UC-NRLF 2fl DDE MODERN BUSINESS ARITHMETIC LIBRARY OF THE UNIVERSITY OF CALIFORNIA. GIFT OF Class 4 SWEET'S Modern Business Arithmetic A TREATISE ON MODLRN AND PRACTICAL METHODS OF ARITHMETICAL CALCULATIONS FOR THL USE. OF Business and Commercial Colleges, Business Universities, Commercial High Schools, Technical Schools, and Commercial Departments in Other Ldu-] cational Institutions BY Typography by J. 5. SWLLT PUBLISHING CO. Santa Rosa. Cal. Press of 1 908 THL HICK5-JUDD COMPANY San Francisco, Cal. Entered according to Act of Congress, in the year 1907 By J. S. SWEET, A. M. In the office of the Librarian of Congress, at Washington, D. C. ELECTROTYPED BY FILMER BROS. ELECTROTYPE CO. SAN FRANCISCO, CAL. Preface IFTER thirty years experience as a teacher of mathematics, the author feels that he is able to present the subject of commercial arith- metic to students and instructors in a man- ner which is not only severely practical and up to date, but attractive and intensely interesting. No claims are made in regard to the discovery of new facts in the science of arithmetic. While the manner of presenting the topics to the class, the method of illustration, exemplification, and practice have been used by the author for many years, no pub- lished work has ever been issued handling the science in this extremely practical manner. Particular attention is called to the different parts into which the work is divided. " Class Work, " "HomeWork," "Test," and "Final Examinations," each has its place in the development of every topic. The topics are made largely independent of one an- other, so that students entering school at different times may take up the work together. This will be found a most excellent feature in business college work. A system of credits is also suggested which will spur the student to do his best at all times. 23656 To the Teacher The following plan of preparation, recitation, test, credits, and examination is suggested : I. PREPARATION: Students should be assigned certain definite work to prepare for each recitation. Such preparation should be made before coming to the class room. II. RECITATION : Students should be required to discuss each topic in class before any blackboard demonstrations are given. " Blackboard examples, fully illustrated and discussed, should bring out the principles of each topic. Every student should be required to solve at least one problem in each subject and discuss it from the board before the class. III. TESTS : Tests may be given at the close of each sub- ject, or may be postponed for two weeks. The latter method is found to be the more satisfactory, as it compels the student to review the subject. IV. HOME WORK : Twenty-five different exercises for -Home Work have been carefully prepared. Each student should be required to hand in a correct solution of these, sys- tematically arranged, as a part of his permanent record. V. CREDITS : A good plan in recording the work of stu- dents is to divide the work into two parts : Class Work and Home Work. Class Work, including recitations, demonstra- tions on the blackboard, and criticisms, may be rated on a basis of 100 credits, the credits being actually earned as the subjects are passed. Home work should consist of the papers filed with the teacher, and may be given 100 credits, an average of four credits for each paper. Only accurate, neat, and tastefully arranged work should be given credits. This work should be filed away for future reference. VI. FINAL EXAMINATIONS : Final examinations may be given, if thought advisable, though experience has taught that with the above system carefully carried out they are hardly necessary. To the Student You are about to begin a course of study that is to prepare you for the active duties of business. As you succeed here, so will your teacher and those about you judge of your success in the real battle of business. Here you will win or lose, t for your school life is but the epitome of your future. Resolve, then, to win. Take up each lesson with a deter- mination to master it from start to finish. Every lesson thor- oughly learned will make those coming after the easier. Test and examination will then become a pleasure instead of a dread, and you will reap an abundant reward. Post yourself thoroughly upon your ' ' class work ' ' by studying the definitions and discussions of each topic, and by such preparation upon the examples and problems as will enable you to recite intellegently and correctly. The "Home Work" should be prepared at home, and should be carefully arranged on your paper so the examiner may note the method of solution and the answer at a glance. Full credits will not be given you unless the above is carefully ob- served. Please note the plan of the ' ' system of credits ' ' used by your teacher, and strive to reach the very highest point possible. Success is yours if you work faithfully, methodically, and per- sistently. RECORD OF CREDITS : No. 1 2 3 4 5 6 7 8 9 10 11 12 Cr. 13 14 15 16 17 18 19 20 21 22 23 24 25 NOTE Should the student .so desire, he may keep a record of his earned credits on the above form. CONTENTS DEFINITIONS . 7 How TO WRITE AND READ NUMBERS - 8 ADDITION - . - 13 SUBTRACTION . - 21 MULTIPLICATION - - - - 25 DIVISION . _ 37 PROPERTIES OF NUMBERS - 41 CANCELLATION - - 47 COMMON FRACTIONS 49 DECIMAL FRACTIONS 53 SIMPLE INTEREST 73 ALIQUOT PARTS 77 ANALYSIS - 81 BILLS, INVOICES, AND STATEMENTS 88 DENOMINATE NUMBERS 95 REDUCTION OF DENOMINATE NUMBERS - 109 LONGITUDE AND TIME - 121 DENOMINATE FRACTIONS - 125 AREAS, SURFACES, AND VOLUMES - 130 PRACTICAL MEASUREMENTS - 140 RATIO AND PROPORTION - 147 PERCENTAGE - - 151 PROFIT AND Loss - 157 TRADE AND CASH DISCOUNTS - 162 COMMISSION . igg STOCKS AND BONDS - 175^ TAXES - . 182' U. S. CUSTOMS OR DUTIES - 184 INSURANCE - - - 188 INTEREST _ - - 194 COMPOUND INTEREST - _ 204 COMMERCIAL PAPER - 207 PARTIAL PAYMENTS - - - 217 DISCOUNT --_._. _ 225 BANKING AND EXCHANGE - - . - 228 EQUATION OF PAYMENTS * - - - - 233 STATEMENTS AND BALANCE SHEETS - 240 PARTNERSHIP - 945 ANSWERS - 251 Modern Business Arithmetic Definitions 1. A Unit is a single thing ; as one, one dollar, one dozen. 2. A Number is one or more units taken as a whole ; as one, five, two cents, fifty feet. 3. An Integer is a number representing whole things ; as six, seven, nine men, twenty dollars. 4. A Fraction is a number representing parts of things ; as one-half, two-thirds, three- fourths of a mile. 5. An Even Number ends in 0, 2, 4, 6, or 8 ; as 10, 32, 54, 76, 98. 6. An Odd Number ends in 1, 3, 5, 7, or 9 ; as 11, 23, 35, 47, 59. 7. An Abstract Number is the number itself without reference to things ; as 7, 25, 142. 8. A Concrete Number always refers to some particular thing ; as 7 quarts, 25 cents, 14 desks, 50 men. 9. A Denominate Number is one whose unit is a meas- ure ; as 2 hours, 5 yards, 37 pounds. The unit of these numbers is the hour, yard, and pound. 10. A Simple Number is a single number ; as four, or 4 feet, 11. A Compound Number is a concrete number of two or more denominations ; as 5 feet 6 inches, or 2 gallons 3 quarts 1 pint. 12. Lfike Numbers refer to the same kind of unit ; as 3 and 8, 2 dollars and 30 dollars. 8 :.i.)r.i':R\:Bps-^XE3S ARITHMETIC 13. Unlike Numbers refer to different kinds of units ; as 3 dollars, and 80 bushels; 5 hours, and 10 boys. 14. Arithmetic is the science of numbers and the art of computation. Science is the amassed knowledge pertaining to a subject. Art is the power or skill to use the knowledge embodied in a science. How to Write and to Read Numbers 15. Figures are used to express numbers; the ten characters used in Arabic notation are : 1234567 89 One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Naught. 16. A number consisting of only one figure is called Units ; as 5, indicates 5 units. 17. A number consisting of two figures contains tens and units; as 45, indicates 4 tens and 5 units, and is read forty- five. "Forty" is a contraction of "four tens." - 18. A number consisting of three figures contains hun- dreds, tens, and units; as 345, indicates 3 hundreds, 4 tens, and 5 units, and is read three hundred forty -five. 19. If the ' ' " occurs in a number it is not read as it has no value ; thus, 305 is read three hundred five ; 740 is read seven hundred forty. 20. Numbers consisting of more than three figures are sepa- rated into periods of three figures each, beginning at the right. Each period is named as follows : 10, 999, 888, 777, 666, 555, 444, 333, 222, 111, 567, 234. 