot begin to draw interest until October 1, and the interest at 4% on $235 from October 1 to January 1 is $*.**. 2. A depositor is credited with the following deposits : Jan- uary 1, 1904, $300; June 26, 1905, $230; August 18, 1905, $70. No withdrawals. What will be the credit of interest on January 1, 1906? 3. On July 1, 1902, a lady deposited in a savings bank $180 ; September 25, $60; February 10, 1903, $140; April 1, $300, and June 16, $280. What will be her credit in bank January 1, 1904, if no withdrawals have been made? 4. Mr. C deposits in a savings bank which allows interest at A% on deposits from the first of each month and credits the in- terest up on January 1 and July 1. His deposits are as follows : January 1, 1905, $400 ; March 16, $130 ; June 28, $186 ; August 18, $260. What will be his balance January 1, 1906? 5. The following account is taken from the ledger of a sav- ings bank, that pays interest at 4% quarterly. Interest com- mences at the first of each quarter, viz. : January 1, April 1, July 1 and October 1. BANKS AND BANKING 289 Date With- drawals Deposits Balances 1905. Sept 11 230 230 Oct. 30 Xov 11 70 200 30U 500 11)00. Jan 1 500 Jan 1 Int 2.30 502.30 Jan 9 177 325.30 Jan 20 300 25.30 Feb 23 .... 287 312.30 Mar 15 135 177.30 Apr 1 . . 177.30 A.pr 1 Int 25 177.55 Apr 8 75 102.55 Apr 20 .... 25 77.55 Mav 16 125 202.55 Julv 1 Julv 1 Int. .77 202.55 203.32 EXPLANATION. The in- terest term being quar- terly the interest is added to the balance on the first of each quarter. Since no interest is allowed on money withdrawn during the quarter, interest is computed only on the smallest balance in the quarter (Art. 425). The smallest balance in the first quarter is $230 and the interest on this for 3 mo. at 4% is $2.30. The smallest balance during the second quarter is $25.30, the interest on which is $.25. The smallest balance during the third quarter is $77.55, the interest on which is $.77, which added to the balance, gives the final balance as $203.32. 6. January 1, 1905, a clerk deposited in a savings bank $250 ; January 18, deposited $63 ; February 2, withdrew $40 ; February 18, deposited $25 ; March 12, deposited $48 ; March 18, withdrew $125; March 30, withdrew $175; April 18, deposited $400; April 25, deposited $36; May 10, deposited $10; June 15, withdrew $140. What was the balance to his credit July 1, 1905, interest 4% quarterly ? NOTE. Arrange in the form of an account and extend the balances as in the previous problem. 7. A opened an account with a savings bank and deposited July 1, 1905, $200, withdrew July 20, $40; deposited August 8, $230; deposited August 20, $78; withdrew September 5, $100; deposited September 28, $185; deposited October 14, $137.50; withdrew October 27, $30; deposited November 13, $150; de- posited November, 18, $75 ; withdrew December 5, $60 ; with- drew December 13, $45. What was due him January 1, 1906, in- terest being % payable quarterly? 19 290 NEW BUSINESS ARITHMETIC S. A deposit account upon the ledger of a savings bank stood as follows: July 1, 1905, balance $198.98; July 1, 1905, in- terest, $1.80; July 15, withdrawal, $75; September 10, deposits $3000 ; September 28, withdrawal, $125 ; October 3, withdrawal, $485 ; October 19, withdrawal, $500 ; December 9, deposit $162.32 ; December 14, withdrawal, $200; December 31, withdrawal, $25. What will be due the depositor January 1, 1906, interest quarterly at 4% ? 9. The balance due a depositor at a savings bank January 1, 1905, was $450; February 3 he deposited $300; February 15, withdrew $85; March 16, deposited $627.50; March 24, with- drew $250; April 5, deposited, $1000; April 18, withdrew $48.60; May 14, deposited $186.30 ; May 16, withdrew $45 ; June 4, de- posited $75.30; June 12, withdrew $280; June 13, withdrew $43; July 17, deposited $78.40; July 24, withdrew $126.80; August 4, deposited $15 ; August 11, deposited $125 ; September 25, with- drew $250 ; September 30, withdrew $175 ; October 5, deposited $80 ; October 18, deposited $145 ; October 27, deposited $437.25 ; November 15, withdrew $160; December 11, withdrew $500; December 18, deposited $25 ; December 24, withdrew $850. What was the amount of his credit on January 1, 1906, interest at 4%, payable semi-ami ually ? 10. What would be due a depositor at the end of the year, who had a balance of $1843 in bank on January 1, 1905 ; January 8, deposited $145.60; January 25, deposited $427.30; February 15, withdrew $180 ; February 26, withdrew $286 ; March 7, deposited $85 ; March 23, withdrew $1240 ; May 16, deposited $275 ; May 23, withdrew $143; June 12, deposited $1438; June 18, with- drew $745 ; July 7, withdrew $100 ; July 26, withdrew $40 ; July 29, deposited $200; August 14, withdrew $1350; August 25, de- posited $180 ; September 14, deposited $460 ; September 28, with- drew $245; October 9, deposited $180; October 23, withdrew $500; October 27, deposited $1500; November 5, withdrew $640; November 17, deposited $340; November 20, deposited $60; De- cember 18, deposited $250; December 31, withdrew $47.50. The BANKS AND BANKING 291 bank allows interest at 4% from the first of each month on all de- posits remaining in during an entire month, credited quarterly. NOTE. Take the smallest balance in each month of the first quarter, add them together, and (Jivide by three to get the average balance on which interest will be allowed. Take 1% of this. The result is the interest allowed for the quarter. Do the same for each quarter. 11. A's account stands credited January 1, 1905, $435: Janu- uary 15, deposited $250; February 1, withdrew $145; March 10, withdrew $84 ; April 17, deposited $75 ; April 25, withdrew $300 ; May 22, deposited $250 ; June 18, deposited $60 ; July 28, deposited $340 ; July 31, withdrew $800 ; August 14, deposited $60 ; Septem- ber 27, withdrew $25 ; October 20, deposited $38.50; November 5, withdrew $150; December 14, deposited $230. What will be the balance January 1, 1906, interest allowed at 4% on average monthly balances, and credited up semi-annually ? NOTE. Take the smallest balance in each month of the first half year, add them together, and divide by six to get the average balance on which interest will be allowed. Take 2% of this. The result is the interest allowed for the half year. Do the same for the second half year. '12. A clerk had on deposit in a savings bank July 1, 1905, a balance of $625; July 20, deposited $40; August 3, withdrew $130; August 17, deposited $65; September 24, withdrew $28.50; October 5, withdrew $90 ; October 27, deposited $54.80 ; Novem- ber 11, deposited $43; November 18, deposited $40; November 30, withdrew $160; December 12, deposited $48.50 ; December 17, withdrew $24.60. What will be his balance January 1, 1906. in- terest allowed at 4% on average monthly balances and credited up quarterly? 13. What will be the amount of John C. Duncan's balance at the end of the year, in a savings bank which allows 4% interest on average monthly balances, and credits up the interest at the end of each quarter, his account standing as follows : January 1, 1905, balance brought down $435; January 17, deposited $86; February 20, withdrew $135; March 13, withdrew $136.25; March 26, deposited $800; April 16, withdrew $475; May 10, withdrew $500; June 4, deposited $36.80; June 28, withdrew $75; July 11, deposited $600; August 14, withdrew $586; Sep- tember 18, deposited $267; October 15, withdrew $56; Novem- ber 15, deposited $180; December 4, withdrew $250; December 26, withdrew $65. TAXES 426. A Tax is a sum assessed on persons or property to pay the expenses of a State, County or City or for other public pur- poses. 427. Taxes levied by the General Government are of two kinds: Duties or Customs and Internal Rei'cnue. 428. Taxes levied by the State, County or City are of two kinds : Property and Poll Tax. 429. Property Tax is a Tax on property reckoned at a cer- tain per cent, on the assessed value. 430. Poll Tax is a tax assessed on persons ; in most of the states on all male citizens over 21 years of age. 431. An Assessor is a person elected to estimate the valua- tion of taxable property. 432. A Collector is an officer whose duty it is to receive and collect taxes. In some states collectors are paid a certain per cent, for their services, and the amount levied must include the amount of money necessary to be raised plus the collector's fee. In computations in taxes, 1. Assessed Valuation = Base. 2. Ta.r= Percentage. ORAL PROBLEMS 1. What is A's tax on property assessed at $4800, the tax levy .being \\% ? \\% ? \% ? \% ? 2. What is a person's tax whose property is assessed at $5000, when the rate of taxation is 2$% ? \\% ? \\% ? 3. A's property is valued at $6000, the assessed valuation is f . What is the tax, the rate of taxation being \\% ? lj-% ?' \\% ? 4. What is a person's tax on property valued at $10000 as- sessed at f valuation when the rate of taxation is 1% and who also pays poll tax for 4 persons at $1.50 each? 5. A tax of $36 is paid on property assessed at a rate of \%. What is the assessed valuation ? 292 TAXES 293 ti. A tax of $50 is paid on property assessed at \%. What is the value of the property, the assessed valuation being at J valua- tion? WRITTEN PROBLEMS 1. A paid tax on $49200 at the rate of $.008^ on the dollar, and paid 2 polls at $1.75 each. What amount of tax did he pay? 2. How much must I pay on property worth $9840, assessed for f its value at $.011f on the dollar, and three polls at $2.10 each ? 3. A village containing 220 taxable persons whose property was valued at $418500, was assessed for the purpose of building a school house, at $.013 on the dollar and $1.80 each for polls. What was the cost of the school house? 4. A tax of $.010 on the dollar and $1.35 for polls was as- sessed in Warren county for the purpose of building a court house. The value of property was $987430, and the number of taxable persons 1342. Allowing 2$% for collecting, what amount was paid for the court house ? o. What amount of tax is paid on $43500 worth of property assessed for f its value at $.01 2 J on the dollar, and 34 polls at $1.20 each? G. For the purpose of paving a street the property owners on the street were assessed on $214700 worth of property at $.009 j on the dollar, and $.85 each on 94 polls. The charges for collect- ing were 4-J%. What did the pavement cost? 7. A town assesses a tax of $.012 on the dollar, and $1.18 each on 115 polls. The personal property worth $86280 is as- sessed for | its value, and real estate $65296 for J its value. What was the amount of tax ? In practical tax computations a Tax Table is prepared by the use of which the labor of finding the tax is greatly reduced. 8. The assessed value of the property in a school district is- $220488, and a tax of $1625 is voted. Construct a tax table similar to the one on the following page. 294 NEW BUSINESS ARITHMETIC TAX TABLE 7.37 MILLS ON $1 1 2 3 4 5 6 7 8 9 1 .07370 .08107 .08844 .09581 .10318 .11055 .11792 .12529 .13266 . 14003 2 .14740 .15477 .16214 .16951 .17688 . 18425 .19162 .19899 .20636 .21373 3 .22110 .22847 .23584 .24321 .25058 .25795 .26532 .27269 .28006 .28743 4 .29480 .30217 .30954 .31691 .32428 .33165 .33902 .34639 .35376 .36113 5 .36850 .37587 .38324 .39061 .39798 .40535 .41272 .42009 .42746 .43483 6 .44220 .44957 .45694 .46431 .47168 .47905 .48642 .49379 .50116 .50853 7 .51590 .52327 .53064 .53801 .54538 .55275 .56012 .56749 .57486 .58223 8 .58960 .59697 .60434 .61171 .61908 .62645 .63382 .64119 .64856 .65593 9 .66330 .67067 .67804 68541 .69278 .70015 .70752 .71489 .72226 .72963 SOLUTION Tax on $1300 = Tax on 80 = >.581 .589 Tax on $1380 = $10.1' From the table find the tax on A's property which is assessed $1380. EXPLANATION. Look in the table op- posite 1 in the left hand column and under 3 in fifth column and we find the tax on $13 is .09581. Removing the decimal point two places to the right which is equivalent to multiplying by 100 and we have the tax on $1300 = to $9.581. Then looking opposite 8 and under and we find the tax on $80 to be .589. Adding these together we have the total tax. P. According to the table what will be the amount of A. C. Bore's tax if his property is assessed $24365' and he pays for 3 polls at $1.80 each? 10. After May 1 a penalty of \% per month is added to all unpaid taxes. S. D. Johnson's property is assessed at $42630 and he pays for 2 polls at $1.50 each. If he pays his tax August 3, what amount must he pay ? 11. The amount of money to be raised by taxes in Ottawa is $212093.20. The taxable property is $11522400, and there are 3350 polls, each at $1.40. Find the rate of taxation. If the assessment is made on a J valuation, what would be the rate? CUSTOMS OR DUTIES 433. Customs or Duties are taxes levied on imported goods for the support of the general government, and the protection of home industries. 434. Ad Valorem Duty is a tax of a certain per cent, on the cost of the goods in the country from which they were imported. 435. Specific Duty is a tax levied on goods without regard to value but estimated on weight or measure. In some cases duties are ad valorem; on some articles they are specific; and some others they are both ad valorem and specific. 436. An Invoice on imported goods is an itemized list of goods shipped and their value in the country of origin. All invoices on imported merchandise must be made out in the currency of the country of export and must be certified by the United States consul, vice consul or commercial agent in the country from which the goods are exported. 437. Consul Fee is a charge made by the consul but it is not a part of the dutiable value. 438. Tare is an allowance made for the weight of a box, bag, etc., containing the goods. 439. Leakage is an allowance made for waste of liquors in barrels. 440. Breakage is not allowed for loss of liquors in bottles, but shortage occurring before shipment will be considered. 441. Gross Weight is the weight before any deductions are made. . 442. Net Weight is the weight after the deductions are made. 443. A Tariff is a list of goods, giving the rate of duty pre- scribed by law. 444. A Custom House is a government building or office where duties are assessed and collected and all other government business concerning that port is transacted. 295 296 NEW BUSINESS ARITHMETIC Goods cannot be legally imported except through the custom house at a regular port of entry. 445. A Port of Entry is a town or city in which a custom house is located. The chief port of entry in the United States is New York, but all of the principal cities are ports of entry. 446. Smuggling is secretly bringing goods into a country to avoid the payment of duties. Smuggled goods when found are subject to seizure and the person or persons found guilty of such violations of the law, liable to a fine or imprisonment or both. 447. A Bonded Warehouse is a building used for the storage of imported merchandise until the duties shall have been paid. Goods held for duties are said to be "in bond" and 10% extra dun- is charged for each year that they remain in bond. If left for more than three years they are considered as abandoned to the government, and are advertised and sold at auction for payment of the duties. 448. Internal Revenue is the taxes levied on goods manufac- tured and sold in this country for the purpose of government sup- port. Internal revenue taxes are usually paid by affixing government stamps to the package containing the articles to be taxed, or by purchasing a government license. In estimating ad valorem duties, 1. Cost = Base. 2. Duty = Percentage. NOTES. 1. In estimating ad valorem duties all charges necessary to prepare goods for shipment must be added to net cost of goods to find the dutiable value. 2. In finding specific duties the long ton (2240 Ibs.) is used. Allow- ances Tare, Leakage, etc., are deducted before the duty is estimated. 