21. Bach period is read as- standing alone, then its name is given; as: 421,672,305 is read "four hundred twenty-one million, six hundred seventy-two thousand ', three hundred five. NOTATION AND NUMERATION 9 Since units is the name of the last period and always a part of the number read, its name is not used. 22. Copy and read the following : / 7 7 L? >- / ^ s^- ^ *, f 7, ^ ^ r J~ tf, 7 ^ ^ 23. Write the following in figures on the blackboard : 1. Eighty- four. 2. Six hundred eighty. 3. Four hundred nine. 4. Two thousand, five hundred ten. 5. Fifty thousand, twenty. 6. Seventy-five million, two thousand, four. 7 . Nine hundred trillion, seven billion, two hundred. 8. Two million, two thousand, two hundred two. 9. One hundred billion, ten million, one. 10. Thirty quadrillion, three hundred three million, two hundred three. NOTE From the above it will be noticed that the word "and" is omitted when writing or reading whole numbers. 10 MODERN BUSINESS ARITHMETIC Roman Method of Writing Numbers 24. In Roman Notation seven capital letters are used in writing numbers, as follows : I V X L C D M One Five Ten Fifty One Five One Hundred Hundred Thousand 25. Principles of Roman notation : 1. Repeating a letter repeats its value, as: II is two, XXX is thirty, CCC is three hundred. 2. A letter placed after one of greater value is added to it ; if placed before, is subtracted from it ; thus : VI is six, IV is four, MC is eleven hundred, CM is nine hundred. 3. A letter placed between other letters is subtracted from their sum ; thus : XIV is fourteen, CIX is one hundred nine. 4. A bar placed over a letter multiplies it by_pne thousand ; a double bar, by one million ; thus : X is ten thousand, X is ten million. NOTE Four is represented on clock and watch dials by IIII ; in all other places by IV. 26. Roman and Arabic notation : I 1 XI 11 XXI 21- C 100 II 2 XII 12 XXX 30 CC 200 III 3 XIII 13 XL 40 CCC 300 IV or IIII 4 XIV 14 L 50 CD 400 V 5 XV 15 LX 60 D 500 VI 6 XVI 16 LXI 61 DC 600 VII 7 XVII 17 LXXII 72 M 1000 VIII 8 XVIII 18 LXXX 80 V 5000 IX 9 XIX 19 LXXXVI 86 XV 15000 X 10 XX 20 XC 90 L 50,000,000 27. Write in Roman notation : 1. Four. 2. Nine. 3. Thirteen. 4. Twenty- two. 5. Thirty-eight. 6. Forty-seven. 7. Sixty- four. 8. One hundred sixty-six. 9. Seven hundred ninety-nine. 10. Nineteen hundred seven. Also 28 74 125" 328 972 1,248 27,853 458,207 2,576,324 17,265,842 NOTATION AND NUMERATION 11 28. Write in Arabic notation : 1. LXXXII. 6. VmCDXIL 2. XLVII. 7. XXXVDCCCLXXII. 3. DXII. 8. DCCIIDCCCIJV. 4. DCCCXXIII. 9. IVCCXXXVIDCCLn. 5. CCLXXIX. 10. XXIVDCCCLVICCLXXI. HOME WORK No. 1 29. Study carefully the following figures and practice them thirty minutes every evening for two weeks, then hand in a full page of your best work : 77777777777777777777 ? f f f f r r r f ? 7 -/ - / ^ ^ S- / ^ ^ 3 / ^^IA. f^l_^_7 <& & 7 f 14 MODERN BUSINESS ARITHMETIC 41. Sums Greater Than 9 : ^r ^ ^ ^ / s^r- -4^- -Lr* > C- ^ ^ --.. JL'JLjL -t-LJl^L A.^ IL 42. To Read at Sight : When a student sees the numbers 1 and 3 written side by side, he instantly knows the number to be thirteen or thirty-one, ac- cording to their positions. The same facility may be acquired in addition ; thus : 4 over or under 8 may be read twelve as readily as the figures 1 and 2 side by side. 43. Read the sums of two figures at a time. Never add sin- gle figures. Name the result of the following as rapidly as possible from left to right, from right to left, and then by "skip- ping about : &_ j^\s_ ^_^2 A_ 7 _ f f >- L/ ^ ^ ^ / ->^ > v*- -v* .^ / ^ r <^ ^77 ^/ ^ / ^ /" / ft r 7 ^ / *3 ? ^77* * ? f r ? 7 7 j r ? t * 7 7 f - /- 7 ' 7 r 7 r / ',JT ; .f >.":/ *- s * * t * r / 7 *" r - 7 -./-< / r f ^ f f 7 * f 7 7 " *" ^ / * Many times it is convenient to add the figures that will make even &m or twenties, etc., keeping in mind the unadded digits until they will unite with another to make few or twenty ; thus : in the right hand column above read the 4 and 6, 7 and 3, 8 and 2, and 1 and 9 as tens, to which add the 3 -f 4 ; as ten, twenty, thirty, forty -seven. 16 MODERN BUSINESS ARITHMETIC 46. When the Columns Are I^ong, add each column separately, writing the sum beneath, then add results, as fol- lows : 7 t ; r > / 7 7 1 j> / f ADDITION 17 This method is almost indispensable in bookkeeping, since an error can be detected in one column without the trouble of hav- ing to add all the others. 47. To add two columns at a time, practice on the following by adding the tens' column first, and by reading the units' col- umn, tell at a glance the number to carry : 2- ^ <3 J~ 6> (, \S f ^7 f f^ -^7 ^ > ^ / c//- 7 y ^ ^ y ^~ f * 7 r * 77 r * /: 7 ^7 7 z^: 48. To Prove Addition, add the second time down, or up, in the opposite direction of the first addition. In short col- umns, and several of them, the addition may be proved by cast- ing out the 9's as shown below : / -J / 7 "* * - f f f 6 ,^? ^ ^- '& /'s\& -7-.? & * f t.& < 7 / x ^ ^r y y r r 2- ^ ^ *~ * > / j- _ ? ? > ^- '-* , J 7 7 / ^ ^ -7-**^ . // <^ J' /---^ / PRACTICAI, PROBI^^MS 64. Solve the following : 1. I,. Cush man's total assets are $9527.15; his liabilities are $3645.85. What is his present worth ? 2. L,. Ayers' resources amount to $17826.45 ; his outstanding indebtedness is $8245.50." What is he worth ? 3. E. L. Payne began business with $2500, borrowed money. At the end of two years he was worth $3528.50. What was his gain ? 4. M. Coy lost $785.25 the first year ; gained $255.75 the sec- ond year, when his present worth was $5964.50. What was his capital at the beginning ? 5. Brown began business with $1840.25 ; the first year he lost $'280.50, the second year he lost $177.25, the third year he gained $'.M;I .25, the fourth year he lost $128.40 ; What was his present worth at the end of the fifth year if his last year's gain was as much as his total losses ? 24 MODERN BUSINESS ARITHMETIC HOME WORK No. 3 6. J. S. Taylor & Co.s' statement at the close of the year was as follows : Resources: Mdse. inventory, $3585 ; Cash, in bank, $2250; Notes on hand, $1275.50; Accounts Receivable, $8960.25; Store and Lot, $4500; Furniture and Fixtures, $1628.75; Horses and Wagons, $785.40. Liabilities: Notes Outstanding, $2147.50; Interest Payable, $74.20; Accounts Payable, $3487.25. Find the firm's present worth. 7 . The following statement of the College National Bank w r as given the board of directors : Resources : Subscription, $25000 ; U. S. Bonds, $20000; Cash on hand, $21859.75; Loans and Discounts, $43260; N. Y. Bank, $6729.50; sundries banks, $335.50. Liabilities: Capital Stock, $50,000; Circulation, $18- 000; Deposits, $45064.10; Business College Bank, $482.50; Chemical Bank, $990 ; College Exchange Bank, $490 ; Surplus Fund, $396.82 ; Dividends, unpaid, $500. What amount should be found in the Undivided Profits Account ? 8. K. P. Heald and F. O. Gardiner became partners in busi- ness with the following resources : Cash, $4000 ; Mdse., $7850 ; Real Estate, $10000 ; Bills Receivable, $5250 ; Accounts Receiv- able $12320. 40 ; Interest Receivable, $782.50; Furniture and Fix- tures, $945; Chattels, $485.75. Liabilities: Bills Payable, $675.25; Interest Payable, $48.35; Unpaid Salaries and Rent, $286.80. If at the end of the year their present worth is $45- 623.25, what is their gain? 9. A milling company's present worth at the beginning of the year is $400000. The first quarter they lose $2432.85, the second quarter they gain $8975.26, the third quarter they gain as much as their net gain for the first half year, the last quarter they gain as much as in the second and third quarters ; what is their present worth at the end of the year ? 10. The resourses of the First National Bank are given on page 20. If the liabilities are as follows : Capital Stock, $500- 000 ; Deposits, $3015485 ; Surplus Fund, $125000 ; National Bank Notes Issued, $135485 ; Due to other National Banks, $1269800 ; Dividends Unpaid, $1176 ; United States Deposits with us, $114697 ; what must be the Undivided Profits ? MULTIPLICATION 65. Multiplication is a short method of making additions of the same number. Thus, 5+5+5+5=4 times 5 = 20. 66. The Multiplicand is the number to be repeated or multiplied ; as 5 in the above example. 67. The Multiplier is the number which shows how many times the multiplicand is taken ; as 4 in the above example. 68. The Product is the result obtained; as 20 in the above example. 69. The Sign of Multiplication is the oblique cross, X ; is read "times" or "multiplied by." Thus 3 times 8 is writ- ten 3X8, and means that 8 is to be taken or added to itself three times and equals 24. 