1. What is the amount of duty on a shipment of 2500 Ibs. invoiced at 3 shillings per pound*, the rate of duty being 7c per pound and 5% ad valorem, 4% being allowed for tare? NOTE. One shilling = 24^ cents. 2. L. M. Hawthorne received from London one case of mer- chandise, weighing 570 Ibs. net. The invoice price was 370 10s; packing charges 10 8s. The ad valorem duty was 28%; the specific duty 12$ cents per Ib. What was the entire duty? CUSTOMS OR DUTIES 297 NOTE. Add all charges to net cost to find dutiable value. 1 = $4.8665. 3. A manufacturer imported from England 35 bales of wool, weighing 440 Ibs. each; tare 5%; cost 2^s. per Ib. ; specific duty 6 cents per Ib. What was the duty ? NOTE. The tare is deducted before finding cost and specific duty. 4. R. G. Waltz & Co. received an invoice of goods from France, amounting to 4250 francs on which there was 8% dis- count. The charges subject to duty were 213.9 francs. What was the duty at 40% ? NOTE. 1 franc = 19.3c. 5. H. J. Graham imported from Paris one case silk shawls. The first cost was 8340 francs ; packing charges 215.05 francs ; the net weight 842. \Vhat was the entire cost, at 60% ad valorem duty ? 6. John W. Hauser & Co. received from Berlin an invoice of books amounting to 3284 marks. Case and packing cost 243.84 marks. What was the duty at 25% ? NOTE. 1 mark = 23.8c. 7. A merchant imported from Germany a box of merchandise invoiced at 2365 marks, on which there was a discount of 8% ; charges 173.95 marks. Net weight was 920 Ibs. What was the duty at 9 cents per Ib. and 25% ad valorem? S. An invoice of merchandise amounting to 3148 guilders was received at the Chicago Custom House. The charges for case and packing were 230.05 guilders. What was the duty at 36% ; the par value of a guilder being 40.2 cents? 0. A merchant received from Brussels 1972 yds. of carpet 24 inches wide invoiced at 6 francs per yd. on which 4.% discount was allowed. The charges were 394.77 francs. What was the entire cost with specific duty 44 cents per square yard and ad valorem duty 40%? 10. A hardware merchant imported from England one box of 50 doz. assorted knives invoiced at 270 6s. 9d., on which he was allowed a discount of 5 and 5%. The charges were 16 18s. 4.8d. ; 298 NEW BUSINESS ARITHMETIC net weight 740 Ibs. What was the entire cost at 20 cents each, specific duty and 40% ad valorem? 11. A dry goods merchant imported from Manchester, Eng- land, 7 cases white muslins containing 1440 pieces, each piece being 27 yards long and 1J yards wide, the muslin was invoiced at 3Jd. per yard, and the total charges were 32 17s. 6d. What was the duty on the invoice at 4| cents per square yard and 20% ad valorem? 12. Invoice received by F. K. RACHLER Co., St. Louis, Mo. Marks Nos. Packages and Contents Cost F. K. R. 61 62 1 Case Carpet 1120 yds.. 18 in. wide, @ 4 francs *** 1 Case Carpet 780 yds., 24 in. wide, @ 3^ francs *** Case and Packing Total cost Specific duty 22c pr. sq. yd. Ad Valorem duty 40$ on $ Entire Cost **** 174.6 #**# ##* ** #### #* NOTE. Find total cost in francs and reduce to U. S. money. 13. Invoice of one case of good,s from B. A. WELSTEAD & Co., Liverpool, England, for R. T. RILEY & Co., Louisville, Ky. Marks Nos. Packages and Contents Duty Ad. Spec. R. T. R. 428 720 vds. Velvet, 22 in. wide, @ 1 12s. yd. I960 " Chiffon Lace @ 2s. 4d. yd. 1120 " Carpet, 18 in. wide, (cb 15s. yd. 2180 " Carpet, 26 in. wide, @ 10s. 6d. yd. Net Cost Duty on Velvet " " Lace " Carpet " " Carpet Total Cost 25# 60;? 40$ 60^ 18c pr. sq.yd. 60cpr. sq.yd. 60c pr. sq.yd. >.>;-.;;:*>;-. ## EQUATION OF ACCOUNTS 449. An Account is a record of business transactions and may embrace either debits or credits or both. 450. Equation of Accounts is the process of finding the time when several debts due at different times, may be paid at one time without loss to either party, or if the account has two sides, when the balance or difference may be paid. 451. Cash Balance is the sum required to pay an account at -any given date. 453. The Term of Credit is the time a debt has to run, as 10 days, 1 month, 90 days, etc. All accounts bear legal interest after they become due. Promissory notes, not containing an interest clause, bear legal interest -after maturity. 453. The Average Term of Credit is the average of the sev- ceral terms he would pay it $500 X 12 = $6000. 3 mo - before il: is du e, and the $100 X 16 = $1600. in terest on $200 for 3 mo. = the interest on $600 for 1 mo $1200 (due me) $10200. chle Weaver The interest on $10200 -r- $1200 = 8J mo. $400 for 5 mo = the interest Jan. 1 + 8| mo. = Sept. 16. on $ 2 000 for 1 mo. due Weaver, The interest on $500 for 12 mo. equals the interest on $6000 for 1 mo. due Weaver. The interest on $100 for 16 mo. equals the interest on $1600 for 1 mo. due Weaver. Adding we find that Weaver owes me $1200 but I owe him the interest upon (or use of) $10200 for 1 mo. Now the interest on $10200 for 1 mo. is equal to the interest on $1200 for S l / 2 mo. Therefore Weaver may withhold the $1200 due me S l / 2 months or until September 16. SOLUTION INTEREST METHOD Assume Jan. 1, 1905 as the date of settlement. Int. on $200 for 3 mo. at 6% = $3. EXPLANATION.-!! Weaver Int. on $400 for 5 mo. at 6% = $10. had P aid the several sums Int. on $500 for 12 mo. at 6% = $30. on J anua ry 1, 1905, I would Int. on $100 for 16 mo. at 6% = $8. have owed him $ 51 interest, - hence he may keep the $1200 $1200 (due me) $51. principal until the interest Int. on $1200 for 1 mo. at 6 % = $6. O n it amounts to $51. Any $51 -i- $6 = 8^ mo. rate of interest may be used, Jan. 1 + 8i mo. == Sept. 16. but it is most convenient to use 6%. NOTES. 1. In finding the average term, fractions of a day of one-half or more are counted as one day; fractions less than one-half are rejected. 2. The product method is recommended because it involves less work and is more easily comprehended by the student, but accountants prefer the interest method. Both methods should be used until thoroughly under- stood. 2. On March 5, 1905, B bought the following bill from A : $240 on 10 days time, $300 on 20 days time, $450 on 30 days time, $600 on 60 days time. Find the date when the whole sum can be paid without loss to either party. EQUATION OF ACCOUNTS 301 3. Jones bought a lot of merchandise for $2100 from Brown of which $400 was payable in 2 months ; $500, in 3. months ; $300, in G months ; $200, in 8 months ; $700, in 9 months. What is the average time of credit of the whole amount? 4. I owe $150 due in 4 months; $300 due in 6 months; $600 due in 1) months; $800 due in 12 months. What is the average time of credit? 5. Lyman bought a house on April 16, 1903, for $2000, pay- able as follows; J cash, -J in 5 months, f in 8 months, the re- mainder in 10 months. What is the equated time for paying the whole, and the maturity of a note for the entire amount ? 6. Graham sold the following^ merchandise on June 3, 1905 : $200 worth of prints on 30 days ; $360 worth of flannels on 2 months ; $420 worth of silks on 60 days ; $560 worth of cotton goods on 90 days. When can the whole amount be paid by the debtor without loss of interest ? 7. A bought a farm on January 10, 1905, for $7200, of which $1200 was paid in cash, $1000 was to be paid in 3 months; $1200, in 6 months; $1400, in 9 months; $1300, in 12 months; the remainder, in 15 months. He gave his note for the amount due after making the cash payment. What should be the ma- turity of the note ? (9. I bought the following goods from Fuller & Co. on July 1, 1905: $180 on 10 days; $210 on 30 days; $340 on 60 days; $620 on 90 days; $750 on 4 months; $200 on 6 months. Find the maturity of my note given, to pay the entire amount. 9. Find the equated time and date of settlement of the fol- lowing, sold on May 21, 1905: $160 on 15 days; $360 on 1 month; $190 on 40 days; $425 on 2 months; $230 on 90 days; $490 with no term of credit ; $85 on 4 months ; $310 on 5 months ; $660 on 5 days; $900 on 10 days; $515 on 20 days; $740 on 25 days. 10. March 20, I bought a horse for $175, on a credit of 4 months; May 5, a harness for $35, on 3 months; and June 15, a carriage for $225, on 6 months. Find the equated time for the payment of these debts. 302 NEW BUSINESS ARITHMETIC SOLUTION July 20 $175 .... Aug. 5 35 16 560 Dec. 15 225 148 33300 $435 $33860 March 20 + 4 mo. May 5 +3 mo. June 15 +6 mo. $33860 -i- $435 = 78 = 78 da. average term of credit. July 20 + 78 da. = Oct. 6, equated time. Find the equated time for the settlement of the following bills : 11. Bill No. 1. Terms cash. 1905 Feb. 2, . Mdse. $425. March 10, $320. May 6, $195. June 30, " $1120. 12. Bill No. 2. Terms 30 days 1905 June 2, Mdse. $247.20. July 14, $165. July 30, " $280. August 4, " $760. William Hammond, IS. Bill No. 3 To P. D . Armour & Co. Dr. 1905 Apr. 2 40 bbl. Beef 30 da. $18.50 May 14 60 Mess Pork 60 da. $10.25 June 8 25 " Short Ribs 90 da. $ 2.75 14. Bill No. 4. 1905 Oct. 22, Mdse. 1 mo., $116.20. Dec. 14, 1906 Jan. 18, March 11, May 4, 2 mo., $275. 3 mo., $79.25. 1 mo., $367.40. 2 mo., $67.85. 15. Bill No. 5. 1905 April 6, Mdse. 10 da., $236.10. May 2, May 23, June 7, July 2, 20 da., $71.15. 15 da., $329. 30 da., $143.50. 60 da., $420. EQUATION OF ACCOUNTS 303 16. Bill No. 6. 1905 Feb. 4, Mdse. 30 da., $72,45. March 12, " 10 da., $16.90. April 23, " (cash) $41.20. May 1, " 20 da., $62. June 6, 15 da., $98.10. July 12, " 30 da., $26.35. 17. 1904 Oct. 30, 1905 April 27, August 1, 1906 Jan. 21, May 1, Bill No. 7. Mdse. 6 mo., $250. " 10 da., $365. 3 mo., $270. " 60 da., $124. " 30 da., $417. 18. Find the equated time for settlement of the following": STATEMENT OF ACCOUNT Boston, Sept. 1, 1905. Charles D. Rogers, In account with French, Potter & Wilson. 1905 January 10 To Mdse. SO da. 162 SO April 19 60 da. 321 45 June 24 Cash 99 August 10 4 mo. 172 754 75 457. To find the equated time for the payment of the balance of an account having both debits and credits. 1. Find the equated time for the payment of the balance of the following account. Dr. A. R. Harmon. Cr. 1905 1905 January 1 Mdse. 400 March 4 Cash 200 Feb. G 720 ( t 25 <( 350 April 2 <( 500 When an account has both debit and credit sides as the above, the equated time for the payment of the balance may be found by either the Product Method or the Interest Method. The above problem is solved by both of these methods in order that the stu- 304 NEW BUSINESS ARITHMETIC dent may familiarize himself with them. Accountants usually prefer the interest method, as it appears more business-like. SOLUTION PRODUCT METHOD FOCAL DATE, JANUARY 1, 1905 ITEMS. TIMES. PRODUCT. Jan. 1, $400 ' Feb. 6, $720 36 Apr. 2, $500 91 $1620 550 000 $25920 $45500 ITEMS. TIMES. PRODUCT. March 4, $200 62 $12400 March 25, $350 83 $29050 $550 $41450 $71420 41450 Subtracting smaller side. $1070 $29970 $29970 -^- $1070 = 28 da. = average term of credit. Jan. 1, 1905 -f 28 da. = Jan. 29, 1905, equated time of pay- ment. EXPLANATION. Assuming Jan. 1, 1905, as the focal date we find the products upon the Dr. and Cr. sides as in previous problems. Then sub- tracting the credit from the debit side we find the balance of the items to be $1070 and the balance of the products to be $29970 both in favor of the debit side. Therefore the balance of the account $1070 is entitled to a credit long enough to equal $29970 for one day, which we find by dividing to be 28 days. This added to the focal date gives Jan. 29, 1905. Should the balance of the items be on one side and the balance of the products on the other side of the account, if the earliest date is taken as a focal date, the balance of the account must suffer a discount, or be due prior to the focal date, and hence we count back of the focal date to find the equated time. SOLUTION INTEREST METHOD APRIL 2, INTEREST. $6.07 $6.60 1905. INTEREST 6#. DUE. ITEMS. TIMES. IN Mar. 4, $200 29 da. Mar. 25, $350 8 da. TEREST. .97 .47 $550 Smaller side subtracted. Int. on $1070 for 1 da. = $1.44 $.17$. $12,67 1.44 $11.23 EQUATION OF ACCOUNTS 305 $11.2-3 -T- $.17ft = 63 da. average term of credit. April 2 63 da. = Jan. 20, equated time of payment. NOTES. 1. Any date may be taken as a focal date, but it simplifies the reasoning to assume either the earliest or the latest date, the result being the same in both cas^s. 2. In an account that contains both debits and credits, the items on the debit of the ledger of one of the parties are the same as those on the credit of the ledger of the other party ; hence, an account equated by both parties must show the same result. 2. Find the average time for the payment of the balance of the following account: Dr. A. E. BAKER. Cr. 1905 1905 May 12 Mdse. 370 June 4 Cash 220 May 31 192 80 July 2 " 175 80 June 14 u 126 July 26 150 July 6 " 217 3. When is the balance of the following account due? Dr. ]. F. SARLEY. Cr. 1905 1905 Jan. Feb. 17 27 Mdse., 30 days 10 " 300 240 Feb. Mch. 1 4 Cash Note, 15 da. 100 150 Mch. April 12 1 " 20 " " 30 " 450 600 April May 6 10 Cash 350 120 NOTE. Find the maturity of each item and use the due dates in equat- ing or add the special credit to time from regular date. 4. Find the date of a note to settle the balance of the follow- ing accounts : Dr. F. W. C. HOLTKAMP. Cr. 1905 1905 A lay 1 30 Mdse., 5 days 15 " 217 192 80 June July 4 1 Note, 20 da. Cash 150 68 30 June 14 30 " 62 30 " 15 209 70 '' 27 10 " 377 90 20 306 NEW BUSINESS ARITHMETIC 5. Average the following account : Dr. D. C. MEYER. Cr. 1905 1906 Nov. 20 Mdse., 3 months 560 Mch. 5 Draft, 15 da. 250 Dec. 27 " 3 " 178 April 3 Note, 1 mo. 130 1906 Jan. Mch. 31 2 " 60 days " 30 " 93 230 45 55 May 1 15 Cash Mdse., 10 da. 75 180 April 17 a 120 6. 1 When is the balance of the following account due? Dr. F. D. NEAGELE. Cr. 1905 1905 Jan. 6 30 Mdse., 30 days " 60 " 272 536 15 Mch. April 2 1 Note, 20 da. Ck. dated 172 Feb. 20 10 " 73 April 15 300 Mch. 18 15 " 121 60 May 24 Cash 150 April 12 10 " 83 25 31 100 7. Average the following account : Dr. C. W. KITT. Cr. 1905 1906 Oct. 1 Mdse., 2 months 190 Jan. 1 Cash 130 Dec. 4 30 days 274 Mch. 19 Acceptance 1906 Jan. 11 20 " 311 40 (t 24 10 days Cash 228 173 Feb. April 21 1 20 " 86 217 20 95 April 1 tt 217 95 8. What is the balance of the following account, and when will it begin to draw interest ? Dr. W. J. FISHER. Cr. 1905 1905 April May 1 4 Cash Note, 10 days 125 200 Jan. Feb. 21 28 Mdse., 60 da. 90 " 166 219 60 28 1 Sight draft 100 April 20 " 20 " 52 80 July 1 Cash 250 June 30 " 10 " 356 Aug. 15 u 199 63 July 14 " 15 " 411 35 30 " $380, 4^ off *** ** Aug. 15 " $210, 3 & 2fc off *** ** EQUATION OF ACCOUNTS 307 9. When must a note be dated and commence drawing inter- est if given in settlement of the following account? Dr. W. W. COFFIN. Cr. 1905 1905 July 1 Mdse., 90 days 208 60 Dec. 1 Cash 360 Oct. 30 $420, Art n ff *** ** 1906 Feb. 19 Note, 30 da. 135 1906 Jan. Mch. 1 3 ^/o Ull 20 days 10 " 114 374 50 90 April May 1 5 Mdse., $220 6^ off Cash *** 123 70 May 1 " $160 5 & 5# off *** ** 10. Find the average date of payment in the following: Dr. D. C. ROBERTS. Cr. 1903 1904 Aug. 30 Mdse., 4 months 210 Jan. 1 Mdse., $120, Nov. 3 3 , 147 20 3^ off **# **. 1904 May 4 " 60 days 379 35 July Dec. 1 1 Note, 3 mo. Cash 230 175 Aug. 6 " 60 " 430 25 1905 *-*o Dec. 12 " 30 " 53 15 Jan. 30 Mdse., 30 da. 291 40 19C5 Jan. 1 " $270, 6 & 2# off *** ** 11. Find the balance due on the following account, July 10, 1905, interest allowed at 6%. Dr. L. H. YOUNG. Cr. 1905 1905 Jan. 4 Mdse., 10 days 400 Mch. 21 Cash 200 Feb. 16 20 " 360 April 30 Note, 15 da. 150 April 5 " 30 " 500 June 3 Cash 120 808 NEW BUSINESS ARITHMETIC 12. If the following account is settled January 1, 1907, money being worth 7%, what amount must be paid? Dr. B. E. IRWIN & Co. Cr. 1905 1905 Nov. 10 Mdse., 60 days 320 April 4 Cash 450 Dec. 23 " 90 " 185 May 16 Draft, 60 da. 95 1906 1906 Mch. 12 " 30 " 236 90 June 3 Note, 1 mo. 120 June 4 " 10 " 468 60 July 20 Cash 186 SO July 3 15 " 241 50 458. To find the date of payment of the net proceeds of a consignment. The sales constitute the credit side of the account. The ex- penses of the consignment (freight, storage, commission, etc.), and the money advanced before the account is closed, constitute the debit side of the account. Find the average due date of the sales, and take this date as the due date of the commission. Find the due date of settlement the same as in previous problems. 