70. The multiplicand and the multiplier are called factors of the product. 71. An Abstract Number is the number itself without reference to things ; as 5, 36, 240. 72. A Concrete Number always refers to some particular thing or quantity ; as 12 hours, 80 miles, 500 horses. 73. The multiplicand may be either abstract or concrete ; the multiplier is always considered an abstract number; the product and multiplicand are always like numbers. Thus, 5 times 7 = 35 ; all abstract numbers. 5 times $7 = $35 ; multiplier an abstract number, the multiplicand and product concrete numbers. NOTE In computing the square units in a given surface where the length and breadth are given, the product of these two dimensions equals the number of square units in a row multiplied by the number of rows. Thus, instead of 3 feet, the width, times 4 feet, the length, the analysis is 3 times the 4 square feet in a row, or 12 square feet. 26 MODERN BUSINESS ARITHMETIC 74. The following Multiplication Table should be thor- oughly memorized before proceeding further : MUI/TIPIylCATION TABI,E 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8- 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27- 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72 7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 103 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144 75. A Square of a number is the product of the number multiplied by itself. Thus, 25 is the square of 5 ; 49 is the square of 7. 76. The squares of all numbers up to 30 should also be mem- orized. They become the basis of further knowledge of num- bers. Thus : 7 / f - y yj.it MULTIPLICATION 27 77. Alternating Numbers are those having, in their reg- ular order, a number between them ; as, 5 and 7 ; 17 and 19 ; 24 and 26. 78. The Product of two alternating numbers is always one less than the square of the intermediate number. Thus, 5 times 7 == 6 x 6 less 1 ; 17 times 19 = 18 X 1$ less 1. Solve the following : 11 X 13 12 X 14 13 X 15 14 X 16 15 X 17 16 X 18 17 X 19 19 X 21 21 X 23 22 X 24 23 X 25 24 X 26 25 X 27 26 X 28 27 X 29 29 X 31 NOTE The product of two numbers having three intermediate num- bers between them is equal to the square of the central number less 4. Thus 8 times 12 equals 10 times 10, less 4. 79. To Multiply a Number Consisting of Two Dig- its by 11. Write the sum of the digits between them; the number thus ex- pressed is the product. EXAMPLES : 11 times 24 264. 11 times 47 = 517. 11 times 32 = 352. 11 times 68 = 748. NOTE When the sum is 10 or more, carry one to the hundred's digit. Solve the following : 11 times 34 11 times 43 11 times 45 11 times 44 11 times 66 11 times 38 11 times 56 11 times 71 11 times 85 11 times 79 11 times 52 11 times 65 11 times 87 11 times 69 11 times 95 11 times 75 11 times 78 11 times 88 11 times 96 11 times 99 80. To Multiply any Number by 11. Write the units figure, the sum of the units and tens, the sum of the tens and hundreds, etc., also the left hand figure, carrying when necessary. EXAMPLE: 11 times 12345 = f 5 5 4 + 5 = 9 3 + 4 = 7 2 + 3 = 5 1 + 2- 3 -| 1 135795 28 MODERN BUSINESS ARITHMETIC Solve the following : 1. 11 times 2134 6. 11 times 345281 2. 11 times 4352 7. 11 times 587634 3. 11 times 6217 8. 11 times 879605 4. 11 times 7172 9. 11 times 378967 5. 11 times 8154 10. 11 times 897968 NOTE To Multiply by 22, 33, 44, etc., multiply by 11 as above, mentally, then by 2, 3, 4, etc., in the same operation. 81. To Multiply by a Single Digit. Multiply the units figure of the multiplicand by the multiplier, then the tens, hundreds, etc. If the product at any time is 10 or more, carry the tens to the next product ; thus: 24682 4 98728 OPERATION : Four times 2 8. Four times 8 = 32, carry 3. Four times 6 = 24, + 3 = 27, carry 2. Four times 4 - 16, + 2 = 18, carry 1. Four times 2 = 8, +1 = 9. Solve the following : 1. 38751 X 3 = ? 6. 55786 X 7 = ? 2. 25684 X 2 = ? 7. 38972 X 8 = ? 3. 62753 X 4 = ? 8. 45876 X 9 = ? 4. 29759 X 5 = ? 9. 82975 X 4 = ? 5. 34287 X 6 = ? 10. 88753 X 6 = ? 82. To Multiply by any Number. Multiply by the units digit as above, then by the tens, then by the hundreds, etc., placing the full product by each digit one place to the left of the one bejore it, then take the sum of the several products ; thus y 24682 = multiplicand 2354 = multiplier 98728 = product by 4 123410 = product by 5 74046 = product by 3 49364 = product by 2 58101428 = TOTAL PRODUCT. NOTE To Prove Multiplication by casting out the 9's : (1). Cast out the 9's of the multiplicand and also of the multiplier. (2). Cast out the 9's from the product of the remainders. This re- mainder should equal the remainder after casting out the 9's of the total product. MULTIPLICATION 29 Solve the following and prove : 1. 3845 X 2625 = ? 6. 83214 X 33654 2. 8227 X 3144 = ? 7. 77558 X 24875 3. 6782 X 4372 = ? 8. 84923 X 71684 4. 9247 X 5428 = ? 9. 98059 X 39563 5. 6782 X 6534 = ? 10. 56789 X 40387 83. To Multiply by any Number between 12 and 2 0. Multiply by the units figure only ; write the result under the number and one place to the right, then add. EXAMPLE : 13 times 235 = (235 < 705 = 3 times 235 (3055. Solve the following : 1. 312 X 13 = ? 6. 14256 X 14 = ? 2. 425 X 14 = ? 7. 26754 X 16 = ? 3. 565 X 15 = ? 8. 30875 X 17 = ? 4. 364 X 16 = ? 9. 59874 X 18 = ? 5. 721 X 17 = ? 10. 78395 X 19 = ? 84. To Multiply by 21, 31, 41, 51, etc. Multiply by the tens figure only, writing the result under the number and one place to the left, then add. EXAMPLE : 31 times 423 = 423 1 269 = 3 times 423 13113. Solve the following : 1. 243 X 21 == ? 6. 724 X 41 == ? 2. 325 X 31 = ? 7. 785 X 61 = ? 3. 472 X 41 = ? 8. 847 X 71 = ? 4. 537 X 51 = ? 9. 875 X 81 = ? 5. 654 X 61 = ? 10. 987 X 91 = ? 85. To Multiply by 15. Anex a cipher to the number and add its half. EXAMPLE : 15 times 28 = ( 2 8 one cipher anexed < 140 = \ of 280 (420. 30 MODERN BUSINESS ARITHMETIC Solve the following : 1. 24 X 15 = ? 6. 274 X 15 = ? 2. 36 X 15 = ? 7. 482 X 15 = ? 3. 44 X 15 = ? 8. 925 X 15 = ? 4. 54 X 15 = ? 9. 896 X 15 = ? 5. 85 X 15 = ? 10. 987 X 15 = ? 87. To Multiply by 51. Take one-half the number, write it two places to the left and add. EXAMPLE : 51 X 72 = ( 72 < 36 = \ of 72 ' 3672 Solve the following : 1. 48 X 51 = ? 6. 324 X 51 = ? 2. 54X51 = ? 7. 468X51 = ? 3. 66 X 51 = ? 8. 525 X 51 = ? 4. 82 X 51 = ? 9. 728 X 51 = ? 5. 95 X 51 = ? 10. 895 X 51 = ? 88. To Find the Product of Complementary Num- bers. Multiply the tens' digit by one unit greater and annex the product of the units. NOTE Complementary Numbers are those whose tens' digits are identical and the sum of whose units' digits is 10. EXAMPLE : 23 times 27 = 621. 2X(2 + 1)= : 6, and annex 3X7= 621. Solve the following : 1. 14 X 16 = ? 6. 52 X 58 = ? 2. 13 X 17 = ? 7. 67 X 63 = ? 3. 26 X 24 = ? 8. 74 X 76 = ? 4. 39 X 31 = ? 9. 85 X 85 = ? 5. 45 x 45 = ? 10. 93 X 97 = ? 89. To Find the Product of Two Numbers whose Units' Digits are 5's. To the product of the tens add one-half their sum in whole num- bers ; if the sum be even, annex 25 ; if odd , annex 75. EXAMPLE : 25 times 45 = 2 X 4 + ^^ == 11 Annex 25 = 1125. MULTIPLICATION 31 EXAMPLE : 35 times 65 = 3 X 6 + LJ5 = 22 Annex 75 = 2275. Solve the following : 1. 25 X 65 = ? 6. 35 X 55 = ? 2. 35 X 55 = ? 7. 25 X 75 = ? 3. 45 X 85 = ? 8. 45 X 95 = ? 4. 65 X 45 = ? 9. 55 X 85 = ? 5. 75 X 95 = ? 10. 75 X 95 = ? 90. To Find the Product of Two Numbers having a Repeated Digit in the Multiplicand, in the Multi- plier, or in the Tens' or Units' Place. Thus : 33 alike in 54 alike in 42 multiplicand 22 multiplier 1386 1188 47 alike in 36 alike in 42 tens' place 56 units' place 1974 2016 Take the product of the units, the product of the like digit times the sum of the unlike digits, and the product of the tens, carrying when necessary. EXAMPLE : 52 times 44. 4X2 8 product of units. 4 X (5 + 2) = 28 product of the like dig- it times the sum of the unlike digits. 5X4 =20 product of the tens. 2288 EXAMPLE : 45 times 42 . 2X5= 10 product of units. 4X7= 28 product of like digit times the sum of unlike digits. 4X4 == 16 product of tens. 1890 NOTE This work should all be mental, answers only to be written. 32 MODERN BUSINESS ARITHMETIC Solve the following : 1. 22 X 71 == ? 6. 82 X 83 = ? 2. 45 X 66 = ? 7. 78 X 48 = ? 3. 34 X 37 = ? 8. 63 X 65 = ? 4. 55 X 28 = ? 9. 49 X 79 = ? 5. 46 X 36 = ? 10. 85 X 86 = ? 91. To Find the Product of any Two Numbers Consisting of Two Digits. . Take the product of the units, the sum of each ten times the other number's unit, and the product of the tens, carrying when necessary. EXAMPLE : 47 times 36. 