1. When are the net proceeds of the following account sales due? Account Sales of Pork. Nashville, Tenn., Sept. 1, 1905. Sold for account of Swift & Co., Chicago, 111. 1905 July 3 25 bbls. Mess Pork @ $12.80, 30 days. *** ** a 23 45 " Mess Pork @ $12.60 cash. *** ** Aug. 6 40 " Prime Pork @ $13, 20 days. *** *# 17 30 Prime Pork @ $12.85, 10 days. *** ## #### ** CHARGES July 1 Freight 71 40 1 Cash advanced 250 Commission (due ) 4# *** #* **** ** Net proceeds (due ) *#** ** 2. When will the net proceeds of the following account sales be due? EQUATION OF ACCOUNTS 309 Account sales of flour sold for account of Geo. F. Snyder & Co., Minneapolis, by Davis & Co. 1905 May 6 110 bbls. XX Flour @ $5.90, 10 davs. *** ** " 30 90 " XX Flour @ $6, 5# off **# ** June 16 76 " XXX Flour @ $6.05, 20 davs. *#* ** 30 125 " XXX Flour @ $6.10 cash. *** ** *#*# *# CHARGES May 2 Freight 86 12 6 Accepted Snyder's draft, 15 days 400 " 25 Cooperage 12 June 30 Storage Commission (due ) 3^ % 23 ** 80 ** Net proceeds (due ) **** ** After having ascertained the date at which the Net Proceeds of a consignment is due, to find the cash balance at any later date, add the interest to the Net Proceeds for the intervening time. 3. Find the date of settlement of the net proceeds, and the cash balance on September 1, 1905 1%. Account sales of produce by John Mason, for account of J. B. Hayes, Detroit, Mich. 1905 March April May March May 12 16 23 4 6 3 3 5 6 300 doz. Eggs @ 15 cts., 30 days 700 Ibs. Butter @ 21^ cts., 10 days 210 doz. Eggs @ 14^ cts., cash 200 Ibs. Butter @ 22^ cts., 2$ off 290 doz. Eggs @ 15 cts., 10 days CHARGES Freight Cartage Cash advanced Storage from March 3 Commission (due ) 4# Net proceeds (due ) ** *** ** ** ** **** ** 90 7 150 31 *** 60 90 50 **** ** **** 4. Find the average due date of sales; the true date of set- tlement of the proceeds and the cash balance on August 10, 1905 310 NEW BUSINESS ARITHMETIC Sales of A. B. Wilson & Co., for account of S. R. Lockwood & Co., Springfield, 111. 1905 Feb. 14 105 bbls. Potatoes @ $1.40, 10 days *** ** March 2 80 " Apples @ $2.80, 3# off *** ** 30 120 " Apples @ $2.75, 20 days *** ** April 3 75 " Potatoes @ $1.35, 30 days #*# ** u 16 20 Potatoes @ $1.45, cash *** ** **** ** CHARGES Feb. 10 Freight 64 28 M 10 Drayage 11 50 15 Accepted their draft at 10 days 200 19 Cooperage 6 20 April 16 Storage from Feb. 10 15 Commission (due ) 4 l / 2 % *** ** **** ** Net procesds (due ) **** ** CASH BALANCE 459. Cash Balance is the amount of money which will settle an account on a given date. Cash balance is the difference be- tween the two sides of an account, with the interest added to all past, due items. In settling mercantile accounts interest is not always reckoned. This is regulated by previous agreement and also by custom. When interest is charged it is calculated from the time the account is due. The cash balance of an account may be found by either the product, or interest method, but the latter is preferable. 1. Find the cash balance July 3, 1905, on the following ac- count, interest at 6%. Dr. Williams & Brown in account with J. R. Wood Cr. 1905 1905 Jan. 24 Mdse 20 da. 168 50 Apr. 2 Cash 150 Mar. 1 Mdse 15 da. 79 20 May 6 Note 13 da. 270 50 May 4 Mdse 10 da. 864 80 ft 6 Cash 63 50 tr 23 Mdse 204 50 June 2 Cash 100 DUE. ITEMS. DAYS. INTEREST. DUE. ITEMS. DAYS. INTEREST. Feb. 13, $168.50 HO $3.93 Apr. 2, $150.00 92 $2.30 Mar. 16, 79.20 109 1.44 May 19, 270.50 45 2.03 May 14, 364.80 50 3.04 May 6, 63.50 58 .61 May 23, 204.50 41 1.39 June 2, 100.00 31 .52 $817.00 $9.80 $584.00 $5.46 584.00 5.46 $233.00 + $4.34 = $237.34 EXPLANATION. If J. R. Wood had paid nothing before July 3, he would owe the items on the Dr. side of the account and also the interest on them to July 3 amounting to $9.80 ; but as he paid some amounts before that date he is entitled to credit for the amount paid and also the interest upon them from the date of payment until July 3, amounting to $5.46. This interest deducted from $9.80 leaves $4.34 the net amount of interest added to the balance of the account gives the total due, or cash balance due on July 3, 1905, $237.34. 811 312 NEW BUSINESS ARITHMETIC NOTES. 1. When the balance of interest is on the same side of the account as the balance of items, it is added to the balance of the items; when it is on the opposite side it is subtracted from the balance of the items. 2. In computing interest regard fractional parts of a dollar less than half as nothing, and equal to or greater than half as one dollar. But in adding these items the exact cents must be taken. 2. Find the cash balance on October 30, 1905, at 6% interest. Dr. E. T. NICHOLS. Cr. 1905 1905 Mar. 5 Mdse. 146 30 May 1 Cash 100 April May 3 17 10 days " 20 " 561 328 40 80 June 4 30 Note, 30 d" Check 165 75 50 June 4 11 15 " 196 50 July 5 Cash 290 50 July 10 " $600 3 & 5# off *** ** 3. Find the cash balance on September 1, 1906, at 5% interest. Dr. E. J. COLLINS. Cr. 1905 1906 Aug. Dec. 1906 30 16 Mdse. 90 days " 30 " 278 123 25 Jan. 1 Note, $250 with in- terest for 8 mo. 10 da., at 8 per *** ** Feb. Mar. 3 21 " $960 5 & 5% off " $820, *** ** Mar. April 12 2 Note, 2 mo. Mdse. $140, 2$ off 540 *** ** April 6 3 & 4# off " 20 days *** 378 15 May 10 " $310, 5 & 6% off *** ** May 1 " $260, 4* off *** ** " 20 Cash 180 4. Find the cash balance on January 1, 1906, at 6% interest. Dr. I. K. JAMES. Cr. 1905 1904 Jan. 13 Note, 60 days 225 June 4 Mdse., 3 mo. 196 30 " 28 Draft, 33 " 172 15 Sept. 10 2 " 211 40 May 1 30 Check Cash 86 123 40 45 1905 Jan. 1 $440, June 10 30 Note, 13 " Cash 75 100 Mar. 1 2 & 4% off Mdse, $175, *** 5^ off *** ** June 1 30 da. 280 26 10 " 192 80 PARTNERSHIP 460. A Partnership is an association of persons who join their capital, labor and skill for the purpose of conducting some business, and who agree to divide the profits and bear the losses in certain proportions. The business association is called a Finn or House. 461. Partners are the persons forming the association. They are active or silent, general or special. 1. An active partner is one who takes an active part in the management of the business. 2. A silent partner is one who furnishes capital, and shares in the profits and losses, but takes no active part in the management of the business. 3. A general partner is one who is responsible for the debts of the company to the amount of his entire property. 4. A special partner is one whose responsibility is limited to a certain amount specified in the written articles of partnership. 462. The Capital is the money or other property invested in the business. 463. Resources, sometimes called Assets, of a firm are its entire property including all debts due the firm. 464. Liabilities of a firm are its debts. 465. Net Capital of a firm is the excess of its resources over its liabilities. 466. Net Insolvency of a firm is the excess of its liabilities over its resources. 313 314 NEW BUSINESS ARITHMETIC 467. Net Investment of a partner is the amount of the capital of the firm which he has invested less the amount he may have withdrawn from the business. 468. Net Gain of a firm is the excess of total gains over total losses. 469. Net Loss of a firm is the excess of total losses over total gains. The Gain is found by subtracting the investment from the net worth at closing. The loss is found by subtracting the net worth at closing from the investment. Gains and losses are divided between the partners according to agree- ment, but in the absence of any express agreement, it is understood that the partners are to share equally in gains or losses. Partnerships are General, and Special or Limited. 470. A General Partnership is one in which each partner is liable for the debts of the firm to the full extent of, not only his interest in the business, but his private property also. 471. A Special or Limited Partnership is one having one or more general partners and one or more special partners. Each special partner is liable for the debts of the firm only to the ex- tent of his investment, and his private property cannot be taken to pay firm debts. The laws relative to special or limited partnerships in most states re- quire : 1. That written articles of copartnership shall be drawn, signed by all the partners, specifying the general and special partners, and the amount invested by each, which articles must be recorded in the public records of the county. 2. There must be at least one general partner, who shall manage the business and who shall be liable for the debts of the firm the same as in a general partnership. 3. Special partners shall take no active part in the management of the business. 4. The investment of each special partner must be fully paid in. An omission of any of these conditions makes the partnership gen- PARTNERSHIP 315 eral and all of the partners equally liable for debts the same as in a general partnership. 472. The investment and the resources and liabilities at clos- ing being given to find the gain or loss. 1. A firm invested cash $2300; merchandise $1180; other per- sons' notes $1500; accrued interest $20. At closing the resources were cash $3900; merchandise $362; notes due $1698; accrued interest $49.20 ; personal accounts due $991.80. Find the gain. NOTE. From the total resources at closing subtract the total invest- ment. 2. A and B formed a partnership for a year. A invested cash $1600; notes $380; Lyman's account $120. B invested merchan- dise $1280; notes $415; horse and wagon, valued $205. The firm had at the close of the year cash $3200 ; merchandise $312.40 ; notes due $480.20 ; personal accounts $1049.90. How much did they gain ? 3. Sanders and Reed formed a partnership and invested as follows: Cash $3300; dry goods invoiced at $600 with a dis- count of 10 and 5% ; Byrne's note of $720, that had been on in- terest 4 months at 9%; personal accounts due $629.10; fixtures $216.50. They had at closing $4217.20 cash in the bank, $370 cash in the safe; $490 worth of fixtures; $1200 worth of mer- chandise. Did they gain or lose and how much ? 4. Smiley, Richards and Bloomer formed a partnership for two years. Smiley invested cash $1000 ; real estate $1800. Rich- ards invested a stock of groceries $2000 with 3% and 5% off; cash $1000. Bloomer invested cash $1250; office fixtures $160; horse and wagon, $270; Brown's note of $450, with accrued interest for 5 months 10 days at 10%. The firm sold all its prop- erty at the end of two years and had $10699.28 cash. Find the gain. 5. A invested $1250 cash; store valued at $2150; personal accounts $382.50. He owed a note of $320 which the firm as- sumed. B invested $3180 cash; office safe valued at $145. He owed personal accounts $653.30 which the firm assumed. C in- 316 NEW BUSINESS ARITHMETIC vested his stock of clothing, invoiced at $2700 on which he al- lowed a discount of 4%. The resources at closing were cash $6394.25; merchandise $1746.35; store $2000; office safe $130; Reeve's note of $980 which had been on interest for 114 days at 9%. Was there a gain or loss and how much? What was each partner's portion of the gain or loss A sharing tV, B 1*1 and C A? NOTE. Subtract the debts of the partners, which were assumed by the firm from their investment to find the net worth at the beginning. 6. Smails, Dorsey, Adams and Piper formed a partnership to share the gains and losses equally, and invested as follows : Smails invested cash $3000 ; 10 shares bank stock worth $126 per share. Dorsey invested his stock of boots and shoes valued at $4000. Adams invested cash $1900; a real estate mortgage of $2000 with accrued interest for 6 months and 20 days at 8%. Piper invested his store and lot valued at $3750. During the time of partnership Smails withdrew cash $300 and merchandise $92.40. Adams withdrew cash $217.20. Dorsey withdrew mer- chandise $37.50. Piper withdrew cash $226. The property at closing was cash $17294.10; outstanding notes $2432.15; per- sonal accounts $234.90. Did the firm gain or lose and how much? What was each partner's share of the gain or loss ? NOTE. The withdrawals of the partners must be added to the re- sources at closing to find total amount as if nothing had been drawn. 473. The investment, the resources and liabilities at closing and the proportion in which the partners share the gains or losses being given, to find each partner's interest in the concern at clos- ing. 1. A and B are partners. A is to share f of the gain or loss, and B f . At the close of business the following is shown to be the condition of their affairs, viz. : Cash on hand $2680. Bills receivable on hand $3620. Five shares Bank stock valued at $520. House and lot valued at $6000. Wilson & Co. owe on account $1800. The firm owe on notes outstanding $2840. They owe C. W. Lane on account $890. A invested $4610. B invested $4860. What* is A's interest in the concern? What is B's interest in the concern ? PARTNERSHIP 317 SOLUTION RESOURCES Cash on hand $2680 Bills Receivable 3620 Bank Stock 520 House and Lot 6000 Wilson Co. owe.. 1800 Net gain 5)1420 net gain. 284 i net gain. 3 $852 B's f net gain. 568 A's f net gain. $14620 13200 $1420 LIABILITIES Notes unpaid $2840 Due C. W. Lane 890 A invested 4610 B invested . . 4860 $13200 A invested 4610 A f net gain 568 A present interest in concern $5178 B invested 4860 B | net gain 852 B present interest in concern.. . $5712 2. C, D and E formed a copartnership, each to share of the gains and losses. At the close of the year the resources and liabilities were as follows : Cash in bank $3600. Stock of goods in store $10680. Bills receivable on hand $5820. Mining stock valued at $8730. Stock in Third National Bank $2850. Store building and lot valued at $28000. Account due from Lyons & Co. $865.30. W. C. Anderson owes the firm $1630. Wm. D. Barr owes the firm $178.50. The firm owe on their notes outstanding $4380. They owe Davis & Morse $1325. C invested $12650. D invested $12400. E invested $12250. What is each partner's interest in the concern at closing? 3. Jones, Brown and Smith entered into a copartnership, they to share gains and losses as follows : Jones f , Brown f and Smith J. After conducting business one year the following are the re- sources and liabilities : Cash on hand $3625. Mill and other real estate $8342. Bills receivable $1230. G. W. Samuels owes the firm $375. A. W. Dakin owes the firm $637. L. M. Painter owes the firm $1632. Stock in Globe National Bank $2430. Brown has withdrawn during the year $350. Smith has withdrawn $180. The firm owe on notes outstanding $5720. They owe H. 318 NEW BUSINESS ARITHMETIC B. Conant $1300. Jones invested $3600. Brown invested $3000. Smith invested $2800. What is each partner's interest at clos- ing? 4. F, G, H and I are partners. They share the gains and losses as follows : F and G each T 3 2, H T \ and I ^. After doing business one year they find the following resources and lia- bilities : Cash in bank $4230. Cash in safe $320. Merchandise in store $12840. Goods shipped away on consignments $1640. Real estate $6400. Horses and wagons $1000. Wheat and corn $930. Lumber $1730. Accounts receivable $2340. F has withdrawn from the business $350. H has withdrawn $260. The liabilities of the firm are notes outstanding $3860. Due Marshall Field & Co. $820. Due John W. Norris & Co. $135.40. Due N. K. Fairbank $216.30. F invested $5834. G invested $6243. H invested $6000. I invested $5635. What is each partner's interest in the concern at closing? 5. There are four partners in a concern, O, P, Q and R. Each partner to share of the gains or losses. At dissolution there is: Cash on hand $6820. Bills receivable $8922, C. B, & Q. R. R. stock $4500. Deposit in National Bank Commerce $3680. O has drawn from the concern $860. P has drawn $575. Q has drawn $630. R has drawn $452. The liabilities are: Notes and Acceptances outstanding $3680. Balance in favor of Smith & Co. $1264, in favor of Collins, Downing & Co. $860, Geo. Warner $575. O invested $5590. P invested $5322. Q invested $5540. R invested $5228. What has been the net gain or loss? What is each partner's interest in the business? 474. The investment and the gains and losses being given, to find the capital at closing. 1. A and B are partners, sharing the gains and losses equally. A invested $2865. B invested $3000. The gain during the year was $1860 on Merchandise. $76.20 Interest. The loss was $246.15 Expenses. $2.20 Exchange. $14.13 Discount on notes paid before they were due. Find the net gain, and the net capital .t closing, also each partner's interest at closing. PARTNERSHIP 319 SOLUTION B Balance $3701.861 Investment $2865 Balance $3836.86\ Investment $300C I Gain 836.86 I Gain 836.86- Profit and Loss Expense $246.15 Exchange 2.20 Discount 14.13 A's gain 836.86 B's gain 836.86 $1936.20 Mdse $1860 Interest 76.20 $1936.20 A's interest at closing $3701.86 B's interest at closing 3836.86 Firm's capital at closing $7538.72 2. Parker, Hammond and Siders formed a partnership for one- year, sharing gains and losses equally. Parker invested cash $3600, and withdrew during the year $230. Hammond invested cash $1200; Merchandise $1480; Notes $365; Accounts due him $240. He withdrew during the year $176. Siders invested real estate $1975 ; Cash $640 ; Potter's note of $220 that had been on interest at 1% for 1 year and 6 months. They gained $2468.45 on Merchandise and $29 interest on notes. The loss was $290.50 expenses for running the store. What was the interest of each partner, and the capital of the firm, at closing? 3. Stewart, Nevins and Barnard are partners in business. Stewart is to share f of the gains or losses, Nevins f and Barnard J. Stewart invested Dry Goods valued at $2250 with 2 and 10% off; White's Note of $1248, due in 6 months, on which he allows true discount at 8%. Nevins invested Cash $2500; Personal Ac- counts $426.80. Barnard invested Store and Lot worth $3250. During the term of partnership Stewart withdrew Merchandise $68.20 and invested $750 Cash. Nevins made an additional in- vestment of $1000 Cash and withdrew $110 worth of Merchan- dise. Barnard withdrew $420 Cash. The gains were $1968 on Merchandise, $220 Rent for part of store, $23.10 Interest. The losses were $360 Expenses, $33.95 on Personal Accounts. What. 320 NEW BUSINESS ARITHMETIC was the net worth of each partner, and the firm's net capital, at closing ? 4. A, B, C and D formed a copartnership for one year. A is to share j of the profits or losses, B f , C -J and D the remainder. On January 1, A invested cash $1200; Merchandise $280; Notes $760; Personal Accounts due him $316.90. On March 3, he withdrew $600. On January 1, B invested Merchandise $2200; on May 1, he invested $400 Cash and withdrew $23.15 worth of Merchandise. On January 1, C invested Cash $1800; Notes $500 with accrued Interest $17.80; Personal Accounts due him $176.40. On January 1, D invested Cash $2000; Merchandise $300 with 4 and 5% off. On June 16, he invested $620 Cash. The losses were $264.18 for Running" Expenses, other than the rent which was $275; 3% of Personal Accounts of $3729.70. The gains were $2394.13 on Merchandise; $23.66 Interest. Find the net worth at closing of each partner and also the firm. 475. To find each partner's gain or loss when the capital of the several partners is invested for the same length of time, and they are to share gains and losses in proportion to the capital in- vested. 1. A, B and C enter into copartnership in the grocery busi- ness for a term of 2 years. A invested $3600, B invested $4200, C invested $2400. At the close of the partnership term it was found that the net profits of the business had been $3570. What was each partner's portion of the profits? SOLUTION $3600 + $4200 + $2400 = $10200 total investment. $3570 -^ $10200 = .35 or 35% the rate of gain. $3600 X .35 = $1260 A's gain. $4200 X -35 = $1470 B's gain. $2400 X .35 = $840 C's gain. 2. Two speculators A and B operated together in buying and selling cattle. A made purchases amounting to $2735, and paid expenses amounting to $484.60. B made purchases amounting to $3687.50 and paid expenses amounting to $387.30. The cat- tle were sold by B for $8214.75. What is the gain or loss? How PARTNERSHIP 321 will the partners settle between them, the gains or losses to be shared in proportion to their investments? 3. Fuller, Irwin and Diers formed a partnership for 1 year and invested as follows : Fuller invested $1500 Cash. Irwin in- vested Merchandise $2000; Notes $200. Diers invested, Store $1250; Notes $350; Personal Accounts $200. Their resources at closing were : Cash $3160.35 ; Merchandise $2500 ; Notes $320 with Interest due $8.75 ; Personal Accounts $335.90. The gains were divided in proportion to the partner's investments. What was the total gain and each partner's gain? NOTE. Find the net gain or net loss by taking the difference between the investments and the resources at closing, then proceed as in the previous problem. 4. A, B and C engaged in business on August 1, 1901. A in- vested $2400, B invested $1700, C invested $2900. On August 1, 1902, the resources were as follows : Cash $3850 ; Merchan- dise $2690 ; Notes $1800 ; Personal Accounts $862.40 ; Horse and Wagon $285. The liabilities were Personal Accounts $192.40, Bills payable $260. During the year A withdrew $90 ; B $100 ; C $85. The gains were divided in proportion to the investment. What was the gain of each ? NOTE. The withdrawals of partners are resources to the business the same as personal accounts of other parties. 5. Jennings, Fuller and Clark engage in business for a term of two years. Jennings invests $3000; Fuller invests $1980; Clark invests $2370. On closing their books they found their gains as follows : On Merchandise $3194.20 ; Interest on Bills Receivable $93.60 ; Discount on their Notes paid before due $28.70. The losses were Running Expenses $150; Rent $200, Personal Accounts $26.50. What was the net gain of each, the gain being shared according to their investments? 6. F, G and H engage in the grocery business, agreeing to share gains and losses in proportion to their investments. F in- vests $1600; G invests $1800; H invests $2000. At the end of the partnership term they find their gains as follows: On Mer- 21 322 NEW BUSINESS ARITHMETIC chandise $1480 ; Discount on bills paid before due $148.30. The losses were: Expenses $540; Bad Debts $78.50. What was the net gain and each partner's share thereof? 476. To find each partner's gain or loss when the capital of the several partners is invested for different lengths of time, and they are to share gains and losses according to the amount of capital invested and time it is employed. 1. On January 1, A and B formed a partnership for one year. A invested $1700 on January 1, and $720 on March 1. He with- drew $600 on June 1. B invested $2000 on January 1, and $800 on April 1. He withdrew $750 on May 1. The net gain was $972. What was the gain of each partner? SOLUTION Find the time in months from the date of each investment and withdrawal to the end of the year. A invested $1700 X 12 = $20400 A invested 720 X 10 = 7200 A withdrew 600 X 7 =^200 | use of ^ 340 for l ' $23400 -J- 12 = $1950, A's average investment for 1 year. B invested $2000 X 12 = $24000 B invested 800 X 9 = 7200 B withdrew 750 X 8 = " ' use of $8520 for l mo " $25200 -f- 12 = $2100, B's average investment for 1 year. $1950 + $2100 = $4050 total investment for 1 year. $972 -r- 4050 = .24 or 24% gain on investment. $1950 X .24 = $468 A's gain. $2100 X .24 $504 B's gain. 2. Hammond and Cowles formed a partnership to run for 1 year from September 10, 1905. Hammond invested $3500 on September 10, $1800 on December 10, and $600 on March 10, 1906. Cowles invested $4200 on September 10, and $900 on Jan- uary 10, 1906. The net gain of the firm was $1990. What was each partner's gain? PARTNERSHIP 323 3. On March 1, 1905, Manning, Miller and Collins formed a partnership for 10 months. Manning invested $1400 on March 1, and $1250 on June 1. Miller invested $1760 on March 1, and $2400 on May 1. Collins invested $2100 on March 1, and $800 on August 1. The firm gained $5500.80. What was each part- ner's gain? 4. F. M. Tyler, H. F. Brady and P. W. Hess formed a part- nership on July 1, 1905, for 1 year. Tyler invested $4600 on July 1 and $1200 on December 1. He withdrew $1800 on February 1, 1906. Brady invested $7400 on July 1, and withdrew $2400 on January 1, 1906. Hess invested $6500 on July 1 and $3000 on March 1, 1906. The firm's net loss for the year was $1245. What was the loss of each partner ? 5. On May 18, 1905, A and B formed a partnership for 1 year. A invested $4000 on May 18 and $2700 on September 18. B in- vested $3500 on May 18 and $1800 on October 18. A withdrew $1900 on November 18 and $600 on January 18, 1906. B with- drew $900 on July 18 and $2100 on February 18, 1906. The net gain of the firm was $1589.50. Find the gain per cent, on the in- vestment and each partner's net gain. 6. On January 1, 1905, A, B and C formed a partnership which was dissolved August 20, 1905. At the beginning of the business each invested $2500. A invested $800 on April 11. B invested $950 on June 3. C withdrew $500 on May 30. The re- sources at closing were cash $8200, Merchandise $1650, Notes $840. Find each partner's gain or loss, there being no liabilities other than the investments. NOTE. Count the exact days in finding the time. 477. To find each partner's gain or loss when interest is al- lowed on the investments and charged on the withdrawals. 1. On April 1, 1905, A and B formed a partnership for one year. A was to share -f% of the gain or loss and B T V Each partner was to receive interest on his investments and pay interest on his withdrawals at 6%. The net gain for the year was $2772. What was the capital of each on April 1, 1906? The accounts on April 1, 1906, were as follows: 324 NEW BUSINESS ARITHMETIC Dr. A. Cr. 1905 1905 Sept. 1906 Jan. 1 1 Cash Bills Pay. 1200 800 April Aug. 1 1 Cash Mdse. 8000 3000 Dr. B. Cr. 1905 1905 Oct. 16 Cash 900 April 1 Cash 15000 SOLUTION Find the interest on each investment or withdrawal from its date to the date of settlement. A. Int. on $8000 for 1 yr. = $480. Int. on $3000 for 8 mo. = $120. $480 4- $120 = $600, A's credit interest. Int. on $1200 for 7 mo. = $42. Int. on $800 for 3 mo. = $12. $42 + $12 = $54, A's debit interest. $600 $54 = $546, A's net credit interest B. Int. on $15000 for 1 yr. = $900, B's credit interest. Int. on $900 for 5^ mo. = $24.75, B's debit interest. $900 $24.75 = $875.25, B's net credit interest. Carry the interest items to the Cr. side of the partner's ac- counts and Dr. side of Profit and Loss. Then close Profit and Loss account and credit each partner with his portion of the gain. PROFIT AND LOSS A's interest $546 00 Net gain . . . $2772.00 B's interest 87525 A's net gain 56282 B's net gain 787.93 I 5 ^ 2772.00 ] $2772.00 3 Cash $1200 Cash . . . .$8000 Cash $900 Cash . . .$15000 Bills Pay, 800 Netcap.,$10108.82 Mdse. . . Interest Net gain . 3000 . 546 . 562.82 Netcap.,$15763.18 Interest 875.25 Net gain 787.93 PARTNERSHIP 325 2. Wakeham, Griffin and Scallard formed a partnership on January 1, 1905, for 1 year; the gains and losses to be shared equally. Interest is allowed at 8% on all sums invested and withdrawn. On January 1, Wakeham invested $5000 ; on March 1, $1400. He withdrew $600 on June 1, and $300 on September 16. On January 1, Griffin invested $7500; on June 16, $1000. He withdrew $1500 on March 1, and $450 on July 1. On Jan- uary 1, Scallard invested $9000; on July 1, $1600. He with- drew $600 on April 1. They gained during the year $11916. What is each partner's capital on January 1, 1906? 3. On September 1, 1905, A, B, C and D formed a partner- ship for 16 months. Interest on partners' accounts is 6%. A is to share J of the gain or loss ; B, J ; C, ; D, J. A invested $4000 on September 1 ; B, $6000 on September 1, $1500 on March 1; C, $8000 on September 1, $2000 on August 16, 1906. D, $10000 on September 1, $2400 on January 1, 1906 ; $900 on June 16, 1906. B withdrew $900 on January 1, 1906; C, $1800 on September 1, 1906 ; D, $1600 on March 16, 1906 ; $840 on August 1, 1906. The net loss during the partnership was $21792. What was each partner's net credit interest and net capital at closing? 4. B. A. Harding, E. D. Wilson and J. P. Parrel formed a partnership for one year from August 20, 1905. Harding shared 25% of the gain or loss; Wilson, 35%; Farrel, 40%. Interest was allowed on all investments and withdrawals at 10%. Hard- ing managed the business at a salary of $1200. At the begin- ning of the business Harding invested $2500; Wilson, $3500 in Merchandise with 3% and 5% off; Farrel, $4000. On January 1, 1906, Harding withdrew $800; Wilson invested $1500; Farrel invested $500. At the close of the business the net gain, not in- cluding A's note of $300 which Farrel took at 60% of its face, was $2786.40. What was each partner's capital at closing, no interest being allowed on the salary ? NOTES. 1. When the time is less than one year find the time by counting the exact number of days. 2. After opening the Profit and Loss Account, charge it with 40% 326 NEW BUSINESS ARITHMETIC of A's note, and charge the remaining 60% to Parrel, and credit Profit and Loss with full amount. 3. Salaries are credited to the partners who earn them and charged to Profit and Loss account the same as interest. 5. A and B formed a partnership on January 1, 1905. A is to conduct the business and receive 65% of the gain, and B, whose time is not employed, is to receive 35% of the gain. On January 1, A invests $4000; on May 3, $1200, and withdraws $1600 on June 15. On January 1, B invests $3800; on March 23, $1800; and withdraws $860 on July 1. Each partner is to receive 8% interest on the amounts he invests, and pays 8% in- terest on all amounts which he withdraws; the interest is to be adjusted on the basis of each receiving ^ of the gain. The part- nership was dissolved on August 25, 1905, with a cash resource of $12000. They owed $450 to C, which B assumes. How much of the cash should each receive ? NOTES. 1. Find the time by counting exact days. 2. Since the interest is not adjusted on the same basis as other profits, it will be necessary to make up the Profit and Loss account with the interest only, and find remainder of gain or loss from the resources and liabilities. G. A, B and C commenced business on June 1, 1905, with re- sources as follows: A invested cash $4000, Merchandise $1800, Fixtures $250. B invested Store $4800, Cash $2750, Personal Accounts $800. C invested Cash $6000, Notes $1200, Accrued Interest $120. The firm assumed a mortgage of $2500 on the store, and A's note of $1450. A was to share 30% of the gain or loss; B, 35%; C, 35%. B was allowed $800 per year for keeping the books. On June 1, 1906, A invested $1500 ; B with- drew $1150; C invested $2000. On January 1, 1907, each part- ner withdrew $1000. June 1, 1907, the partners agreed upon a dissolution, the ledger showing: RESOURCES. LIABILITIES. Cash $9786.20. Notes $940! Mdse. $2314.30. Interest on notes $30. Notes $1420. Mortgage-balance $1500. Real estate $4000. B for salary $1600. Personal accts. $2694.40. PARTNERSHIP 327 Find the net gain or loss not counting interest on the partners' accounts. What was each partner's net worth at closing, if in- terest was allowed at 9% ? (No interest allowed on B's salary.) 