6X7= 42 product of units. (6 X 4) -f- (3 X 7) = 45 sum of products of tens and units 4X3 = 12 product of tens. 1692 Solve the following : 1. 24 X 35 = ? 6. 46 X 39 = ? 2. 52 X 46 = ? 7. 52 X 47 == ? 3. 71 X 84 = ? 8. 63 X 81 .-= ? 4. 38 X 57 = ? 9. 85 X 92 = ? 5. 63 X 49 = ? 10. 93 X 47 = ? 92. To Multiply by Complements. From either number subtract the complement of the other \ and annex the product of the complements. NOTE A complement of a number is 100, 1000, etc., less the number. Thus, the complement of 97 is 3, of 88 is 12, of 996 is 4, etc. EXAMPLE : 94 complement 6 97 complement 3 18 product of complements 91 = 94 3 or 97 6 9118 EXAMPLE : 998 complement 2 989 complement 11 022 product of complements 987 = 998 11 or 989 2 987022 NOTE When the numbers consist of three digits, the product of the complements requires three places, as 022 above. MULTIPLICATION 33 Solve the following : 1. 92 X 87 = ? 6. 996 X 995 = ? 2. 94 X 75 = ? 7. 975 X 994 = ? 3. 99 X 93 = ? 8. 988 X 997 = ? 4. 97 X 91 == ? 9. 994 X 998 = ? 5. 88 X 95 = ? 10, 999 X 989 = ? 93. To Multiply by Excesses. From the sum of the numbers subtract 100 or 1000, as required, and annex the product of the excesses. NOTE An excess is the amount greater than 100, 1000, etc. EXAMPLE : 115 times 104 == 11960. 115 + 04 = 119 To 119 annex 15 times 4 =.60 = 11960. EXAMPLE : 1008 times 1007 = 1015056. 1008 + 007 = 1015, annex 056 = 1015056. Solve the following : 1. 1005 X 1007 = ? 6. 1012 X 1005 = ? 2. 1004 X 1008 = ? 7. 1015 X 1004 = ? 3. 1003 X 1009 = ? 8. 1025 X 1002 = ? 4. 1002 X 1004 = ? 9. 1035 X 1006 = ? 5. 1007 X 1009 = ? 10. 1012 X 1025 = ? NOTE This principle may be carried to numbers a little over 200, 300, 400, 2000, 3000, etc. 94. To Find the Product of Two Numbers, one of which is More and the other I/ess than 100, 1000, etc. From the sum of the numbers subtract 100 or 1000, as required, annex two ciphers and subtract the product of the excess and com- plement. EXAMPLE : 108 excess 8 98 comp. 2 10600 Ifi product of excess and comp. 10584 Solve the following : 1. 102 X 94 == ? 6. 1004 X 992 = ? 2. 103 X 97 = ? 7. 1008 X 995 = ? 3. 115 X 96 = ? 8. 1015 X 993 = ? 4. 125 X 92 = ? 9. 1025 X 994 = ? 5. 116 X 95 = ? 10. 1075 X 998 = ? 34 MODERN BUSINESS ARITHMETIC PRACTICAL, PROBLEMS 95. Solve the following- : 1. If I receive $1800 salary, pay $260 for board, $187.50 for clothing, $135.75 for books, $45.50 for charity, and $105.25 for other expenses anually, what can I save in five years ? 2. A merchant bought 17 bolts of calico at 4 cents per yard, 12 bolts sheeting at 7 cents per yard, 21 bolts silesia at 8 cents per yard, and 14 bolts cambric at 3 cents per yard. If the bolts contained 43 yards each, what was the amount of the bill ? 3. Jones paid $1537.50 for 375 barrels of flour. If he sold the same at $4.35 per barrel, what would be the gain ? 4. A man owing $15760, gave in payment 5 lots of land, each worth $730, 5 horses valued at $236.50 each, an interest in a mine worth $2000, and $1728.75 in money. How much re- mained unpaid ? 5. Bought 250 barrels of flour for $1150 ; finding 25 barrels of it worthless, sold the remainder at $4.75 per barrel. Did I gain or lose, and how much ? 6. Brown's inventory of stock consisted of the following : 18 horses worth $75 each, 13 mules worth $52.50 each, 124 milch cows worth $41.25 each, 345 beef steers worth $61.75 each, and 87 calves worth $7.50 each. What was the value of his stock ? 7. Find the total amount of the following inventory : 7 bar- rels N. O. Molasses, 52, 53, 54, 45, 47, 49, 44, @ 35 cents per gallon; 4 barrels granulated sugar, 325, 334, 328, 317, @ 5 cents per Ib. ; 19 sacks "A" sugar, 100 Ibs. to the sack, @4 cents per Ib. ; 5 bags Rio coif ee, 121, 128, 124, 131, 132, @ 19 cents per Ib. 8. If a man earns $55 per month the first year, $65 per month the second year, $75 per month the third year, $85 per month the fourth year, and $95 per month the fifth year ; what will be his earnings for the whole five years ? 9 . Smith bought bonds as follows : 105 shares Ohio 4 ' s @ 117, 108 shares of Pensylvania 5's @ 113, 98 shares N. Y. Central @ MULTIPLICATION 35 92, 88 shares of Baltimore & Ohio @ 95, 112 shares of water bonds @ 98, and 85 shares of Santa Rosa Municipal 4V s @ 105 ; what was his total investment ? 10. Find the amount of the following bill by using short methods of multiplication : 48 yards of cloth @ 11^, 34 yards @ 22^, 45 yards @ 450, 62 yards @ 68^, 35 yards @ 37^, 84 yards @ 54^, 65 yards @ 85^, 75 yards @ 45^, 36 yards 72 yards 1. HOME WORK No. 4 Portland, Oregon, January 5 , 1908 , MR. C. C. DONOVAN, 328 Fourth Street Bought of A. P. ARMSTRONG & CO. DEALERS IN Terms: 30 ds. GRAIN, HOPS AND FARM PRODUCE 42 bu. Barley 75 24 Oats 35 18 " Flax 92 76 " Millet 84 225 " Wheat 95 358 " Corn 55 *** ** 2. Chicago, 111*, February 10, 1908. MR. 0. M. POWERS, City Bought of N. K. FAIRBANK & CO. DEALERS IN Terms: 60 ds. , 5% 10 ds. BEEF, PORK, FEED, and PRODUCE 84 bbls. Prime Corned Beef 12. 66 " A 1 Salt Pork 23. 720 " XXX R. M. Flour 6. 476 Sacks Barley .96 7340# Hazen Cheese .17 1644# Dairy Butter .30 48 bbls. N. Y. Salt .98 *** ** 36 MODERN BUSINESS ARITHMETIC 3. R. L. GOODYEAR, PRESIDENT L. S. GOODYEAR, SEC. TREAS. St. I^ouis, Mo., January 10, 1908. MR. HARRISON L. MEYER, Memphis, Tenn. BOUGHT OF THE GOODYEAR TEA CO. Net 60 ds. TERMS: 5% 30 ds. TEAS, COFFEES, and SPICES 10 % 10 ds. 85 Ibs. Fancy "A" Oolong 85c 64 Ibs. Choice " 66c 53 Ibs. English Breakfast 57c 48 Ibs. Choice Blend 42c 39 Ibs. Fine Black 31c 75 Ibs. Japan Extra 75c 9 4. All bills due subject to sight draft E. M. Huntsinger & Company TEAS, COFFEES, COCOA, AND CHOCOLATE TERMS: 30ds.net China and Glassware 5 % 10 ds. SOLD TO W. F. PRICE Hartford, Conn., Mar. 4, 1908. 135# Old Gov't Java 32c 162# Extra Mocha 35c 147# Costa Rico 22c 132# Guatemala 23c 144# Salvador 18c 152# Vienna Blend 24c ? 5. O. M. BRIGGS, PRESIDENT ELWYN SEA TON, SECRETARY J. S. TAYLOR, TREASURER If arin ufark Utanrit Qlnmpang AGENTS FOR GOLDEN GATE AND NATIONAL BISCUIT COMPANIES BOOK 5, Folio #7 SALESMAN Smith TERMS 30 ds. CINCINATTI, OHIO, April 1, 1908, SOLD TO U. S. ARLAND, Omaha, Neb. 132 Ibs. American Lunch lie 244 * * Cocoanut Wafers 18c 220 ' ' Chocolate Wafers 22c 230 ' ' Ginger Snaps 14c 260 * * Graham Wafers 13c 65 " Pretzels 12c 325 * ' Sodas 9c 9 DIVISION 96. Division is the process of ascertaining how many times one number is contained in another. 97. The Dividend is the number divided. 98. The Divisor is the number by which to divide. 99. The Quotient is the result obtained by division. 100. The Remainder is the number left after dividing when the division is not exact. 101. The Sign of Division is *-, and indicates that the number before it is to be divided by the one after it. 102. PRINCIPLES : 1. If the divisor and dividend are like numbers, the quotient is an abstract number. 2. If the divisor is an abstract number, the quotient is always like the dividend. 3. The remainder is always like the dividend. 103. PROOF : Multiply the quotient by the divisor, add the remainder, if any, and the result should equal the dividend. EXAMPLES : 48 -^ 4 == 12. Proof, 4 times 12 = 48. 56 -*- 9 = 6 and 2 remainder. Proof, 9 times 6 + 2 = 56. Short Division 104. When the Operation is Performed Mentally. Write the divisor at the left of the dividend with a line between. Divide the left hand digits by the divisor and write the result be- low. If there be a remainder prefix it mentally to the next digit and divide as before. 38 MODERN BUSINESS ARITHMETIC EXAMPLE : 215 9 ) 47846 5316 and 2 remainder. OPERATION : 47 -+- 9 = 5 and 2 remainder ; mentally prefix 2 to the next figure, and 28 -f- 9 = 3 and 1 remainder ; 14 -*- 9 = 1 and 5 remainder ; 56 -?- 9 = 6 and 2 remainder. PROOF : 9 times 5316 + 2 = 47846. NOTE The superior figures should not be written, but wholly carried in the mind. Solve the following : 1. 2. 3. 4. 5. 3426 -*- 3 = ? 4732 -s- 4 = ? 9678 -5- 2 = ? 8535 -s- 5 = ? 9122 -*- 6 = ? 6. 426713 -*- 7 =J 7. 726645 -*- 8 = ? 8. 432756 -s- 9 = ? 9. 407301 -4- 6 = ? 10. 891530 -5- 7 = ? I/ong Division 105. When the Operations are Written. Write the divisor at the left of the dividend with a line between. Divide as in mental operations, writing the figure of the quotient at the right or above the dividend. Multiply the divisor by the quo- tient figure and subtract the product from the left hand digits of the dividend. Bring down the next figure and proceed as before. Thus : 135 ) 62352 ( 461 quotient 540 835 810 252 135 117 remainder. Solve the following : 1. 4272 -s- 16 = ? 2. 7175 -s- 25 = ? 3. 9676 -s- 34 = ? 4. 73521 -r- 40 = ? 5. 87965 -*- 57 = ? 6. 125789 -s- 61 = ? 7. 473826 + 79 ? 8. 587634 * 145 = ? 9. 590430 -*- 470 = ? 10. 787945 -# 1255 = ? DIVISION 39 106. When the Divisor Ends in Ciphers. Cut off as many figures from the right of the dividend as there are ciphers on the right of the divisor, and divide as before. The remainder will be the figures cut off annexed to those left after the last subtraction. EXAMPLE : Divide 3576 by 400 OPERATION : 4,00 ) 35,76 8 and 376 remainder. Solve the following : 1. 4500 -s- 30 = ? 6. 75620 -*- 200 = ? 2. 7650 -5- 50 = ? 7-. 89437 -*- 700 = ? 3. 3842 -4- 70 = ? 8. 296753 + 3000 = ? 4. 9250-^80 = ? 9. 576780 +- 8000 = ? 5 38520 -*- 90 = ? 10. 5548237 -*- 90000 = ? PRACTICAL PROBLEMS 107. Solve the following : 1. A grocer bought two kinds of syrup ; one for 54 cents a gallon, and the other for 62 cents a gallon. What was the aver- age cost a gallon ? 2. Hill's sales Monday were $104; Tuesday, $97; Wednes- day, $126; Thursday, $99; Friday, $142; Saturday, $120. What w r ere his average daily sales for the week ? 3. Frese bought 140 acres of land for $7560, and sold 86 acres at $75 per acre, and the remainder at cost. How much did he gain ? 4. Jewett's gain the first year was $2140, the second year it was double the first, the third it was as much as in both former years; if he lost $750 the fourth year, and gained $1250 the fifth, what was his average gain per year? 5. Olson paid $750 for a horse and carriage ; if the horse cost $120 more than the carriage, what was the cost of each? 6. A grocer wishes to put 351 pounds of tea into three sizes of boxes, using the same number of boxes of each kind. If the 40 MODERN BUSINESS ARITHMETIC sizes are respectively 4, 8, and 15 pounds each, how many boxes will be required ? 7. A, B, and C are in partnership. A's gain is twice B's, and B's is twice C's. If their total gain is $2464, how much is each one's gain? 8. A farm raises 12775 bushels of wheat, averaging 25 bush- els to the acre ; 3663 bushels of oats, averaging 37 bushels to the acre ; and 4992 bushels of corn, averaging 52 bushels to the acre. How many acres are there in the farm ? 9. If the population of the United States is 91,020,000, what is the average number of in habitants represented by each of the 444 Congressmen? 10. Prindle & Co.'s sales averaged $1252 per week for the year. Counting 52 weeks and 313 days to the year, what were his average daily sales ? HOME WORK No. 5 1. Solve : ( 15341 -5- 29 ) X ( 8430 * 1405 ) == 1587 X ? 2. The divisor is 15, the quotient 78, and the remainder 4; what is the dividend ? 3. My taxes for 5 years were as follows : $47 the first year, $54 the second, $65 the third, $88 the fourth, and $106 the fifth; what was my average yearly taxes ? 4. A and B are together worth $15760, and A is worth $1240 more than B ; what is each man worth ? 5. I sold a lot of wood for $423, thereby gaining $2 per cord ; if the wood cost me $329, how many cords did I sell ? Properties of Numbers 108. An Integer is a whole number. 109. An Even Number is a number whose unit figure is 0, 2, 4, 6, or 8. 110. An Odd Number is a number whose unit figure is 1, 3, 5/7, or 9. 111. A Prime Number is one that is not exactly divisible except by itself or 1 ; as 2, 3, 5, 7, 11, 13, etc. 112. A Composite Number is divisible by some number besides itself and 1 ; as 4, 6, 8, 9, 12, 15, etc. 113. An Exact Divisor of a number is one that will di- vide it without a remainder. Thus, 7 is an exact divisor of . 21. 114. A Factor of a Number is an exact divisor of the number. Thus, 3 is a factor of 15. 115. A Common Factor, or Common Divisor, of two or more numbers is a number that will exactly divide all of them. Thus, 5 is a common factor of 10, 15, 20, 25, etc. 116. The Highest Common Factor, or Greatest Com- mon Divisor, of two or more numbers is the greatest number that will exactly divide all of them. Thus, 15 is the highest com- mon factor of 45, 60, and 75, although both 3 and 5 are common factors. 117. To Factor a number is to find its factors or divisors. 118. A Multiple of a number is a number that is exactly divisible by that number. Thus, 32 is a multiple of 8. 119. A Common Multiple of two or more numbers is a number that is exactly divisible by each of them. Thus, 84 is a common multiple of of 6 and 7. 120. The Least Common Multiple of two or more num- bers is the least number that is divisible by each of them. Thus, 42 is the least common multiple of 6 and 7. 42 MODERN BUSINESS ARITHMETIC 121. PRINCIPLES : 1. A divisor of a number will divide any multiple of that num- ber. 2. A common divisor of two or more numbers will divide their sum and also their difference. 3. Every multiple is equal to the product of its prime factors. 4. A common multiple of two or more numbers contains the prime factors of those numbers. 122. Cancellation is a process of shortening operations in division by rejecting common factors from both dividend and divisor. 123. Divisibility of Numbers : 1 . All even numbers are divisible by 2 . 2. Any number is divisible by 3 if the sum of its digits is divisible by 3. 3. By 4 if the two right hand digits express a number that is divisible by 4. 4. By 5 if the number ends in or 5. 5. By 6 if the number is divisible by 2 and 3. 6. By 8 if the three right hand digits express a number divis- ible by 8. 7. By 9 if the sum of the digits is divisible by 9. 8. By 10 if the number ends in 0. 9. By 12 if the number is divisible by 3 and 4. 10. By 15 if the number is divisible by 3 and 5. 11. By 18 if the number is divisible by 2 and 9. 12. By 7, 11, and 13 if the number is 1001 or any multiple of it; as, 20Q2, 5005, 12012, etc. 124. PRINCIPLE : A number is divisible by any number whose factors it contains. 125. To Find the Prime Factors of a Number. Divide the number by one of its prime factors, this quotient by another, and so on until the last quotient is a prime number. The several divisors and the last quotient are the prime factors. PROPERTIES OF NUMBERS 43 What are the prime factors of 1386 ? 2)1386 3)693 The divisors 2, 3, 3, 7, and the quo- 3)231 tient 11 are the prime factors. 7)77 1 1 Find the prime factors of the following : 1. 2445 5. 2366 2. 2934 6. 1140 3. 2205 7. 1155 4. 2310 8. 6300 126. To Find the Highest Common Factor of Two or more Numbers. Take the product of all the common prime factors ; the result will be the highest common factor . What is the highest common factor of 48, 72, and 120. 2)48 72 120 2)24 36 60 The product of the prime 2 ) 12 18 30 factors 2 X 2 X 2 X 3 = 24, 3 ) 6 9 15 the highest common factor. 235 Find the highest common factor of the following : 1. 42 and 112 6. 143 and 1001 2. 96 and 144 7. 138 and 529 3. 45, 75, and 105 8. 165, 255, and 285 4. 72, 128, and 192 9. 420, 630, and 840 5. 120, 310, and 360 10. 462, 1078, and 1694 127. To Find the Greatest Common Divisor when the Numbers are not Readily Factored. Find the greatest common divisor of 364 and 925. 975 ANALYSIS : This operation is based on 728 principles 1 and 2, article 121. A divisor 247 f 364 will divide twice 364 or 728, and the 284 G. C. D. of 728 and 975 will divide their I % difference, 247 ; if this G. C. D. will divide 247 and 364, it will divide their difference, 117 ; if it will divide 117, it will divide twice 117, or 234; if it will divide 234 and 247, it will divide tJieir difference, 13 ; if the 44 MODERN BUSINESS ARITHMETIC G. C. D. will divide 13, it will divide 9 times 13, or 117. Since 13 is the greatest divisor of itself, it must be the G. C. D. of the given numbers. Find the greatest common divisor of the following : 1. 632 and 1328 6. 1372 and 1650 2. 527 and 1207 7. 4082 and 8476 3. 378 and 648 8. 10907 and 14482 4. 906 and 2192 9. 4746 and 6667 5. 1358 and 3738 10. 14256 and 32562 128. To Find the I/east Common Multiple of Two or More Numbers. Take the product of all the prime factors of the greatest number, and sue h prime factors of the other numbers as are not found in the greatest number, and the result will be the L. C. M. of the num- bers. What is the least common multiple of 18, 24, and 54 ? 2) 18 24 54 2X3X3X4X3 = 216. 3) 9 12 27 ANALYSIS: Reject the factors 2, 3, and 3 3) 3 4 9 which are common to two or more of the num- ~j~~ ~~^ bers ; the product of these common factors and the factors not common will give the least common multiple of the numbers. Find the least common multiple of the following : 1. 27, 36, and 45 6. 8, 12, 18, 27, and 36 2. 32, 42, and 56 7. 