7. J. W. White and H. Murray associating together, pur- chased a flouring mill for $8400, in which White holds a two- thirds interest and Murray one-third. During the year White paid out on account of the mill $1548.26, and received $4862.48. Murray paid out $956 and received $2686.40. A settlement is now made, the mill having just been sold for $9000; $4500 re- ceived, in cash and the balance a note at 60 days which both agree that White may take to apply on his account at 20% discount; and the $4500 is then properly divided between them; make the division. INVOLUTION 478. A Power is the product obtained by multiplying a number by itself, or using it as a factor. Thus, 9 = 3 X 3 is the second power of 3 ; 27 = 3 X 3 X 3 is the third power of 3. 479. The Exponent of a power is the number denoting how many times the factor is repeated. The exponent is usually a small figure, placed at the right and a little above the factor. Thus, 3 2 signifies that 3 is to be raised to the second power ; 3 3 signifies that 3 is to be raised to the third power, etc. 480. The Square of a number is the second power of the number. 481. The Cube of a number is the third power of the number. 482. Involution is the process of raising any number to a given power. From the preceding we have the following : To Raise Any Number to a Given Power a. Multiply the number by itself until it has been used as often as there are units in the exponent of the power. 1. Find the second power of 18. 2. What is the third power of 54 ? 3. What is the second power of 4.36 ? 4. Find the fourth power of 75. 5. What is the sixth power of 1.12 ? 6. What is the second power of 4.86 ? 7. What is the fifth power of 4? 8. Find the third power of .3 to three places. 9. What is the third power of -J-? 10. What is the fifth power of 1.04? 11. Raise 1.05 to the sixth power. 12. What is the eighth power of f ? 13. What is the second power of 4|? 14- Expand the expression 6 5 . 328 INVOLUTION 329 15. What is the second power of 5? 16. What part of 8 3 is 2 6 . 17. What is the difference between 5 C and 4 6 ? 18. Expand 3 5 X 2 4 ? 19. Express with a single index, 47 3 X 4? 5 X 47 6 . 20. How many acres are in a square lot, each side of which is 135 rods? 21. What is the sixth power of .01? 22. What is the fourth power of .03 ? 23. What is the fifth power of 1.05? 24. What is the third power of .001 ? 25. What is the second power of .0044? 26. Each side of a room is 12 feet long. How many square yards of carpet will be required to cover the floor ? 21. A box in cubical form is 6J feet long on any inner side. How many cubic inches will it contain ? 28. From 2.125 4 subtract 1 T V 3 . 29. From the fifth power of | take the fourth power of -J . EVOLUTION 483. A Root is the number which is multiplied by itself a given number of times to produce a given power. 484. Evolution is the process of finding or extracting the root of a power. Evolution is the exact reverse of Involution. 485. The Radical Sign is a character V placed over the num- ber considered as the power to indicate that the root is to be ex- tracted. 486. The Index of the root is a small figure placed above the radical sign to indicate what root is to be extracted. Thus <& in- dicates that the third or cube root of 64 is to be extracted. The square root is indicated by the radical sign alone without any in- dex. 487. A Perfect Power is a number whose root can be exactly extracted. Thus 64 is a perfect power whose third or cube root is 4. 330 NEW BUSINESS ARITHMETIC 488. An Improper Power is a number whose root cannot be exactly extracted. Thus 10 whose square root is 3.1622-}-. The only roots that are of much practical use are the Square and Cube roots. SQUARE ROOT 489. The Square Root of a number is one of the two equal factors that produce the number. Thus the square root of 25 is 5. By trial and inspection we find that the square of any number has twice as many or one less than twice as many figures as the number. Hence the square root of a number will contain as many figures as one-half the number of figures in the power and one figure more for an odd figure in the power. 1. Find the square root of 576 sq. ft. SOLUTION 5'76|2 4 44 176 176 20 rr 20 FT EXPLANATION. Pointing off the power into periods of two places each by the principle just laid down we see that there will be two figures in the root. Now it is required to con- struct a square which shall contain 57G sq. ft. We can see that the root of the left period is 2 and since there will be two figures in the root, this must be 2 tens or 20 ft. Construct a square which shall be 20 feet on each side as in the diagram. The surface. of this square is 20 X 20 = 400 sq. ft. But subtracting this 400 ft. (expressed as 4 in hundreds place in the solution) we still have 176 sq. ft. Our square must be increased to absorb this 176 sq. ft. This can be done by adding to two sides, and still retain the figure as a square. These two additions will together be 40 ft. long, and this explains why we "double the root al- ready found," in the solution. Now the length of our additions being 40 ft. the width will be as much as the length is contained times in the area. 176 + 40 = 4 ft. and this gives the second figure of the root. But our square is not yet complete. We still require a corner which we find is 4 ft. square. This corner added to the additions on the two sides gives the length of the three additions as 44 ft. INVOLUTION 331 2O FT and thus may be seen why we add the last fig- ure of the root to double the first. 44 ft. being the length of our additions and 4 ft. being their width, multiplying we have 176 sq. ft. as the area, and this we find exactly absorbs the re- maining area given in the power. We have therefore constructed a square, each side of which is 24 feet long, and the area of which exactly equals the area given, therefore we conclude that 24 feet, the length of one side is the square root of the given area, 576 feet. From this solution and explanation we have the following: To Find the Square Root a. Begin at the right hand and point off in periods of two figures each. b. Find the greatest square in the left hand period and place its root in the quotient. c. Subtract the square from the left hand period and bring down the next period. d. Double the root already found and place this at the left of the dividend for a trial divisor. Find how often this is contained in the dividend, exclusive of the right hand figure, and place the quotient in the result as the second figure of the root. e. Annex the last figure of the root to the trial divisor for the complete divisor. Multiply the complete divisor by the last figure of the root, write this under the dividend, subtract, bring dotvn the next period if any, and continue as before. NOTE. The square root of a fraction consists of the square root of its numerator over the square root of its denominator. Or, the fraction may be reduced to a decimal and then the root ex- tracted 2. Find the square root of 1024. 3. Find the square root of 1849. 4. Find the square root of 4225. 5. Find the square root of 61504. 6. Find the square root of 444889. 332 NEW BUSINESS ARITHMETIC 7. Find the square root of 390625. 8. Find the square root of 1679616. 9. Find the square root of *?j. 10. Find the square root of 30 J. 11. Find the square root of yVsV 12. Find the square root of 277?. 13. Find the square root of J. 14. Find the square root of 3. 15. Extract the square root of f . . 16. Extract the square root of 17f. 17. Extract the square root of .008836. 18. Extract the square root of .00006561. 19. What is the value of \/~3? 20. What is the value of V 125? APPLICATIONS OF SQUARE ROOT 490. An Angle is the space included between two straight lines which meet. Thus the two lines B A and C A meet and form an angle at A. 491. A Triangle is a figure bounded by three straight lines. The accompanying figure is a triangle. 492. A Right- Angle is the space between two lines when one is perpendicular to the other. Thus the angle at B is a right-angle. 493. A Right- Angled Triangle is a triangle having in it a right angle. 494. The Hypotenuse is the longest side, or the slanting side. Thus A C is the hypotenuse. B 495. The Base is the side upon which the tri- angle rests. Thus B C is the base. 496. The Perpendicular is the side which stands at right angles with the base. Thus A B is the perpendicular. INVOLUTION 333 It is a known principle, discovered and demonstrated over two thousand years ago by a Greek philosopher and mathe- matician that the area of the square de- scribed on the hypotenuse of a right- angled triangle is equal to the sum of the areas of the squares described on the other tivo sides. From this principle we have the following: To Find the Hypotenuse a. Add the square of the base and perpendicular together and extract the square root. To Find Either of the Shorter Sides Subtract the square of the given side from the square of the hypotenuse, and extract the square root. 1. The base of a right-angled triangle is 30 ft. and the per- pendicular is 40 ft. What is the hypotenuse? ' 2. The base of a right-angled triangle is 18 ft. and the hypot- enuse is 22 ft. What is the perpendicular ? 3. The perpendicular of a right-angled triangle is 64 inches and the hypotenuse is 82 inches. What is the length of the base? 4- A church steeple is 128 ft. high and stands 72 feet from the opposite side of the street. What is the length of a rope which will reach from the top of the steeple to the opposite side of the street ? 5. A window is 16 ft. 4 in. from the ground. What length of a ladder the foot of which placed 14 ft. 8 in. from the house, will reach to the window ? 6. A square field contains 40 A. How many rods of fence will be required for one side of it? How many rods of fence will be required to entirely enclose it? 7. A city lot in the form of a rectangle contains 5650 sq. ft. and its length is twice its width. What are its dimensions? S. A maypole broke off 23 ft. from the ground and in falling the top struck the ground 14 ft. from the bottom of the pole. How high was the pole? 334 NEW BUSINESS ARITHMETIC 9. A park is one mile square. What is the length ot a diag- onal path across it? 10. How many rods of travel does A save who goes diago- nally across a field 1 mile square in preference to going by its two sides ? 11. A room is 30 feet long, 25 feet wide and 12 feet high. What is the distance from one of the lower corners of the room to the opposite upper corner? CUBE ROOT 497. The Cube Root of a number is one of three equal factors which produce the number. Thus the cube root of 64 is 4. By trial we find that the cube of any number consisting of one figure can never exceed three figures, the cube of a number con- sisting of two figures can never exceed six figures, etc. Hence if we point off the power into periods of three figures each the number of periods will indicate the number of figures in the root. 1. Find the cube root of 91125 cu. in. SOLUTION 91'125|45 64 5425 480027125 600 25 27125 E X P L A N A TION. Pointing off the power into periods of three places each, by the principle just given, we see that the root will contain two places. It is required to construct a cube which shall contain 91125 cu. in. We see by inspection that the cube root of the left period is 4 and since there are to be two figures in the root this is 4 tens or 40. Construct a cube which shall be 40 in. on each side as in the diagram. The solid contents of this cube is 40 x 40 X 40 = 64000 cu. in. But subtract- ing the 64000 cu. in. (expressed in the solu- tion as 64 in thousands place) we still have 27125 cu. in. left. Our cube must be increased so as to absorb this, which can be done by adding to three sides of the cube, and still re- INVOLUTION 335 tain its cubical form. The surface of one face of the cube contains 40 X 40 = 1600 sq. in. and 3 faces will contain 3 times 1600 sq. in. or 4800 sq. in. This explains why we "square the root found and multiply it by 300 for a trial divisor," 300 being used instead of 3 because we have used the root found as units when they are really tens. We find that our trial divisor is contained in the dividend 5 times and this gives us the thickness of the additions. But our cube is not yet perfect. We must add three rectangular pieces at the cor- ners. These pieces will be 40 in. long and 5 in. wide and there being three of them their sur- face will be 40 X 5 X 3 = 600 sq. in. This ex- plains why we "multiply the last figure of the root by the last and by 30;" 30 being used in- stead of 3 because we called the 40 four units instead of 4 tens, which they really are. But our cube is still imperfect. We must add a small block at the corner. This will be 5 in. long and 5 in. wide and hence its surface will be 5 X 5 = 25 sq. in. which is also written in the divisor. Our complete divisor then is 5425 sq. in. which is the surface of all of the additions that we have made. Now multiply- ing this by the thickness, 5 in., we have the solid contents of all of these additions, 27125 cu. in. and this, we find, exactly consumes the cubical contents given. From this solution and explanation we have the following : To Find the Cube Root a. Begin at the right hand and point off in periods of three places each. b. Find the greatest cube in the left hand period and place its root in the quotient. c. Subtract the cube from the left hand period and bring down the next period. 336 NEW BUSINESS ARITHMETIC d. Square the root found and multiply it by 3 for a trial di- visor and affix or add two ciphers. Find how often this is con- tained in the dividend and place the quotient in the result as the next -figure of the root. e. Multiply the last figure of the root by the rest and by 3 and add or affix one cipher, and write the result under the trial divisor. f. Square the last figure of the root and place the result under the trial divisor. g. Add together the trial divisor and the two quantities beneath it and this will be the complete divisor which multiply by the last figure of the root. Write the product under the dividend, sub- tract , bring down the next period ', if any, and continue as before. 2. Find the cube root of 46656. 3. Find the cube root of 250047. 4- Find the cube root of 2000376. 5. Find the cube root of 5545233. 6. Find the cube root of 10077696. 7. Find the cube root of 46268279. 8. Find the cube root of 85766121. 9. Find the cube root of 153990656. 10. Find the cube root of 250047000. 11. What is the cube root of 926.859375? 12. What is the cube root of 44.6 ? Extract the cube root of the following numbers: 13. ^ 1 16. V 9 14. ^ 2 17. V 13. 15. y~3~ 18. &~W APPLICATIONS OF CUBE ROOT 1. What is each side of a square box, the solid contents of is 59319 cu. inches? INVOLUTION 337 6. What is the length of each side of a cubic vessel whose solid contents is 2936.493568 feet? 3. A store has its length, breadth and height all equal ; it can hold 185193 cubic feet of goods; what is each dimension? 4. How many linear inches must each dimension of a cubic vessel be which can hold 997002999 cubic inches of water? 5. What will be the length and depth of a bin which shall contain 160 bushels of corn, if its length is twice its width, and its depth and width are equal ? G. A bin is 18 ft. long', 12 ft. wide and 10 ft. deep. What must be the length of a cubical bin having the same volume ? 7. Give the dimensions of a cube having the same volume as a box 5 ft. 4 in. long, 2 ft. 8 in. wide and 3 ft. 6 in. deep. S, What is the surface of the six faces of a cube containing 91125 cubic feet? 9. A cistern in the form of a cube holds 150 barrels of water. What is each of its dimensions ? 10. A cubical bin holds 350 bushels of wheat. What is its length ? 11. Find the length of a cubical cistern which holds 5000 gallons of water. 22 MENSURATION 498. Mensuration is the art of computing lengths, surfaces and volumes. 499. A Line is that which has length only. All lines in men- suration and surveying are imaginary. 500. A Straight Line is the shortest distance between two points. 501. A Curved Line is a line having no part straight. 