10, 25, 75, 150, and 2:25 3. 21, 44, and 126 8. 18, 24, 36, 48,. 72, and 96 4. 30, 42, 66, and 78 9. 17, 51, 85, 153, and 187 5. 24, 32, 72, and 96 10. 5698 and 9324 PRACTICAL PROBLEMS 129. Solve the following : 1. Find the greatest common divisor of 792, 2592, and 3456. 2. Find the least common multiple of 32, 44, 132, and 352. 3. What is the greatest number that will divide 5184 and 6924? 4. What is the least number that can be exactly divided by 17, 51, 85, and 119? PROPERTIES OF NUMBERS 45 5. Johnson's farm is in the form of a rectangle, and is 2925 feet wide by 3458 feet long. What is the length of the longest board that can be used to fence it without cutting, and how many boards will be required to build a fence six boards high ? 6. What is the smallest sum of money that can be paid for shoes at $1.75, $2.50, or $3.25 ? 7. If Brown, White, and Green have $630, $1134, and $1386 respectively, and agree to purchase horses at the highest price per head that will allow each man to invest all his money ; what will be the price paid and how many horses will each one buy ? 8. What is the length of the shortest rope that can be cut into 14, 28, or 35 foot lengths? 9. What is the smallest quantity of wine that will fill casks holding either 44, 48, or 56 gallons each? 10. Arland has three wine tanks that hold respectively 2109, 3363, and 3819 gallons each. He wishes to empty these tanks into casks of uniform size, the largest that will contain exactly the contents of each tank. What must be the size of the casks, and how many will it take ? HOME WORK No. 6 1. What is the least quantity of grain that exactly will fill bins holding 36, 45, 63, or 72 bushels each? 2. What is the least sum of money that exactly can be spent for horses at $140, cows at $91, or sheep at $7 per head ? 3. A commission merchant wishes to ship 30584 bushels of wheat, 3040 bushels of corn, and 1004 bushels of oats. If it must all be shipped in bags of equal size, what will each bag hold, and how many bags will be required ? 4. A, B. and C have respectively $315, $567, and $693 with which to purchase horses. If they pay the highest price possi- ble, and all pay the same price, how many horses will each buy? 5. \Vhat is the least sum of money that can be spent for tea at 72^, or 54^, or 45^, or 36^ per pound ? 46 MODERN BUSINESS ARITHMETIC Outline for Review I. Addition : 1. Definitions. 2. Sum. 3: Sign of Addition. 4. Sign of Kquality. 5. Sign of Dollars. 6. Reading Method. 7. Proof. II. Subtrac tion : 1. Definitions. 2. Minuend. 3. Subtrahend. 4. Difference. 5. Sign of Subtraction. 6. Parenthesis and Bar. 7. Principle and Proof. III. Multiplication : 1. Definitions. 2. Multiplicand. 3. Multiplier. 4. Product. * 5. Sign of Multiplication. 6. Abstract and Concrete Numbers. 7. Short Methods. IV. Division. 1. Definitions. 2. Dividend. 3. Divisor. 4. Quotient. 5. Remainder. 6. Sign of Division. 7. Short and Long Division. V. Properties of Num- bers : 1. Integers. 2. Odd and Even. 3. Prime and Composite. 4. Divisors and Factors. 5. Greatest Common Divisor and Highest Common Factor. 6. Multiples. 7. Common and Least Com- mon Multiple. 8. Divisibility of Numbers. 9. To Find the Highest Com- mon Factor or Greatest Common Divisor. 10. To Find the Least Common Multiple. CANCELLATION 130. Cancellation is the shortening of operations in divis- ion by rejecting common factors from both dividend and divisor. EXAMPLE : Divide 12 X 15 X 32 X 40 by 8 X 5 X 9 X 2. 43 % It X *3 X 32 X 40 = 32 * X $ X X 20 * 3 SOLUTION : Reject the factors 20, 5, 3, 3, 4, and 2 in the order named ; the quotient will be 32. Solve the following : 1. 9 X 14 X 34 -s- 18 X 17 2. 28 X 45 X 11 -^ 22 X 36 3. 63 X 25 X 18 -f- 12 X 45 4. 54 X 36 X 49 -s- 7 X "9 X 12 5. 81 X 96 X 64 *- 128 X 54 6. 144 X 84 X 16 -*- 1728 X 28 7. 85 X 92 X 55 -5- 44 X 34 X 46 8. 1050 X 312 -f- 35 X 10 X 52 9. 4096 X 1024 H- 256 X 512 10. 5280 X 12 -*- 3 X 33 X 40 X 8 PRACTICAL PROBLEMS 131. Solve the following : 1. How many tons of hay at $18 per ton must be given for 33 cords of wood at $6 per cord ? 2. How many barrels of flour at $4 per barrel will pay for 256 bushels of wheat at $1 per bushel ? 3. How many crates of eggs, each containing 54 dozen, worth 25 cents per dozen, will pay for 9 barrels of sugar, each barrel containing 325 pounds, worth 6 cents per pound ? 4. A man worked 17 days for 119 bushels of barley worth 40 cents per bushel. What was his' work worth per day? 48 MODERN BUSINESS ARITHMETIC 5. How many bushels of wheat at 60 cents per bushel will pay for 12 tons of coal at $7.20 per ton ? 6. Brown exchanged 320 bushels of corn worth 75 cents per bushel for barley worth 90 cents, and oats worth 60 cents, of each an equal amount. How many bushels of each did he re- ceive ? 7. How many chests of tea, each containing 72 pounds worth 35 cents per pound, will pay for 70 boxes of prunes, each box containing 42 pounds worth 6 cents per pound ? 8. L. W. Scarlett bought two kinds of cloth, one kind at 70 cents per yard, the other at 95 cents per yard. If he took twice as many yards of the first as of the second and paid for both with 329 pounds of butter at 35 cents per pound, how many yards of each kind did he buy ? 9. J. S. Taylor exchanged 470 bushels of corn worth 60 cents per bushel, and 300 bushels of barley worth 70 cents per bushel for tea at 50 cents per pound, coffee at 30 cents per pound, and cocoa at 40 cents per pound, of each an equal amount. How many pounds of each did he receive ? 10. D. M. Cook gave 12 bales of hops, 250 pounds to the bale worth 17 cents per pound, for calico worth 5 cents per yard, muslin worth 10 cents per yard, and gingham, worth 15 cents per yard. If there were twice as many yards of muslin as of cal- ico, and twice as many yards of gingham as of muslin, how many yards of each did he buy ? HOME WORK No. 7 ( Solution and answers required.) 1. Bring in an original problem in the subjects of Addition and Subtraction, containing at least twenty different numbers. 2. Bring in an original problem in Multiplication containing ten different short cuts. 3. Bring in a model bill of not less than ten items, extended, and footed, in which short methods are used. 4. Bring in an original problem in which the greatest com- mon divisor is to be found. 5. Bring in an original problem in which the least common multiple is to be found. FRACTIONS 132. Fractions represent parts of units or things. 133. A Simple Fraction represents one or more of the equal parts of a unit. As, one-half and two-thirds are fractions. 134. A Fractional Unit is one of the equal parts into which a unit is divided. As, one-third is a fractional unit. 135. The Denominator of a fraction is written below the line and shows the number of parts into which the unit is divided. 136. The Numerator of a fraction is written above the line and shows the number of parts taken or considered. 137. The Terms of a fraction are its numerator and denom- inator. Thus, f is a fraction. The denominator 8 shows that the unit is divided into 8 parts. The numerator 5 indicates that 5 parts are taken. The terms are the 5 and the 8. 138. A Proper Fraction is one whose numerator is less than its denominator. As, f , f, J, etc. 139. An Improper Fraction is one whose numerator is equal to or greater than its denominator. As, y, f , V, etc. 140. A Simple Fraction is one having a single number for its numerator and a single number for its denominator, but may be either proper or improper. As, f , 1, etc. 141. A Compound Fraction is a fraction of a. fraction or two or more fractions to be multiplied together. As, f X f X -j. 142. A Complex Fraction is one that has a fraction in either its numerator or in its denominator, or in both. Thus, -4- -5- are complex fractions. 5 f 1 143. A Mixed Number is a whole number and a fraction united. As, 4^, 5^1 144. The Value of a fraction is the quotient of its numera- tor divided by its denominator. Thus, the value of V" is 5, of 1 .-> is 31. 50 MODERN BUSINESS ARITHMETIC 145. Principles of Fractions : 1. Multiplying the numerator or dividing the denominator multiplies the fraction. 2 . Dividing the numerator or multiplying the denominator divides the fraction. 3. Multiplying or dividing both numerator and denominator by the same number does not change the value of the fraction. 146. The Reciprocal of a number or of a fraction is 1 di- vided by the number or by the fraction. As, the reciprocal of 5 is 1 -*- 5 or i ; of f is 1 -H f or f . Reduction of Fractions 147. Reduction of Fractions is changing their form without altering their value. 