502. A Horizontal Line is a line parallel with the horizon, or with the water level. 503. A Vertical Line is a line perpendicular to the horizon. 504. An Angle is the space between two lines which meet. Thus the space between the lines A C and B C is an angle, called the angle A C B. 505. A Right Angle is an angle formed by the meeting of a horizontal line and a perpendicular angle. Right angle. An obtuse angle is one which is greater than a right angle. An acute angle is one which is less than a right angle. __ ._ _, . 1 . < 1 1 Obtuse / Acute 506. A Surface is that which has length angle. / angle. and breadth. B A Plane is a surface such that any two points of it can be joined by a straight line, which lies wholly in the surface. The application of a straight line is the test of a plane. 507. Area is a term applied to the quantity of surface con- tained in a figure having only length and breadth. 338 MENSURATION 339 508. A Solid is that which has length, breadth and thickness. PLANE FIGURES 509. To find the area of a square or rectangle. 510. A Square is a figure having four equal sides. A SQUARE. 511. A Rectangle is a figure having four right angles and its opposite sides equal. The reason for the following rule will be found by referring to Art. 172. A RECTANGLE. Rule. Multiply the length by the breadth, and the product will be the surface or area. PROBLEMS 1. What will it cost to pave a sidewalk 80 ft. long and 15 ft. wide at $1.50 per sq. yard? 2. How much will a farm cost which is 185 rods long and 125 rods wide at $45 per acre ? 3. How many small squares each containing 4 square inches, are contained in a large one which is 4 feet square ? 4. What will it cost to plaster a room 15 ft. 6 in. long 12 ft. 9 in. wide and 10 ft. 3 in. high at 37-J- cents per square yard? '). How many yards of carpeting f yd. wide will cover a floor 16 ft. 9 in. long by 15 ft. 9 in. wide, if laid lengthwise? 512. To find the area of a triangle. 513. The Base of a triangle is the side on which it rests. 514. The Altitude of a triangle is the perpen- dicular distance from the base to the opposite angle called the apex. Since every angle in equivalent to one-half of a square or parallelogram having the same base, we may find the area of the squares or parallelogram and divide by two, or 3/*-cording to the following: 340 NEW BUSINESS ARITHMETIC Rule. Multiply the base of the triangle by its height, and di- vide the result by two. PROBLEMS 1. How many square yards in a triangle whose base is 27 yards and altitude 36 yards? 2. The gable end of a house was 34 ft. 6 in. from eave to eave and the perpendicular height of the ridge above the eaves is -13 ft. How many feet of boards will be required to cover three such gables ? 3. A lot of ground 80 ft. long by 20 ft. wide was cut diago- nally by a railroad, leaving a triangular plot of the same base and altitude ; what was its area ? 4. What is the rent of a triangular field whose base is 80 rods and perpendicular height 48 rods, at $4.50 per acre? 515. To find the circumference or diameter of a circle. 516. A Circle is a plane figure bounded by a curve line, every part of which is equally distant from a point within called the center. 517. The Circumference of a circle is the curved line by which it is bounded. 518. The Diameter is a straight line drawn through the center, terminating at each end in the circumference. 519. The Radius is a straight line drawn from the center to the circumference, and is equal to half the diameter. It has been proven in geometry that the circumference of every circle great or small is 3.1416 times its diameter, hence the Rule. a. To find the circumference of a circle multiply the diameter by 3.1416. b. To find the diameter of a circle divide the circumference by 3.1416. PROBLEMS 1. What is the diameter of a circular piece of land measur- ing 5 J miles around it ? MENSURATION 341 2. The diameter of a circular race course is f of a mile, how many rods of fence will be required to enclose it? 3. A circular park is two miles in circumference; what is its diameter ? 4. A horse is fastened to a tree by a rope 37 feet long. What is the circumference of the circle in which he may graze ? 5. What is the diameter of a wheel which makes 420 revolu- tions in a minute when the cars are running at the rate of 45 miles per hour ? 520. To find the area of a circle. Rule. Multiply the diameter by the circumference and divide the product by 4- Or, multiply the square of the diameter by .7854. PROBLEMS 1. What is the area of a circle whose diameter is 36 feet? 2. A circular park requires 145 rods of fence to enclose it, how many acres does it contain? 3. Find the area of a space on which a horse may graze when confined by a rope 125 feet long. 4. A circular fish pond has a radius of 75 feet; what is its area? 5. How many square feet in a circular grass plot 75 feet in diameter ? SOLIDS 521. A Solid is that which has length, breadth and thickness. 522. A Prism is a solid whose bases are similar, equal and parallel, and whose sides are parallelograms. 523. All rectangular solids are prisms. 524. A Right Prism is one whose sides are perpendicular to its bases. 342 NEW BUSINESS ARITHMETIC 525. A Rectangular Prism is one whose bases are rectangular and its sides perpendicu- lar to its bases. 526. A Triangular Prism is one whose bases are triangles. NOTES. 1. Prisms are named from the form of their bases, as triangular, quadrangular, pentag- onal, hexagonal, etc. 2. When their sides are all equal to each other they are called cubes. 527. A Cylinder is a round prism, or one hav- ing circles for its ends. 528. A Pyramid is a solid having for its base any plane figure and for its sides triangles which terminate in a common point called the vertex. 529. A Cone is a body which has a circle for a base and whose sides terminate in a point called the vertex. 530. A Frustum of a pyramid or cone is the part which is left after the top is cut off by a plane parallel or inclined to the base. 531. To find the surface of a prism or any figure having plain sides. Rule. Find the area of each surface separately, and add the re- sults. PROBLEMS 1. Each side of a triangular prism is 3 ft. long and 9 inches wide. What is the area of its surface, not including the ends ? 2. What is the area of a pyramid having 6 sides each 2 feet at base by 6 feet in slant height ? 532. To find the convex surface of a cylinder. Rule. Multiply the circumference of the base by the altitude. PROBLEMS 1. How many square feet of surface in the sides of a cylinder 16 J feet long and 12 feet in circumference? MENSURATION 343 2. A smoke stack is 40 feet high and 9 feet 4 inches in cir- cumference. How many square feet of sheet iron are contained in it? 3. What is the surface including the ends, of a cylinder 5 feet long and H feet in diameter? 4- A log is 60 ft. long and 10 ft. in circumference. What is the surface of its sides? 533. To find the solid contents of a prism or cylinder. Rule. Multiply the area of the base by the altitude. PROBLEMS 1. Find the solid contents of a square prism, the base being 5 feet each side, and 17 feet high. 2. A well is 45 feet deep and 4 feet in diameter. How many gallons of water will it hold? 3. A cistern is 8 feet by 6 feet and 14 feet deep. What is its solid contents in gallons? 534. To find the solid contents of a pyramid or a cone. It has been demonstrated in geometry that a pyramid is l /z of a prism of the same base and height and a cone is y$ of a cylinder of the same base and height. Rule. Multiply the area of the base by the altitude and divide by 3. PROBLEMS 1. What are the contents of a pyramid whose base contains 144 square feet and its altitude is 36 feet? 2. What are the contents of a cone whose base contains 3624 square feet and its altitude is 27 feet? 3. A monument in the form of a pyramid is 18 ft. 6 in. by 16 ft. 9 in. at the base, and its altitude is 67 ft. 3 in. What is the amount of solid stone contained in it? 4- A pyramid is 430 ft. high and each side of its base is 520 feet. What are its solid contents? 535. To find the surface of a globe, the circumference and diameter being given. 344 NEW BUSINESS ARITHMETIC 536. A Globe or sphere is a body every point of the surface of which is equally distant from a point within called the center. 537. The Diameter of a sphere is a straight line passing through the center and terminating both ways at the circumfer- ence. 538. A Hemisphere is half a sphere. Rule. . Multiply the square of the diameter by 3.1416. PROBLEMS 1. A perfect sphere is 34 feet in diameter. What is its sur- face? 2. What will it cost to gild a ball 12 inches in diameter at 10 cents a square inch? 3. If the earth is 7912 miles in diameter what is its area, sup- posing it to be a perfect sphere ? 539. To find the solid contents of a sphere. Rule. Multiply the cube of the diameter by .5236. PROBLEMS 1. What is the solid contents of a cannon ball 15 inches in diameter ? 2. A balloon is 30 ft. in diameter. How many cubic feet of gas does it contain, supposing it to be a perfect sphere? 3. The basin of a fountain is a hemisphere 22^ ft. in diameter ; what are its cubical contents? 4. How many hogsheads of water will it contain? METRIC SYSTEM 540. The Metric System of weights and measures is a system in which the denominations increase and decrease by the decimal scale. The metric system originated in France, and on account of its sim- plicity has been adopted in nearly all European countries, Mexico, South America, and in 1866 by the Congress of the United States. Its use in the United States has not become general, but is confined mostly to the arts and sciences, the coast survey and a portion of the mint and post office. For this reason the subject will not be extensively treated in this book. 541. The Meter is the base of the system and is one ten millionth part of the distance from the equator to the pole, or 39.37 inches, nearly. The Metric System has three principal units, the Me'ter (meeter), Li'ter (leeter) and Gram. To these are added the Ar and Ster for square and cubic measure. Each of these units has its multiples and divisions. 542. The Lower Denominations are formed by prefixing to the name of the unit, dec'i, cen'ti and mil'li. Thus from dec 1 i, yV we have dec'i me'ter yV meter. from cen ti, T^ we have cen'ti me'ter TOIT meter, from mil'li, -nnnr we have mil'li me'ter nAnr meter. 543. The Higher Denominations are formed by prefixing to the name of the unit, dek'a, hek'to, kil'o and myr'ia. Thus from dek' a, 10 we have dek'a me'ter 10 meters. from hek' to, 100 we have hek'to me'ter 100 meters, from kil'o, 1000 we have kil'o me'ter 1000 meters, from myr ' ia, 10000 we have myr ' ia me ' ter 10000 meters. 345 346 NEW BUSINESS ARITHMETIC Metric Linear Measure TABLE 10 mil'li-me'ters (mm.) = 1 Cen'ti-me'ter cm. (^ m.) 10 cen'ti-me'ters = 1 dec'i-me'ter dm. (^ m.) 10 dec'i-me'ters = 1 METER m. 10 me'ters = 1 dek'a-me'ter Dm. (10 m. ) 10 dek'a-me'ters = 1 hek'to-me'ter Hm. (100 m.) 10 hek'to-me'ters = 1 Kil'o-me'ter Km. (1000 m.) 10 kil'o-me'ters = 1 myr'ia-me'ter Mm. (10000 m.) NOTES. 1. The principal unit of each table is printed in capital let- ters ; those in common use in full-faced Roman. 2. The Accent of each unit and prefix is on the first syllable, and remains so in the compound words. 3. Abbreviations of the higher denominations begin with a capital, those of the lower with a small letter. Metric Square Measure TABLE 100 square centimeters, sq. cm. = 1 square decimeter = 15.5 -f sq. in. 100 square decimeters, sq. dm. = 1 square meter = 1.196 sq. yd. NOTE. It will be observed that the units of square measure are the squares of the units of linear measure. Therefore 100 units of any de- nomination are the equivalent of 1 unit of the next higher denomination. Metric Land Measure TABLE 1 centare, ca. = 1 sq. M. 100 centare = 1 are, A. 100 A =1 hectare. NOTE. The hectare is the unit used in the measurement of land as the acre is the common unit in this country. It is the equivalent of 10,000 square meters. Metric Cubic Measure TABLE 1000 cu. millimeters, cu. mm. = 1 cu. centimeter. 1000 cu. centimeters, cu. cm. = 1 cu. decimeter. 1000 cu. decimeters, cu. dm. = 1 cu. meter. NOTE. It will be observed that the units of cubic measure are the cubes of the units of linear measure. Therefore 1000 units of any de- nomination are the equivalent of 1 unit of the next higher denomination. METRIC SYSTEM 347 Metric Wood Measure TABLE 10 decisters, ds. = 1 ster. 10 sters, s. =1 dekaster. NOTE. In wood measure the ster is the unit. It is the equivalent of one cubic meter. Metric Measure of Capacity TABLE 1 milliliter, ml. = ujfoj of a liter. 10 milliliters = 1 centiliter, cl. 10 cl. = 1 deciliter, dl. 10 dl. = 1 liter, 1. 10 1. =1 dekaliter, Dl. 10 Dl. = 1 hectoliter, HI. 10 HI. = 1 kiloliter, Kl. NOTE. There is but the one table for both dry and liquid measure and the unit is the liter. The liter is the equivalent of a cubic decimeter, 1.0567 wine quarts or .908 dry quarts. Measure of Weight TABLE f gram = 1.543 gram gram, g. dekagram, Dg. hectogram, Hg. kilogram, Kg. or Kilo, myriagram, Mg. quintal, Q. ton. In the metric system there is but one table of weight, all articles both heavy and light being measured by it. 1 decigram, dg. = 10 dg. 10 g. 10 Dg. 10 Hg. 10 Kg. 10 Mg. 10 Q. Tables of Equivalents 1 inch = 2.54 centimeters. 1 foot = .3048 of a meter. 1 yard = .9144 of a meter. 1 rod = 5.029 meters. 1 mile = 1.6093 kilometers. LINEAR MEASURE centimeter = .3937 of an inch, decimeter = .328 of a foot, meter = 1.0936 yards, dekameter = 1.9884 rods, kilometer = .62137 of a mile. 348 NEW BUSINESS ARITHMETIC SQUARE MEASURE 1 sq. inch = 6.452 sq. centimeters. 1 sq. centimeter = .155 of a sq. inch. 1 sq. foot = .0929 of a sq. meter. 1 sq. decimeter = .1076 of a sq. foot 1 sq. yard = .8361 of a sq. meter. 1 sq. meter = 1.196 square yards. 1 sq. rod = 25.293 of a sq. meter. 1 are = 3.954 sq. rods. 1 acre = 40.47 ares. 1 hectare = 2.471 acres. 1 sq. mile _ 259 hectares. 1 sq. kilometer = .3861 of a sq. mile. CUBIC MEASURE 1 cu. inch = 16.387 cu. centimeters. 1 cu. centimeter .061 of a cu. inch. 1 cu. foot = 28.317 cu. decimeter. 1 cu. decimeter = .0353 of a cu. ft. 1 cu. yard = .7645 of a cu. meter. 1 cu. meter = 1.308 cu. yard. 1 cord = 3.624 ster. 1 ster = .2759 of a cord. MEASURES OF CAPACITY 1 liquid quart = .9463 of a liter. 1 liter = 1.0567 liquid quarts. 1 dry quart = 1.101 liter. 1 liter = .908 of a dry quart. 1 liquid gallon = .3785 of a dekaliter. 1 dekaliter = 2.6417 liquid gallons. 1 peck = .881 of a dekaliter. 1 dekaliter - 1.135 pecks. 1 bushel = .2524 of a hektoliter. 1 hektoliter = 2.8375 bushels. MEASURES OF WEIGHT 1 grain, Troy = .0648 of a gram. 1 gram = .03527 of an ounce, Avoir. 1 ounce, Avoir. = 28.35 gram. 1 gram = .03215 of an ounce, Troy. 1 ounce, Troy = 31.104 grams. 1 gram = 15.432 grains, Troy. 1 Ib. Avoir. = .4536 of a kilogram. 1 kilogram 2.2046 pounds, Avoir. 1 Ib. Troy = .3732 of a kilogram. 1 kilogram = 2.679 pounds, Troy. 1 ton (short) = .9072 of a tonneau. 1 tonneau = 1.1023 tons (short). PROBLEMS 1. Reduce 763217 meters to kilometers. 2. Reduce 318.462 kilometers to meters. S. Reduce 395.16 kilometers to centimeters. 4. Reduce 51626 centimeters to meters ; to kilometers. 5. If a man traveled 171 kilometers in a day, how many miles did he travel ? 6. If it cost $.22J per meter for a fence, what will be the cost of a similar fence f kilometers long? 7. If it is 980 miles from New York to Chicago, how many kilometers is it ; how many hectometers ? 8. 18.5 yards are how many meters ? 9. Write 6 meters, 3 decimeters and 5 centimeters as one number with the meter as the unit. METRIC SYSTEM 349 10. Express 19.763 m. in decimeters ; in centimeters. 11. In 5638 square meters how many ares; how many hectares? 12. In 218.75 hectares how many square meters; how many centares? 