148. To reduce a fraction to Higher Terms is to express its terms in greater numbers. As, f = A = If 149. To reduce a fraction to I^ower Terms is to express its terms in less numbers. As, -ff = \% = |. 150. A fraction is reduced to its lowest terms when its num- erator and denominator have no common factors. 151. To reduce a fraction to its lowest terms, reject from both numerator and denominator all common factors, or divide both numerator and denominator by their greatest common di- visor. Reduce to their lowest terms : 1. 6. 2. If 7. 3. JA- 8. 4. W* 9. 5. T & 10. 152. To reduce a whole or mixed number to an improper fraction, multiply the whole number by the denominator, and to FRACTIONS 51 the product add the numerator of the fraction, and write the re- sult over the denominator. EXAMPLE : Reduce 8| to an improper fraction. ( 8 X 5 ) + 2 == 42. Answer," - 4 /. Reduce to improper fractions : 1. Hi 5. 96 r 4 r 9. 1264f 2. 17 J- 6. 148-H 10. 3240J-H 3. 35J 7. 785H 11. 5674 r Wg 4. 78| 8. 725f 12. 34216f 153. To reduce an improper fraction to a whole or mixed number, divide the numerator by the denominator. EXAMPLE : Reduce -HP to a whole number. 132 -5- 4 = 33. Reduce to whole or mixed numbers : 1. *** 5. W 9. 2. *i* 6. W 10. 3. W 7. -W- 11. 4. -41- 8. 4t A 12. 154. To reduce fractions to a common denominator, find the the least common multiple of the denominators for the least common denominator. Divide this least common denominator by the denominator of each of the given fractions and multiply its numerator by the quotient. The result will be the new num- erators. EXAMPLE : Reduce |, i\, and yV to their least common de- nominator. 4 ) I A 1 5 4 X 3 X 2 X 3 = 48, the least 2)23 4 common multiple of the denomi- 132 nators. 48 -4- 8 = 6 6X3=- 18 48 -*- 12 = 4 4 X 5 = 20 ^ Answer, i?, i, 48 -s- 16 = 3 3 X 17 = 51 52 MODERN BUSINESS ARITHMETIC Reduce the following to their least common denominator : I- I, A, I 6. 4i, V, I 2. *, A, H 7. A, 7i, if 3. f, -H, 8. A, A, A, if 4. if, li, I 9. 6i-, I, 9A, 17H 5. W, H, 10. iH, H, M, H Addition of Fractions 155. To Add Fractions Having a Common Denom- inator. Add their numerators, write this sum over their common denom- inator, and find the value of the fraction. Add the following : 1.' t + I + t '+ 1 6. A + if + H 2. f+ 4 + i + * 7. T fc + T fe + | 3. A + A + A + H 8- 8i + i + 18f 4. + ii + + !f 9. 27i + 45f + 85J 5. I! + i! + If + 10. 12f + 35J + 124| NOTE Whole numbers and fractions may be added separately. 156. To Add Two Fractions Having a Common Numerator. Add the denominators, multiply this sum by the common numer- ator, and write the result over the product of the denominators. Add the following : 1. f + ? 6. H + -B 2. I + I 7. 9f + 17| 3. f + A 8. 43 T 5 T 4. 1 + A 9. 125A + 94A 5. if + M 10. FRACTIONS 53 157. To Add Fractions Having neither a Common Numerator nor a Common Denominator. Multiply each numerator by the product of all the denominators except its own for new numerators, write their sum over the pro- duct of all the denominators. EXAMPLE : Add \ + f + f 2 X 4 X 5 = 40 4/~) I 4 r _i_ 40 loo 3 X 3 X 5 = 45 4 x 4 X 3 = 48 60 60 Add the following : !.'*+! 6. i + f + | 2. I + I 7. i + f + 4 3. 4 + | 8. f + A + U 4. A + A 9. t+i+| 5. A + if 10. ? + A + 158. To Add Fractions by Reducing Them to their Least Common Denominator. Reduce the fractions to their least common denominator, add their numerators, write the result over the least common denominator, and find the value of the fraction. NOTE Add whole numbers and fractions separately. EXAMPLE : Add 5A + ?U + 12H- Adding 5 + 7 + 12 = 24, sum of the whole numbers. A + ii + == + 44 + == W - W. 24 + 1H = 25H- Add the following : 2. A + W + i* 7. 23I + 47A + 82H 3. H + if + 41- 8. 5. iVoV + Toy + TVvV 10. W + 145A + 54 MODERN BUSINESS ARITHMETIC Subtraction of Fractions 159. To Subtract Fractions Having a Common De- nominator. Write the difference of the numerators over the common denomi- nator. Solve the following : i. A A = ? 6. m ^==? 2. H tt = ? 7. 15| 7t = ? 3. *f H==? 8. 45--4lA==? 4. ** ** = ? 9. 82A 53 = ? 5. ! = ? 10. 175JI 120ft = ? NOTE If the fraction of the subtrahend is the greater, write one less than the difference of the whole numbers for the integral part, and the complement of the difference of the fractions for the fractional part. Thus 5-J- 2f = ( 5 2 ) less 1 = 2, and the complement of *\ i which is f. Answer, 2f. 160. To Subtract Fractions Having a Common Numerator. Multiply the difference of the denominators by the common num- erator and write the result over the product of the denominators. EXAMPLE : | 4= (7 4) X 3 = 9, the numerator. 4 X 7 = 28, the denominator. Answer, ^. Solve the following : 1. i-l==? 6. fJ-M = ? 2. *-* = ? 7. *-* = ? 3. !-*? 8. ?-?=? 4. A A = ? 9. 5. -=? 10. 161. To Subtract Fractions Having neither a Com- mon Numerator nor a Common Denominator. From the product of the first numerator times the second denomi- nator take the product of the second numerator times the first de- nominator. Write this difference over the product of the denomi- nators, FRACTIONS 55 3X3 = 9. 4X2 = 8. 9 8'= 1, the numerator. 4 X 3 12, the denominator. Answer, iV EXAMPLE : I f 3X3 = 9. 4 4 X 3 = 12, tl Solve the following : 1. i f = ? 6. |i- = ? 2. |- * = ? 7. - f-? 3. * A==? 8. 5i 2f = ? 4. A ---4==? 9. 17& 14* = ? 5. if ~ II = ? 10. 48i 32| = ? 162. To Subtract Fractions by Reducing Them to a Least Common Denominator. Reduce the fractions to their least common denominator. Write the difference of their numerators over the least common denomina- tor. Solve the following : 1. H-T 7 by multiplying denominator. Solve the following : 1. Divide A by 4 6. Divide 4f by 8 2. Divide! if by 6 7. Divide 12$ by 9 3. Divide }f by 7 8. Divide 32} by 49 4. Divide ft by 9 9. Divide 48 f by 64 5. Divide ft by 18 10. Divide 54^ by 119 171. To Divide a Whole Number by a Fraction. Multiply the whole number by the denominator and divide the re- sult by the numerator of the fraction. EXAMPLE : 8 -*- f . 8 X 3 = 24. 24 ^ 2 = 12. Solve the following : 1. Divide 9 by I 6. Divide 65 by f 2. Divide 15 by | 7. Divide 78 by if 3. Divide 28 by | 8. Divide 96 by if 4. Divide 42 by }f 9. Divide 144 by \\ 5. Divide 57 by if 10. Divide 272 by \\ 172. To Divide a Fraction by a Fraction. Reduce whole or mixed numbers to improper fractions. Invert the divisor and proceed as in multiplication of fractions. Cancel if possible. EXAMPLE : Divide f X f by 3J X 4. | X f X A X i = | Ans. Solve the following : 1. * X * -*- iV X A 6. 41 X 1\ -+- 3 T 3 4 X 2i 2. | -X A X | H- I X if 7. 21 -f- i X | X | X | 3. f X ii -* If X | X | 8. f X * X f X f *- If 4. * X X if -s- ii X if 9. 5f -*- 5i X 5J 5- X if -s- | X A X A 10. 7i X 9J -f- 1 J X 6A 60 MODERN BUSINESS ARITHMETIC 173. To Reduce Complex Fractions. Divide the numerator of the complex fraction by the denomina- tor as in division of fractions. EXAMPLE : Reduce fi = 3 -5- 7i = t X A = ff . 7i Reduce the following : 15? 2 251 4A 7 5 6. _2 ! 3_ 1* X 3i 4i 4- 3* ' 7i- + 5A 8. 156} 2i ji 9. il 7 1 n * + (f X 3iO--(2rx H) J.U. 2i 2 oV + 2f X i? X 7i PRACTICAL, 174. Solve the following : 1. A man gave % of his fortune to his son, YZ to his daughter, and the remainder, $3500, to his wife. How much did his son and daughter each receive ? 2. A man owned YI of a business, and then bought % as much more. He then sold % of his interests for $1200. What was the value of the whole business ? 3. A's income is $2500 per year. If he spends \ of f of it for board, f of f of the remainder for clothes, | of fV of the re- mainder for books, and saves f of the remainder, how much can he save in three years ? 4. A man at his death left his wife $12500, which was \ of | of his estate. At her death she left f of her share to her daugh- ter. What part of her father's estate did the daughter receive from her mother ? 5. Jones's investment is 4 of Brown's, and Brown's is of Green's. If their total investment is $4830, what is each one's share ? 6. Brown lost ^ of his investment the first year. The sec- ond year he gained $400, and then had $800. What was his original investment? FRACTIONS 61 7. Smith bought a stock of goods and sold }i of it at a gain of $300, y* at a gain of $500, and the remainder at a loss of $200. What was the first cost of the goods, if the net gain was l /6 of the cost ? 8. Muir, Nunn, and Hakes receive $920 for doing a job of work. How much should each one get if the money is divided in proportion to % , ^ , and ^ . 