13. How many hectares in a farm 2.168 Km. long and 1.33 Km. wide? 14- What is the cost of a cement walk 5.64 m. long and f m. wide at $2.60 per sq. m.? 15. A farm contains 192 hectares, if it is .376 Km. wide how long is it? 16. Express in hectares the equivalent of 247.1 acres. 17. Write as cubic meters 15 cubic decimeters, 4 cubic centi- meters and 8 cubic millimeters. 18. Write the equivalent of these numbers in cubic deci- meters: 14 cu. m., 18 cu. dm., 36 cu. cm. 19. A vessel is 1 m. long, f m. wide and 1J m. high ; how many liters does it contain ? 20. If a gallon of milk costs $.25 what should be the price per liter? 21. A bin contains 5689.35 hectoliters of wheat. What is it worth at $.32 per dekaliter?, 22. A cistern 2.75 m. by 3.25 m. by 7.5 m. will hold how many dekaliters ? How many cu. m. ? 23. Write as liters in one number 3 L, 6 dl., 4 cl. and 5 ml. 2Jf. How many grams in 1 Kilo. ? 25. How many kilograms in 1 ton? 26. 5 Kilos, equal how many pounds? 27. 1 ton equals how many pounds av. ? 28. How many powders of 7 grams each can be made from 637 kilograms? 29. How many sters in a pile of wood 1 m. wide, 3 m. long and j m. high ? 30. How many cubic meters in a box f m. wide, 1 j m. high and 3 m. long? 31. In 46328 cu. dm. how many cu. meters? 82. In 68.4 ares there are how many square meters? 350 NEW BUSINESS ARITHMETIC VALUES OF FOREIGN COINS IN UNITED STATES MONEY (Proclaimed by the Secretary of the Treasury, October 1, 1903) COUNTRY. Stand. Monetary unit. So!,; S*J5 |l:i >~ Coins. Argentine Rep. Aust.-Hungary Belgium . Bolivia Brazil British Posses. N. A. (except Newf'nd) Cen. Am. St. Costa Rica.... Brit Honduras Guatemala.. "] Honduras... 1 Nicaragua . . f Salvador.... j Chile China Gold Gold Gold... Silver.... Gold Gold Gold Gold Silver . Peso- Crown Franc. Boliviz Milreif Dollar Colon.. Dollar Peso.. . mo $0.965 .203 .193 .408 .546 1.000 .465 1.000 .408 .365 .659 .657 .630 .644 .610 .671 .617 (t) .652 .618 .634 .643 .602 .609 .663 .639 .408 .926 .268 .487 4.943 .193 .193 .238 4.866^ .193 .965 4.866^ .193 .498 1.000 .443 Gold: argentine ($4.824) and % argtii- tine. Silver: peso and divisions. Gold: former system 4 florins ($1.929), 8 florins ($3.858\ ducat ($2.287) and 4 ducats ($9. 149). Silver: 1 and 2 florins. Gold: present system 20 crowns ($4.052); 10 crowns ($2.026). Gold: 10 and 20 francs. Silver: 5 francs. Silver: boliviano and divisions. Gold: 5, 10 and 20 milreis. Silver: X, 1, and 2milreis. Gold: 2, 5, 10 and 20 colons ($9.307). Silver: 5, 10, 25 and 50 centimes. Silver: peso and divisions. Gold: escudo ($1.825), doubloon ($3.650\ and condor ($7.300). Silver: peso and divisions. [dor. Silver: peso. Gold: condor ($9.647) and double-con - Gold: Doubloon Isabella, cent en ($5.017). Alphonse ($4.823). Silver: peso. Gold: 10 and 20 crowns. Gold: 10 sucres ($4.8665). Silver: sucre and divisions. Gold: pound (100 piasters), 5, 10, 20 and 50 piasters. Silver: 1, 2, 5, 10 and 20 piasters. [($1.93). Gold: 20 marks ($3.859), 10 marks Gold: 5, 10, 20, 50 and 100 francs. Silver: 5 francs. Gold: 5, 10 and 20 marks. Gold: sovereign (pound sterling) and ^ sovereign. [Silver: 5 drachmas. Gold: 5, 10, 20, 50 and 100 drachmas. Gold: 1, 2, 5 and 10 gourdes. Silver: gourde and divisions. Gold: sovereign (pound sterling.) Silver: rupee and divisions. [5 lire. Gold: 5, 10, 20, 50 and 100 lire. Silver: Gold: 5, 10 and 20 yen. Silver: 10,20 and 50 sen. Gold: dollar ($0.983), 2&, 5, 10 and 20 dollars. Silver: dollar (orpeso> and divisions. Gold Silver.... Peso... Tael.. , JO a M 48 47 : & \ Buckwheat. I Shelled corn. 1 c o . ,C I- 1 u > JO United States.... Alabama 70 =55 56 Alaska 60 60 60 Arizona 60 60 60 60 60 60 56 56 54 56 56 32 32 32 32 32 45 48 50 48 48 52 4( 5_ 48 54 56 52 S( 56 =56 "70 60 57 57 60 60 "SO 56 "so 60 45 45 Arkansas Colorado 70 60 60 57 52 50 60 60 "48 55 Connecticut Dist. of Columbia Florida 60 60 60 60 60 60 60 56 56 56 56 56 56 56 32 32 32 32 36 32 32 56 60 48 47 48 48 48 48 52 56 56 Sfi 70 70 60 60 56 57 54 55 c60 60 48 56 50 45 60 Georgia Idaho . .. . 42 52 50 56 56 56 "70 d68, 60 60 60 57 48 55 55 "60 60 45 56 56 "so 45 45 60 60 60 Indiana Indian Territory. Iowa 60 60 60 60 60 56 56 56 f32 32 32 32 32 30 ?fi 48 4* 1 52 50 56 56 56 56 S6 70 70 *70 60 60 60 57 57 57 55 60 60 60 60 48 48 56 56 56 SO 50 50 45 45 45 60 60 60 Kansas Kentucky Louisiana Maine Maryland..! 48 56 60 56 52 50 60 44 .. .... 45 Massachusetts .. Michigan 60 60 60 60 60 60 60 56 56 56 56 56 56 56 52 32 32 32 32 32 32 48 48 48 48 48 48 48 48 48 50 48 52 52 52 56 56 56 56 56 56 56 "70 70 72 70 70 70 60 60 60 60 60 60 60 52 54 57 57 57 57 48 52 55 42 55 60 60 60 60 60 60 60 48 48 50 1-48 MS 55 56 56 56 56 56 *% 48 50 50 "so 45 45 45 45 45 45 45 60 60 60 60 60 60 60 Minnesota Missouri. . . Montana Nebraska Nevada New Hampshire. New Jersey New Mexico 60 60 56 56 32 30 "48 50 56 56 .... 60 60 57 .. 62 60 50 55 55 55 56 56 56 64 60 60 60 60 60 60 60 "so 50 45 42 45 42 New York.. . . 60 60 60 60 60 60 60 56 56 56 56 56 56 56 32 32 32 32 32 32 32 48 48 48 48 48 46 47 48 50 42 50 \2 42 48 56 56 56 56 56 56 56 "70 68 70 60 60 60 60 60 56 57 52 55 52 50 60 60 60 60 "60 60 60 48 50 '4s North Carolina.. North Dakota.... Ohio Oklahoma Oregon Pennsylvania. . . . Philippines Porto Rico Rhode Island Samoa 60 56 32 48 48 56 70 60 50 50 60 48 56 50 45 60 South Carolina.. South Dakota.... Tennessee 60 60 56 56 32 32 48 48 42 50 56 56 70 70 6052 6056 60 50 60 60 'so 56 56 'so 42 45 60 60 LEGISLATIVE ENACTMENTS. Act July 18, 1866. Tariff act, 1897. Act Feb. 18, 1891. Comp. Laws, 1864-71. Act Mar. 30, 1887. Code and Stat., 1886. Gen. Stat., 1891. Gen. Stat., 1902. Acts 1853, 1867, 1896. Webb's Laws, 1868. U. S. Stat., 1896. Stat., 1901. Code, 1895. Penal Laws, 1897. Laws, 1899-1903. Rev. Stat., 1899-1901. Rev. Stat., 1897. Rev. Code, 1897, and Laws, 1902. Gen. Stat., 1901. Gen. Stat., 1888. Rev. Laws, 1884-1897. Rev. Stat., 1883, Sup. 1895, Act, 1897. Code, 1888, and Sup. 1890-1900. Rev. Laws, 1902. Com. Laws, 1897. Rev. Stat. 1897. Code, 1892, and Act Mar. 12, 1900. Rev. Stat. 1899. Stat. 1888, 1901. Com. Stat., 1901-1903. Pub. Stat:, 1901. Gen. Stat., 1895. Gen. Laws, 1902. Act, Jan. 31, 1885. Code, 1899, and Act, Mar. 1901. Rev. Stat., 1902. Rev. Stat., 1903. Code, 1902. Digest, 1700-1901. Metric system. Do. Pub. Laws, 1900. English Weights and Measures. Laws of 1903. Stat., 1901. Act, 1887. STATUTORY WEIGHTS OF THE BUSHEL 353 STATUTORY WEIGHTS OF THE BUSHEL Continued. d 4 STATES AND TERRITORIES. 1 sd corn. on cob. .2 U I) 1 ri I s 1 1 ** -o JS 1 LEGISLATIVE ENACTMENTS. i u 2 S ^ s d en s c a X > * & a 3 23 J3 V3 3 O * P. .^4 U Texas.. . 60 S6 V- 48 4? 56 70 60 57 55 60 45 56 SO 45 60 Act, Apr. 18, 1901. Utah. . .. Vermont 60 56 V, 48 48 56 60 5? 60 6? 46 45 60 Stat., 1894. Virginia 60 V) 48 5? 56 70 56 57 55 60 45 56 50 45 60 Code, 1887, and Act, Feb. 24, 1898. Washington 60 S6 V 48 4? 56 60 45 56 60 Stat., 1897. West Virginia... 60 56 32 48 52 56 60 60 56 45 60 Code, 1899. 60 56 "P 48 50 56 70 60 57 -P 60 50 56 50 45 60 Stat 1898 and Act Mar. 30, 1901. Wyoming c Velvet beans in hull, 78. d Before Dec. 1, 70. May 1 to Nov. 1, 68. f So in statutes, but an evident error. e Japanese barnyard millet. ANSWERS ADDITION Article 34. 6. 13054. 22. $15667. 38. $22290. 2. 889. 7. 17059. 23. 10060 Ibs. 39. 695 head. 3. 698. 8. 3127. 24. $15762. $5698. 4. 967. P. 31945. 25. $641. 40. $5155. 5. 898. 10. 122223. 26. $9079. 41. $196910. 6. 6546. 11. 469294. 27. $5285. 42. 40000. 7. 786. 12. 2601786. 28. 4305 bu. 43. 26520. 8. 766. IS. 15448707. 25. 4619. 44- 23029. P. 9657. 14. 2134. 30. 4915. 45. 176597. W. $583. 15. 11932. 31. 4320. 46. 1106771. Article 35. & 186. 16. 149271. 17. $3162. .15. $21367. 32. 4623. 33. 3871. 34. 39267. 47. 1349248. 48. 18366751. 49. 15971078. 3. 1492. 19. 32515 ft. 35. $11024. 50. 7556628. 4. 2715. 00. 77604. 36. $8304. 51. 4187383. 5. 9767. 21. 504689. 37. $435. SUBTRACTION Article 41. 12. 62114 bricks. 13. 50435 yds. ilO. 21078. ( 11. 142. 22. 1902001. 23. $1482. 2. 32. 5. 72. Article 42. \12. 762301. 13. 138. 24. $5457. 25. $4251. 4. 55. 2. 335. 14. 4786. 2ft $4315. 5. 542. 5. 2561. 15. 36824. 27. $9860. (5. 261. 4. 561. 1ft 22988. 28. $4644. 7. 712. 5. 3769. 17. 89093. 29. $2948. 5. $232. ft 269. 18. 296853. 30. $1288. 5. $235. 7. 4509. 19. 15744. 31. 1250. 0. $2855. 5. 1288. 20. 4373. 32. $1316. /. 2307 bu. 9. 30616. 21. 988606. 33. $683.65. 34. $498.30. 35. $23107.02. MULTIPLICATION Article 43. 2. 3248. 3. 7308. 4. 7348. 5. 16310. 6. 50550. 7. 20909. 8. 25632. 9. 41616. 10. 13140. 11. 27738. 12. 42115. 13. 44289. 14- 25374. 15. 131235. 1ft 327872. 17. 163215. 18. 194076. 19. 348096. 20. 222848. 21. 348921. 354 22. 10588 gal. 23. $13225. 24. $1911. 25. $2072. 2ft $32778. 27. 768 mi. 28. $261051. ANSWERS 355 Article 49. t. 17155. 3. 16668. 4. 13936. 5. 54128. 6. 113542. 7. 1067616. 8. 15824. ft 1007616. 10. 407000. 77. 5460200. 72. 5031110. 13. 5254000. 14. 10800000. 75. 17313936. 16. $171784. 77. $208656. 18. $51121. 70. 792000. 20. 8820000. 21. $34692. 00. $153832. 23. 152000 Ibs. 04. 53640 Ibs. 25. $16560. 00. 205821 gal. 27. 545622 cu. in. 28. 52752 Ibs. 05. 208250 cents. 30. 7878000 steps. 31. 770400 words. 32. 846720 Ibs. 33. 2016000 cents. Addition, Subtraction and Multiplication Article 50. $102. 8. $27. 70. $7700. 38400 cents. 5. $2865. 9. $261. 13. $11960. $595. 6. B, $600. 70. 1296 miles. 74. $310. $344. 7. $171. 77. $200 gain. 75. $5025. DIVISION Article 56. 19. 1162. 10. 212, Rem. 92. 07. $176. 3. 432. 312. 20. 21. 1324. 1214. 11. 12. 958. 7198. Article 58. '/. 110. 22. 420. 13. 1489, Rem. 33. 0. 6034, Rem. 3d 5. 3124. 23. 2853. 74. 329916. 3. 25. 6. 3212. 24. 4754. 75. 14142. 4. 19, Rem. 20. 1. 1221. 25. 16227. 16. 12152, Rem. 9. 5. 15, Rem. 65. 8. 9. 4312. 3102. Article 57. 17. 18. 1444. 8862. 6. 7. 478. 75, Rem. 550. 10. 20120. 2. 213. 19. 463**. 8. 469, 11. 10203. 3. 34. 20. 329. Rem. 1470. 12. 10420. 4. 67. 21. 479AV- 9. 350. 13. 1011. 5. 247. 22. 535*}. 10. 1285, IS. 430. 6. 314. 23. 128. Rem. 2080. 16. 735. 7. 48. 24. $108. 11. 75. 17. 832. 8. 135. 25. $96. 12. $240. W. 382. 9. 344. 26. HI Addition , Subtraction, Multiplication and Division Article 59. 10. 516. 18. B, $4200 ; C, 05. 45 yards. 1. $154. 11. $18394. $15780; all 26. 2474. $981. 12. $2953. $20940. ' 27. $1490. .5. 12. 13. 12. 19. Gained $13. 28. $8269. * 390. 74. 80. 20. 20 yrs. 29. $10185. 5. $712. 75. $8. 21. $9150. 30. 450 sheep. 6. $336. 16. $3468. 22. $4. $5050. 7. 240. 17. Daughter 23. Grocer owed .9. $120. $12923; each farmer 12 cts. .9. $2904. son $13763. 24. 15 cents. FACTORING Article 67. 6. 5,7. 11. 2, 2, 3, 3, 3. 16. 3, 7, 11. j 3, 3. 7. 2, 3, 7. 12. 2, 2, 2, 3, 5. 77. 2, 2, 2, 2, 2, $'. 2, 2, 3. 8. 2, 5, 5. 13. 2, 2, 31. 3,3. 4- 3, 2, 3. 9. 3, 2, 11. 14. 2, 3, 31. 18. 2, 3, 7, 7. 5. 3, 3, 2, 2. 10. 2, 2, 2, 2, 2, 3 . 15. 5, 5, 3, 3. 19. 3, 3, 3, 11. 356 NEW BUSINESS ARITHMETIC 20. 2, 2, 3, 5, 5. 25. 2, 2, 2, 2, 41. 30. 2, 3, 3, 7, 23. 34. 2, 2, 11, 79. 21. 5, 7, 11. 20. 2, 2, 3, 3, 3, 7. 31. 2, 2, 29, 37. 35. 2, 5, 17, 31. 22. 3, 5, 31. 27. 19, 67. 32. 3, 2, 29, 53. 30. 2, 2, 3, 19, 3, 13. 23. 3, 5, 5, 7. 2& 2, 2, 2, 5, 73. 33. 3, 11, 13, 19. 37. 11, 29, 43. 24. 2, 2, 7, 23. 0P. 3, 449 CANCELLATION Article 70. 5 54 9. 49. 12. 60. 2. 11 6. 21. 10. $76. 13. $2. 3. 16 7. 48. 11. 24. 14. 96. 4. 24. 3. 161. GREATEST COMMON DIVISOR Article 72. 4 14 7. 6. 10. 14. & 19. 5. 19. 8. 56. 11. 60. 3. 4. 0. 13. 9. 4. LEAST COMMON MULTIPLE Article 76. 5 J260. 8. 8400. 11. 300. 2. 2835. 0. 288. S. 224. 12. 90. 3. 5040. 7. 2520. 10. 240. 13. 378. 4. 960. FRACTIONS Article 93. 5 2 1 10. -^w . 5. H, I!, iS, H. 2. *, H, H, ft. ft 22. 1L ?i' ft 2 8 4, ft, sV A. 3. f, ft*>* I fit / T20> 8. tH, tHt, t!!8 6. ff V 11. 411. Iff. -V-. fill, ttt. 7. 11 10. 83?. Article 94. 18. 347J. 17. --. 1ft H 4 - S-7.fi- fiU.0 630 ** 7"J(X> 720> 720' MB, fltf, ?S- (2 6 14. 72f. IP. -*/-. 10. ||, f^, -f^ 5 -, f Ij 15. 188|. #0 5..JJ.6 ~ 4 4V~, fl- t if 10. 37. f 1. - 3 rV . 11. ti, -w-, it 5. Xv Article 96. || ~^ I!' iv ft if 7; i 2. -V-. g^. -JLl^j 6 - 8 ^. * lie', m! ili- . }' O l 3. *f. J25. - L7 ^- L -. 13. A, T <&, T ff , o. g- p 61 F j- 4. - B t 4 . ^g JL^lA.. TO. 10! j; j 4 5 ' -W -^y* irticle 95. 7] i||o' Article 97. . ft, H, 11- *' iff, fit', III: . 12 oz. 3 dr. 4- 177 bu. 1 pk. 7 qt. in. 5. 26 mi. 244 rd. 5 yd. 4 in. 6. 280 A. 142 sq. rd. 12 sq. yd. 6 sq. ft. 29 sq. 7. 17 16' 37". 70. 7 fur. 18 rd 15 8. $116.83. ft. 6f in. 9. 53 hhd. 40 gal. 77. 6A. 113 sq. rd 1 qt. 1 pt. 21 sq. yd. 5 sq. ft. 66i sq. in. 364 NEW BUSINESS ARITHMETIC SUBTRACTION OF COMPOUND NUMBERS Article 206. 2. 11 Ib. 11 oz. 3 pwt. 15 gr. 3. 32 yr. 273 da. 10 hr. 46 min. 19 sec. 4. 57 bu. 2 qt. 1 pt. 5. 55 gal. 1 gi. 6. 2 T. 15 cwt. 94 10. 2 yr. 6 mo. 21 Ib. 6 oz. da. 7. 363 4s. lid. 11. 1 mo. 18 da. 1 far. 12. 1 rm. 16 qr. 8 8. 197 A. 129 sq. sh. rd. 22 sq. yd. 7 18. 47 17' 22". sq. ft. 72 sq. in. 14. 1 yr. 7 mo. 16 * da. 5 hr. 15. 9 cwt. 10 Ib. 16. 8 wk. 15 hr. 12- min. 17. 26 gal. 1 qt. MULTIPLICATION OF COMPOUND NUMBERS Article 207. 4. 342 A. 114 sq. 5. 94 gal. 3 qt. 3 7. 99 T. 6 cwt. 94 t 41 bu. 1 pk. 6 rd. 3 sq. yd. 1 gi- Ib. 2 oz. qt. 1 pt. sq. ft. 37 sq. in. 6. 37 cu. yd. 8 cu. 3. 33 Ib. 7 oz. 11 ft. 160 cu. in. pwt. 12 gr. DIVISION Article 208. 2. 3 bu. 2 pk. 6 qt. 1 pt. 3. Ib. 1 10 36 gr. 19f OF COMPOUND NUMBERS 4. 38 mi. 147 rd. 3 yd. 2 ft. 5iV in. 5. 2 cwt. 72 Ibs. 6. 106 A. 106 sq. rd. 20 sq. yd. 1 sq. ft. 72 sq. in. 7. 5 oz. 8 pwt. 8 8. 52 bu. 3 pk. 5 qt If pt 9. 5 Ib. 5 oz. dr. 10. 10. LONGITUDE AND TIME Article 210. 2. 2 hr. 3. 1 hr. 6 min. 16 11. 2 hr. 8 min. 19. 15fc sec. 12. 4 hr. 5 min. 49 min. 33f sec. past 7 p. m. Article 211. 1. 8 min. past 4 a. m. Wednes- sec. 17i sec. 20. 13 min. 17{f day. 4. 52 min. 44 sec. 13. 7 hr. 38 min. sec. past 10 p. 2. 52 min. past 5. 37 30'. 8 sec. m. noon next day. 6. 5 hr. 8 min. 1 14. 5 hr. 34 min. 21. 10 min. 19 sec. 3. 32 min. 19& sec. 7. 1 hr. 19 min. 6f sec. 15. 35 min. 18| sec. 22. past 11 a. m. 58 min. 7^ sec. past 11 p. m. Monday. 12| sec. past 11 a. m. sec. past 4 p. 4. 14 min. 56{| 8. 1 hr. 4 min. 16. 12H sec. past m. sec. past 8 a. 44f sec. 3 p. m. 23. 59 min. 13 sec. m. next day. 9. 2 hr. 37 min. 17. 40 min. 12 sec. past 10 a. m. 5. 3 p. m. Satur- 39 T \ sec. past 6 p. m. 10 min. 47 sec. day. 10. 36 min. 28H 18. 33 min. 4j past 4 p. m. sec. sec. past 7 p. m. Saturday. REVIEW PROBLEMS Article 212. 1. 12540. 2. 553357. 3. 30. 4. $1.52. 5. $1.60. 6. 6 bu. 2 pk. 2 qt. 7. 49m*. 8. $96055.31-1 . 9. $373J. 10. 168. 11. 49. 12. 4 hr. 26 min. 24 sec. 13. 2 rd. 16. 502 gal. 1 qt. 3gi. 17. $2.58. 18. .2278-K 19. 2 Ib. 7 oz. 19 pwt. 9 gr. 20. .3918+ . 21. 45 rd. 3 yd. 2 ft. 9f in. 22. I cwt. 45 Ib. 23. 225 A. 127 sq. rd. 27| sq. yd. 24. 203 rd. 3 yd. 1ft. 15,1 in. ANSWERS 365 25. 6| in. 30. 44 yr. 4 mo. on the pre- 36. 1418.9+bu. 26. .04093. 12 da. vious day. 37. 9+bu. 27. 28. $17.75+. $37.27+. 31. 1 hr. 39 min. 30 T 4 5 sec. 33. 34. July 29, 1895. 20 A. 37A sq. 38. 39. 1536.01+. 29 Ibs 2 oz. 29. $10164. 32. 9 min. 36 sec. rd. 40. $50.97. past 6 p. m. 35. 3284f$. Article 218. 2. 4. RATIO 9. 12. 70. 17. 77. 31.32. 12. A- . 2. 73. 3f. Article 226. & 114U. 3. $400. 5. $131*. SIMPLE PROPORTION 6. $58.80. 77. $25.30. 16. 16| da. 7. 34. 12. 5 mo. 13 da. 77. $17.50. 8. 19 hr. 13. $2.09i 18. $2.10. 9. 600 bu. 14. 249f ft. 19. 8| Ibs. 70. 5096. 75. 90 men. 20. 15. COMPOUND PROPORTION Article 228. 2. 8 r V 5. 30. 4. $18J. 5. $9804.26. 6. $396. 7. 8 ft. 8. $1600. 0. $118|. 70. $512.58. 77. 5^ hrs. 12. $731.25. 13. $35.64. 7i $128. 15. 4f f. 70. 7*V da. . 18. $51.08. 65*f 5^V ft. 258. 36ff da. MEASUREMENTS USED IN BUSINESS 1. 2. 3. 4. 5. 6. Article 240. $270.56. $31.66. 1800. 68H bd. ft $233.73. $760.32. 7. 8. 9. 10. 11. 12. 13. $1447.04. $6566.40. 67 iVg perch. $27.30. $30.47. 133} ft, $2.87. $10.60 14. 15. 16. 17. 18. 164340. $1314.72. 3' U". 15 sq. ft. 128 sq. in. 127440 bricks. 19. 20. 21. 22. S3. 24. e < < ( < \ ] >4.5818+ perch 5314.84. 5365.63. 5823.20. 5227.50. $114.98. L8300. 366 NEW BUSINESS ARITHMETIC PERCENTAGE Article 251. 2. $24. 3. $114. 4. $259.20. 5. $518.40. 6. $612.50. 7. 810 bu. 8. 10660 men. 9. 3981.3 ft. 10. 4042.5 Ib. 77. $41.28. 12. 1674.75 bu. IS. M. 14. .19|. 9. 10. 11. 12. 2. 3. 5. 6. 7. 8. 9. 16. $.1881. 17. $3.36. 10. 5688.80. 11. 1410, $4230. 72. #16. 13. 21. $10.60. 20. 25*, $1125. 23. Jones $841.50. 14. Brown $486.88. 15. 24* I, i. #. 25. $5.30. 77. 2ff. $5.40. I& 27. 45*. 28. 3085f bu. 29. 3152. 50. $666f. Article 252. 19. 1. $112. 20. 2. 320 bu. 3. 1215 yd. 2. I. 238 Ib. 3. 5. $178|. 4. 6. 226| yd. 5. 28| doz. $179. $90. 1218. 14 bbl. $368. Article 253. $324. $5.76. 182 gal. 150 ft. 2812$ yd. $360.."' $5917 $168.74. $105.82. 767.25 bu. 198 sheep. $6.25. $427.30 lost. $3845.70 re- mained. $4749.50. 548. $18290. $3637J. Wife $13500, 6. $2100. 13. 7. $1800. 8- $900. 14. 9. 400 sheep, 310 sheep left. 15. 10. 600 yds. 16. 11. $3600, $3888. 17. 12. Smith $800, 18. Brown $3000. 13. $140.40. 19. 14. $1190. 15. Claim $3900, 2. com. $93.60. 3. 16. $20000. 4. 17. $1193.75. 5. 1$. Bought 160, 6. had 460. 7. 19. $10, $4.50. 8. 20. Had $2000, 9. gave wife $150, 10. gave daughter 11. 1st year $600, 2d year $500. First cost $1000. Lost $18.331. $53331. 1600. Men 54, women 24, children 9. $7800. Article 256. 5*. 12*. 7*. 25*. 40*. 33J*. $62.50. Article 255. 2. $500. 3. $300. 4. $200. 5. $500. elder son $6300, 6. 3400ft. younger son 7. 3000 bu. $6300, daugh- ter $18900. $31229.41. $301.50. Article 254. 5250. 1400. 2250. Article 257. 1. 66 horses. 2. $254.76. 3. $1.47r- 4. $134.90. 5. $24.67. 0. $1062. 7. 1053 bu. 8. $5525.52. 9. $2.12. 10. $14.81. 71 $53.01. 12. $5504. 15. 16. 17. 18. 19. 21. 22. 23. 24. 25. REVIEW $85.50, $71.25. $448,10*. $500. $9300, 93 shares, 35 * paid out, 8. $1600. 9. 1191 Ib. 10. Cost $225, selling price $267. 21. 11. Principal $700, 22. Interest $56. 23. 12. 200 sheep, 10 24. A, 9 B, 6 C. PROBLEMS 27. $6300. 8J*. 25*. 30*. 22* *. 20*. 5*. 16*. 6i*. 60 *, $516. 12*, 15*. 40*, 3.5*, 25*. West 28*, Packard 26 *, Young 24 *, Retained 22 *. 28. 8J*. 29. $2681.87. 30. $1600.80. 31. $4269.67. 32. 15*. 65 % remained. 33. 1062 bu. 38. 39. 40. 41. 42. 43. $197.20. 15 & $20 loss. 3900 bu. B, 2958H bu. C. $180, 15*. $5260.39. $300. $89.60. 84. 25*. 35. 45 * currency, 44. 35 % gold, 20* silver. 36. $2496. 45. 37. Horse $156.52, 46. wagon $250.44. reaper $313.04. 75*. 10*. $16000. $100. $2000, $3000. $155357*. $1920, $2880. A> $691.20, B's $576, Cs $720. Oysters $92, fisli $41.40, clams $33.35. $36824. 15*. ANSWERS 367 PROFIT AND LOSS Article 264. 18. $1080.08. 32. 25*. 48. 38f *. 0. $22.20. 19. $280. 33. 8*. 49. $72. 3. $25.20. 00. $440. 34. 16|*. 50. $2019.40. 4. $47.60. 07. $310.63. 35. 16*. 57. $9, $6.60. 5. $42.53. 00. $106. 30. 16*. 50. A $163.04. 0. $530. 03. $3250 Hall. 37. $10. 53. $279.06. 7. $417. $3900 Miller. 38. $11250. 54. '$76.50. 8. $30. $4524 Davis. 39. $42.04. 55. $864. 9. $59.65. 04. 7500 bu. 40. $1499.88. 50. 44*. JO. $6.40. 05. $24. 41- 27i*. 57. 19^r*. 77. $460. 00. $65. 40. 10*. 58. $112.50. 70. $300. 07. $1.19. 43. 70|*. 59. 10*. 13. $180. 28. $810. 44- $35.70. . 00. $6675. 74. $120. 29. $27, $9. 45. $537.60. 07. $3525.72. 75. $11750. 30. $203.28. 40. $1.50 gain. $3966.43. 70. $1600. 37. $502.91. 47. $6.75,6*. 00. 6*. 77. $1380. 03. 9&*. MARKING GOODS Article 267. n \ 8 jj m. et 1* m. oe 7. $5.76 w. t. i. ' yus. as ' a. tag 1 ' p. ex 7 * as 70 CR 1K $M 2 "* bp >* 8 id i_ ' $17.50 n. ao 8 yu - as **' e- e 19. o. li 3. os ao ji t 5 - 75 00. b. ex *3 /\ .at $8.05 * 5T 75. 40*. 07. $1.043 c. thi 00. g. oe c o. rs 70. o. pn JQ $3.80 03. r. gnf. . TRADE DISCOUNT Article 275. 7. $5.60. 70. $164.15. 18. $48. 0. $507. 8. $2.54. 73. $252.67. 19. $25. 3. $15.75. 9. $259.20. 74. $373.93. 00. $12. 4- $27.30. 70. 35|*. 75. $42.34. 07. $8. 5. $156.05. 77. $384.75. 70. $454.48. 00. h. n r. 0. $15.84. BILLS Article 280. 4. $410.96, 7. $36725.52, 70. $1839.63, 7. $40.75. $398.63, $34889.24. $1614.28. Article 281. S388.66. 8. $1599.30, 77. $264.04. 0. $149.98, 5. $847.40, $1535.33, $258.76, $144.04. 55805.03, $797.23. $1489.27. 12. $212.54. 3. $1935.03. 0. $873.17, 9. $160.52, 13. $37.86. $1783.32. $804.63. $154.17. $37.10. COMMISSION Article 295. 0. $2.66. 70. $1756.30. 18. $1216. 0. $18.50. 7. $100.99. 73. $495.85. 19. $1100. 3. $30.40. 8. $43.29. 74. $138.46. 00. 870 bu. 4. $2.57. 9. $37.15. 75. $175.68. 07. $960. 5. $5.75. 70. $37.13. 16. $820.52. 00. $817.26. 368 NEW BUSINESS ARITHMETIC .25. $656. 51 2. 55. 4* 45. $390. .24. 250. 52. ! 5641.48. 40. 6 JT. 46. i 51897.27. 25. $1055.15. 55. 5 51.20. 41 $743. 47. 5 51033.69. 27. $400. 54. : 5520. 42. 5 5790.91, 48. i 5319.35. 28. $650. 55. 5 5960. i 5869.41. 49. i 5144.64. 29. 100. 50. 1500 bu. 45. 5 510661. 50. 5 52301. 30. 600 bu. 55. 3*. 44. 5 5280. 51. $564.73. 45694- lb. FIRE INSURANCE Article 311. 11. J 3428.57*. 15. Mutual $621, United States 2. $160. 54571.42f Springfield $828. $10050, Lancas- 5. $24. .72. i 52743.13. Local $920, ter $16750, 4. $75. .75. 5 5903.16. Commercial Orleans $6030. 5. $639. .74- ^tna $700, $1242. 17. $7200, $4698. 6. $21. Home $980, 16. Metropolitan 18. \\%. 7. $93.65. Essex $1225, $12060, Great 19. } i* 8. $3160.80. Phoenix $1470. Western $14740, 20. 3| %. 10. $9200. American $8710, MARINE INSURANCE Article 315. 4. 5 53037.50. 8. Paoli $1659.38, $1235.31, 1. $1912.60. 5. < 562.18. Leipsic $2655, Litchfield 2. $1900. 6. 5 51028.13. West Baden $2489.06. 5. $89.25. 7. 5 J90.49. $3171.25, Custer LIFE INSURANCE Article 325. 4. $60.90. 7. $150.30. 10. $983.50. 1. $161. 5. $2036.70. 8. $960.25. 11. $6320. 2. $166.18. 0. $96. 9. $432.50. 72. $65. 5. $168.75. REVIEW PROBLEMS IN PERCENTAGE Article 326. 10. $457.14. 19. $9500. 25. 400 bu. 1. 1U& 11. $2800. 20. $10.40. 29. $167.75, 2. \ 5149J. .72. $2.00 A. WX. 21. 19 #. 18f 1 1 5 ( 54i- 13. 8*. 22. ^ 526. 30. $.80. 4. S 53520. 14- $2.80. 25. $3640, $3328. 31. $64.29 gain. 5. 5 4801 .75. 42*0. 24. $109.20 1'wise. 52. 56J #. $ ! .70. 31B*. 108.00 c'wise. 55. 2 7iVff $ 7] < 52.80. 17. First $1260, 2J. $320. 54. $3500. & 33J & Second $1449. #0. $200. 55. $4900, $5100. 9. $20. 18. $3021.74. 27. $2575. 50. $57. INTEREST Article 339. P. $40. 70. $ ,515.36. 25. J 2004.17. & $21.20. 10. \ 516.80. 17. $ 5311.67. 24. i 5663. 5. $21.27. 11. ( 574.60. - 18. 5 5379.32. 25. 5 54980. 4. $43.20. 12. i 520.48. 19. i J517.50. 20. 5 5360. 5. $19.20. 13. i 718.75. 20. 5 51496.24. Article 340. 6. $15.96. J.04. 10! i 1.87. 15. < 5122.55. 00. 2 17s. lid. 2 + far. 5i i 5.07. 11. i .25. 17. 5 57.09. 23. 459 lid. 3 -far. 6. i .10. 10. 5 .02. 13. 4 14s. 10d.2-far. Problems in Interest Article 345. 7. 2 yr. 2 mo. 12 Article 346. 9 8 So 0. 2 yr. 6 mo. da. 2. 8*. m 6*! 3. 1 yr. 2 mo. 12 8. March 19, 3. 1%. 11. 10*. da. 1907. 4. 4*. 10. 8*. 4. 3 yr. 7 mo. 6 9. Sept. 28, 1904. 5. 10 *. Article 347. da. 10. Nov. 30, 1902. 6. \\%. 0. $500. 5. 8 mo. 4 da. 11. June 28, 1909. 7. 9*. 3. $319.52. 6. 27 da. 10. May 31, 1906. 3. 8*. 4. $218. 24 % 370 NEW BUSINESS ARITHMETIC 5. $136. 6. $433.61. 7. $760. 8. $103.33. 9. $799.32. 70. 131 77. 500 bu. Article 348. $240. 3. $370. 4. $1170. 5. $180. (5. $650. 7. $550. 8. $2175. P. $95. 70. $286. 77. $728. Annual Interest Article 350. 2. $915.14. 3. $428.65. 4. $1284.24. 5. $507.73. 0. $687.42. 7. $1342.37. 8. $214.92. 9. $174.88. 70. $3709.99. 77. $1395.85. Compound Interest Article 352. 0. $129.30. 5. $212.42. 4. $1019.86. 5. $146.08. 6. $399.65. 7. $1239.08. 8. $9.17. P. $35.15. 70. $128.50. 77. $398.03. 70. $1091.75. 13. $10690.54. 74. $2805.86. 75. $500. 16. $5340. 77. $1000. 18. $680. 75. $460. 00. $850. 21. $1250. 00. $18.22. 23. $.44. 24. $.13. 25. $1.58. 0tf. $762.20. Commercial Paper Article 367. 1. $715.85. Aug. 19, 1905 $875.48. . 3. Feb. 28, 1906, $1279.25. 4. $883.07. 0. June 15, 1905, Partial Payments Article 369. $262.88. & $728.16. 4. $719.33. 5. $393.75. 6. $212.17. 7. $2904.54. 8. $923.04. 9. $995.35. 10. $11777. Article 370. 1. $425.50. $265.44. 3. $938.42. 4. $81.60. 5. $401.47. tf. $1353.87. 7. $979.78. 8. $413.01. 9. U. S. Rule, $.21. 70. U. S. Rule, $1.09. 77. $559.69. Article 371. 7. $6625.38. Annual Interest with Partial Payments 0. $790.00. TRUE DISCOUNT Article 375. 0. $170. 3. $940. 1. $810. 5. $1339.94. 6. 400 bu. 7. $480. 8. $150.78. 9. $5. 13. $700. 70. $4.95. 14. $103.63. 77. Gain $6.73. 75. 900 bu. 12. $107.52. BANK DISCOUNT Article 379. 5. I 517.39. 9. $2692.83. 1905, 53 da vs. 0. $3.30. 6. i 562.63. 70. $193.34. $2.89, $277."! 1 5. $3.70. 7. < 5912.33. 11. July 12, Proceeds. 4. $2.80. 8. ! 5459.30. ANSWERS 371 72. Feb. 25, 1906, 74. June 5, 1906, 10. $275.16 Pro- 23. $1200. 111 days, 65 dars, ceeds. 24. $1500 Face, $21.46 bank dis ., $38.03 bank dis.77. $1814.94. $1487.50 Pro- $972.79 Pro- $2068.16 Pro- 18. $1006.82. ceeds. ceeds. ceeds. 19. $943.55 25. $360. 73. Oct. 1, 1905, 75. Apr. 26, 1906, 20. $608.11. 20. $593.42. r r8 days, 115 days, 21. $720. 27. $1196.64. $17.64 bank dis i P8 bank dis., 22. $552.92. $1339.16 Pro- $305.12 Pro- ceeds. ceeds. STOCKS AND BONDS Article 403. 77. $409.50. 35. 112f. L for 1 A, 7. < ^378. 18. $252, $3348. 30. 8*. I for 2 B. 2. 5 5304. 19. $20846.87. 37. 60. 2 for 5 C 3. 5 5270. 20. < 5408.50. 33. $19000. 50. $27270. 4. J 5247.50. 27. < 5513.50. 39. 60. 57. $300. 5. < 1182.25. 22. < 51457. 40. 52. 52. Latter $85.50 0. ! 5247. 23. 5 520830. 41. 40. 53. 3 5883.41. 7. $207. 24. i 5840, 284 . 42. 5 54. 5 5158.27. 3. $2288. 26. 27 snares. 43. 5jV %. 55. ! 5187.50. 9. $3741.10. 27. $3300. 44. 4$. 50. 5 51056.25. 70. $6855. 23. 41 shares. 45. $262.50, 12A %. 57. < 5629.67. 77. $1642.20. 29. $ 51400. 40. < 53. 5 5128.50. 12. $7546. 30. $ 59150. 47. $528, 5&V %. 5P. $35827.50. 73. $4089. 31. < 54315.31. 43. Latter &%. 00. $1059.54 Loss. 74- $1226.25. 32. I 500, $18650. 4P. $1000000 A, 07. $80, 15. $330. 33. 300. $750000 B, 02. i ^lilf^j 4r 4 a#. 70. $150. 34. * !6f . $250000 C, $12445. DOMESTIC EXCHANGE Article 410. 9. $223.50. 18. $370. 27. $1229.52, 7. 5560.70. 70. $1875.50. 19. i 5465. 23. 1500 bu. 2. ; 5728.63. 11. $930.09. 20. < 51178. 29. i ^510.64. 3. * 51307.78. 72. $589.21. 27. ! 51849.15. 30. < J599.69. 4 51839.49. 73. $864.20. 22. i 5272.11. 37. i 5947.91. 5! $627.75. 14. $326.42. 23. 1 55772. 32. < 5433.22. 0. $2817.10. 75. $1256.75. 24- 5 56748.42. 33. $109.23. 7. $287.68. 70. $322.59. 25. $333.91. 34. $1801.80. 3. $482.40. 77. $925. 20. $133.84. 35. 20 shares. FOREIGN EXCHANGE Article 415. 0. $492.83. 77. $840.32. 70. 710. 7. $4332.08. 7. $5918.86. 72. $80. 77. 8000 marks. 2. $780. 8. $782.78. 73. 583 12s. 6d. 73. 526 4s. 2d. 3. $660.34. 9. 2200 bu. 74. 4193.98 fr. 19. $32, 1905.32 fr. 4. $1546.05. 70. $1320. 75. 660 marks. 20. 1021.27+ yd. 5. $375. NATIONAL BANKS Article 422. $50000, $12500 5. $212565. to $50000 0. $2235, $2115. 8. $643.25. 9. $3265, $11885. 7. $62500, 3. 3 5480000, 7. $21250, 70. $51400, $62500. 3 524000. $425000. $55897.50. 2. 5 persons, 4. c Hi*, $156.25. 372 NEW BUSINESS ARITHMETIC SAVINGS BANKS Article 425. 4. $1003.27. 8. $1973.90. 11. $243.90. 1. $2.35. 6. $352.92. 9. $755.15. 12. $493.69. 2. $30.02. 7. $787.64. 10. $1910.63. 13. $135.17. 8. $992.94. TAXES Article 432. 3. $5836.50. 6. $1972.92. 9. $184.97. /. $421.70. 4. $12164.04. 7. $1466.85. 10. $329.87. 2. $81.08. 5. $467.10. 11. .018. .09. CUSTOMS OR DUTIES Article 448. 4. $318.36. 8. $488.87. 11. $2770.86;. 1. $255.60. 5. 2641.79. 9. $3754.25. 12. $2197.80. 2. $590.27. 6. $209.91. 10. $1897.54. 13. 24782.66.. 3. $877.80. 7. $222.61. EQUATION OF ACCOUNTS Article 456. 10. Oct. 6. Article 457. 10. April 1, 1904U 2. April 10, 1905. 11. May 8, 1905. 2. April 27, 1905. 11. $808.96. 3. 5 mo. 21 da. 12. Aug. 20, 1905. 3. April 2, 1905. 12. $595.48. 4. 9 mo. 12 da. 13. June 14, 1905. 4. May 28, 1905. Article 458. 5. Oct. 16, 1903. 14. March 14, 1906. 5. Jan. 28, 1906. 1. Auer. 21. 1905-.. 6. Aug. 9, 1905. 15. June 29, 1905. 6. Jan. 2, 1905. 2. Tune 19 '. 1905. 7. Oct. 15, 1905. 16. May 13, 1905. 7. Oct. 21, 1905. 3. June 17, 1906 8. Oct. 2, 1905. 17. Oct. 28, 1905. 8. July 30, 1905. $19.83. * 9. June 23, 1905. 18. July 1, 1905. 9. Oct. 16, 1905. 4. April 19, 1905* $499.69. CASH BALANCE Article 459. 3. $1311.41. &.. $1188.63. 4. $724.03. PARTNERSHIP Article 472. 3. Jones Hammond C $2935.88;. 1. 2001. $4552.40, $3844.65, D $3114.44,. 2. $1042.50. Brown $3602.40, Siders Firm 3. Smith $3096.20. $3593.75, $11688.27. 4. .28. 4. F $6308.08, Firm 5. $2552.33 G $7067.07, $11544.05. Article 475. A $1160.15, H $6838.77, 3. Stewart 2. Gain $920.35, B $928.12, I $6184.38. $4593.16, A $406.22, C $464.06. 5. O $4325, Nevins B $514.13. 6. Gain $4835.36, P $4342, $4543.66, 3. Gain $825, share of each Q $4505, Barnard Fuller $225, $1208.84. R $4371. $3193.43, Irwin $330, Article 473. Firm Diers $270. 2. C $19099.60, Article 474. $12330.25. 4- A $792, D $18849.60, 2. Parker 4. A $2398.58, B $561, E $18699.60. $4105.65, B $3239.37, C $957. ANSWERS 373 5. Jennings Collins $320, $3277.89, $1200, $1626.49. B's cr. int. Wilson Fuller $792, 4. Tyler $310.40, $501, $5394.93, Clark $948. Brady $422.96, C's cr. int. Farrel 6. Gain $1009.80, Hess $511.64.' $649, $5038.83. F $299.20, 5. 20.0568 %, D's cr. int. 5. A $5668.58, G $336.60, A $932.64, $876.25, B $6331.42. H$374. B $656.86, A's cap. 6. Loss $975.10, Article 476. 6. A $707.69, $296.96, A $4743.69, 2. Hammond B $675.85, B's cap. B $4716.55, $1030, C $556.46. $1066.44, C $8284.66. Cowles $960. Article 477. C's cap. 7. White 3. Manning 2. W $9353.11, $802.91, $1848.86, $1480.11, G $10470.11, D's cap. Murray Miller S $14142.78. $5701.69. $2651.14. $2394.20, 3. A's cr. int. 4- Harding INVOLUTION Article 482. 8. .027. 16. i 23. 1.27628. 1. 324. 9. f|i 77. 11529. 24, .000000001. 2. 157464. 10. 1.21665+. 18. 3888. 25. .00001936. 3. 19.0096. 11. 1.340095+. 19. 47 14 . 26. 16 yd. 4. 31640625. 1%. rfStk- 20. 113 A 145 sq. 27. 421875 cu. in. 5. 1.97382+. IS. 23||. rd. 28. 19.19140625. 6. 23.6196. 14. 7776. 21. .000000000001. an 633 44 3_ *' ToffSTSS- 7. 1024. 15. 301 22. .00000081. SQUARE ROOT Article 489. 6. 667. 11. \l 16. 4.168+. 2. 32. 7. 625. 12. 16|. 17. .094. 3. 43. 8. 1296. 13. .866+. 18. .0081. 4. 65. 9. ,V 14. 1.732+. 19. 1.732+. 5. 248. 10. 5J. 15. .8164+. 20. 11.180. Applications of Square Root Article 496. 4. 146.86 + ft. 7. Width 53.15+ 9. 452.54+ rd. 1. 50 ft. 5. 21 ft. 11 in. ft, length 10. 187.46+ rd. 2. 12.64+ ft. 6. 80 rod, 106.30+ ft 11. 40.85+ ft 3. 51.26+ in. 320 rod. 8. 49.92+ ft CUBE ROOT Article 497. 6. 216. 11. 9.75. 15. 1.44+. 2. 36. 7. 359. 12. 3.54+. 16. 2.08+. 3. 63. 5. 441. 13. 1. 77. 2.35+. 4. 126. 5. 536. 14. 1.25+. 75. |. 5. 177. 70. 630. Applications of Cube Root Article 497. 4. 999 in. 6. 12 ft 10.8+ 9. 8 ft. 6+ in. 1. 39 in. 5. Depth 55.6+ in. 10. lit. 6.9+ in. 2. 14.32 ft. in., length 7. 3 ft 8+ in. 77. 8 ft. 8+ in. 3. 57 ft 111. 2 + in. 8. 12150 sq. ft 374 NEW BUSINESS ARITHMETIC MENSURATION Article 511. 3. 203.71+ rd. Article 532. 4. 1435456f* cu. 1. $200. 4. 235.62ft 1. 198 sq.ft. yds. 2. $6503.91. 5. 3 ft. 2. 373^ sq. ft. Article 538. 3. 576. Article 520. 3. 27.0963 sq. ft. /. 3631.6896 sq. ft 4. $32.36. 1. 1017.87+ ft 4. 600 sq. ft 2. $45.24. 5. 39^ yd. 2. 10. 456+ A. Article 533. 3. 196663355.7504 Article 514. 3. 1A 20+ sq. rd. 1. 425 cu. ft. sq. mi. 1. 486 sq. yd. 4. 1963i sq. yd. 2. 4230.144 gal. Article 539. 2. 672f sq. ft. 5. 441 7"| sq. ft. 3. 5026f? gal. 1. 1767.15 cu. in. 3. 800 sq. ft. Article 531. Article 534. 2. 14137.20 cu. ft 4. $54. 1 6 sq. ft 108 1. 1728 cu. ft. 3. 2982.0656+ Article 519. sq. in. 2. 32616 cu. ft. cu. ft. 1. 9243.7 ft. 2. 36 sq. ft. 3. 6946|| cu. ft 4. 354.08+ hhd. 2. 376.99+ rd. METRIC SYSTEM Article 543. 9. 6.35 m. 16. 100 ha. 23. 3.645 1. 1. 763.217 km. 10. 197.63 dm. 11. .015004008 24. 1000 g. 2. 318462m. 1976.3 cm. cu. m. 25. 907.2 kg. 3. 39,516,000cm. 11. 56.38 a. 18. 14018.0036 26. 11.023 Ib. 4. 516.26m. .5638 ha. cu. dm. 27. 2204.6 Ib. .51626 km. 12. 2187500 sq. m. 19. 10001. 28. 91000. 5. 106. 25427 miles 2187500 ca. 20. $.066. 29. 2| s. 6. $168.75. 13. 286.176 ha. 21. $18205.92. 30. 3 cu. m. 7o 1577.114km. 14. $12.83. 22. 6703.125 Dl. 31. 46.328 cu. m. If 771.14 hm. 15. 5. 106383 -km. 67.03125 cu. m. 32. G840 sq. m. 8. 16.9164m. ^^RA^^ ff OFTHE*^ UNIVERS/TY -