9. Bought 27 % yards of matting at 23 X cents a yard, and paid for the same in eggs at 13 K cents a dozen. How many dozen eggs were required ? 10. A merchant invested % of his money in shoes, }i $100 in groceries, ^ + $200 in tea and coffee, Y% + $250 in hay and grain, and deposited the remainder, $588, in the bank. What was the total value of his property, and how much did he invest in each kind of stock ? HOME WORK-NO. 8 1. The sum of two numbers is 12% ; their difference is 3%. What are the numbers ? 2. A can do a piece of work in 4/^ days. If it takes B twice as long as A, and C ft as long as B, how long will it take C to do it? 3. A and B together have $1190. If Y\ of A's equals ^ of B's, how much has each ? 4. A 120 gallon tank has a pipe that will flow 15 gallons in 12 minutes. If another tank holding 180 gallons has a pipe that flows 20 gallons in 10 minutes, which tank will empty first, and in how much less time ? 5. Blank saves ^ of YZ of his income, and Black, having the same income, spends 2>^ times as much as Blank, and at the end of the year finds himself $150 in debt. What is the income of each ? 6. Willis sold goods for $2340 and gained ys of the cost. If he had sold them for $2050, would he have gained or lost, and how much ? 62 MODERN BUSINESS ARITHMETIC 7. Brown bought a house and lot paying % the price down, and the second payment was X the remainder due. If the sum of the two payments thus made was $2100, what was the cost price of the place ? 8. A boy lost YZ of ^ of his kite string, then added 60 feet. He then lost /^ of what he then had, then by adding 60 feet found it Y^ of its original length. What was its length at first? 9. A pole is y? in the mud, X i n the water, and the part in the air is >i its length plus 23 feet. What is the length of the pole? 10. A's automobile travels 21 miles in 45 minutes, and B's will travel 30 miles in 65 minutes. If the race course is 195 miles long, which will win, and by how much time? DECIMALS 175. A Decimal Fraction is a fraction whose denomina- tor is 10, 100, 1000, etc. Thus, T \, -ffo, T VoV are decimal frac- tions. 176. A Decimal has the same value as a decimal frac- tion, and is expressed by writing the numerator only, the de- nominator being indicated by the number of decimal places. Thus, .3, .27, .125, are decimals and are read three- tenths, twenty-seven hundred ths, etc. 177. The Decimal Sign ( . ), called the decimal point, is used to separate the decimal from the units place. 178. A decimal always contains as many decimal places as there are ciphers iu the denominator of an equivalent decimal frac- tion. 179. A Pure Decimal consists of a decimal only. Thus, .5, .25, .375. 180. A Mixed Decimal consists of a whole number and a decimal. Thus, 4.5, 6.25, 27.375. 181. Decimals increase from right to left and decrease from left to right in a ten fold ratio, the same as whole numbers. 182. Decimals are read the same as d'ecimal fractions. Thus, .8 is read eighth- tenths, and .75 is read seventy-five hundredths. 183. Read the following : 1. .9 6. .04 2. .34 7. .2045 3. .345 8. .00705 4. .2487 9. 234.010735 5. .35362 10. 2004.4002 184. Write the following : 1. Eleven hundredths. 2. Forty- two thousandths. 3. Seven hundred five ten thousandths. 64 MODERN BUSINESS ARITHMETIC 4. Five thousand two hundred ten hundred thousandths. 5. Two hundred five thousand six hundred four millionths. 6. Twenty-seven and two- tenths. 7. One hundred ten and thirty-five thousandths. 8. Thirty-three and one-third, hundred ths. 9. Three thousand and three thousandths. 10. Seventy-two million and seventy-two millionths. Reduction of Decimals 185. To Reduce a Decimal to a Common Fraction. Write for the denominator I with as many ciphers as there are decimal places in the decimal and reduce the resultant fraction to its lowest terms. Reduce to common fractions : 1. .8 6. .121 2. .75 7. .37} 3. .625 8. 4.125 4. .1525 9. 18.41875 5. .4875 10. 145.33J 186. To Reduce a Common Fraction to a Decimal. Annex ciphers to the numerator and divide by the denominator. Point off as many decimal places as ciphers used. Reduce to decimals : 1. \ 6. 5i 2. | 7. 27i 3. 1 8. 64| 4. A 9. 4.2A 5. H 10 - 87 A Addition of Decimals 187. To Add Decimals. Reduce all fractions to decimals. Write units of like order in the same columns. Add as in whole numbers, placing the decimal point between the units' and tenths^ places. FRACTIONS 65 Find the sum of the following : 1. .245, .76, .358, .1976, .40257, .38964 2. .25.2, 1.8, 325.4, 60.02, 7.6025 3. 425., .785, 30.972, .046, .0002, 880 4. i, f, T 3 6, I, TV 5. 2t, 27i, 6.2i, 387.5, .3125, 8f Subtraction of Decimals 188. To Subtract Decimals. Reduce all fractions to decimals. Write units of like order in same columns. Subtract as in whole numbers, placing the decimal between units 1 and tenths 1 places. Solve the following : 1. From 42.5 take 35.3 6. From f take .54 2. From 212.25 take 93.5 7. From 8.02 take 8.002 3. From 1216J take 93.5 8. From 126.5 take 12.65 4. From ?i take 3A 9. From 47i take 2.5i 5. From 1.275 take .031 10. From 7896 take 69.87 Multiplication of Decimals 189. To Multiply Decimals. Multiply as in whole numbers. From the right point off as many decimal places in the product as there are in both multiplier and multiplicand. Solve the following : 1. Multiply .75 by .5 6. Multiply 4^ by 7.5 2. Multiply 1.25 by .25 7. Multiply .375 by 6J 3. Multiply 41.75 by .03 8. Multiply 23.54 by 41.5 4. Multiply 2.1875 by 1.5 9. Multiply 7^ by 6i 5. Multiply .0525 by .0035 10. Multiply 1.5} by 93J. 66 MODERN BUSINESS ARITHMETIC Division of Decimals 190. To Divide Decimals. If necessary , annex ciphers to the dividend and divide as in whole numbers. From the right, point off as many decimal places in the quotient as those in the dividend exceed those in the divisor. Solve the following : 1. Divide 2.16 by 3.6 6. Divide \1\ by .35 2. Divide 9.654 by .03 7. Divide 8^ by .625 3. Divide 102.4 by .32 8. Divide .00261 by 300 4. Divide 1850 by .25 10. Divide 202.002 by .006 Circulating Decimals 191. A Circulating Decimal is a decimal in which a fig- ure or set of figures are repeated indefinitely. Thus, ^ .3333 + , and A = .727272 + . 192. A Repetend is the repeated figure or figures, and is represented by a dot over the repeated part. Thus, .3333 + .3, .727272+ = - .72, and .135135135+ : - .135. 193. A repetend arises from the reduction of a common frac- tion whose denominator is not a factor of 10, 100, 1000, etc. 194. A repetend may be reduced to a common fraction by using for its denominator as many 9's as there figures in the re- petend. Thus, .3 == | == i .72 == -5 == -A, .135 == iSi = iV\ 3 5 T- 195. To add or subtract repetends, continue repetend of each number until they terminate at the same place. Add or subtract as in finite decimals, carrying when necessary. Thus, .333333 .727272 .135135 1.195741 196. In multiplication and division of decimals, it is best to reduce repetends to common fractions and then multiply or di- vide as required. DECIMALS 67 197. Solve the following : 1. Reduce f to a circulating decimal. 2. Reduce f to a circulating decimal. 3. Reduce ^ to a circulating decimal. 4. Reduce .45 to a common fraction. 5. Reduce .513 to a common fraction. 6. Reduce .142857 to a common fraction. 7. Add .35 + .7 + .137 + .18 + .241.* 8. Add i\ + .230769 and reduce to a common fraction. 9. From f take .432 and reduce to a repetend. 10. From .758241 take .571428 and reduce to a common frac- tion. PRACTICAL PROBLEMS 198. Solve the following : 1. How many acres in a farm consisting of five fields as fol- lows : 55/4 acres of wheat, 72.75 acres of corn, 27^ acres of oats, 18^ acres of barley, and 21.625 acres of pasture land? 2. How many chains in length will be the total distance around three fields, each 77.15 chains long and 54.375 chains wide? 3. A's ranch consisted of 1274.3 acres, and B's of 935.25 acres. How much more land did A own than B ? 4. Find the difference between $932 X and $9.32^. 5. A man who owned 2460| acres of land, sold 375| acres to A, 1050.25 acres to B, and 428.1875 to C. How many acres re- mained unsold ? 6. If a cord of wood is worth $5.75, what are 12.25 cords worth ? 7. If wheat is worth $.87/4 per bushel, how many bushels can be bought for $93.625 ? 68 MODERN BUSINESS ARITHMETIC 8. How many bushels of oats at $.16/i per bushel can be bought for $51.50? 9. An automobile travels at the rate of 27 1 miles per hour. How far will it travel in 12^ hours ? 10. A man sold a horse for $125, and received in payment 12 }4 yards of cloth worth $3/^ per yard, and the remainder in tea at $.62)4 per pound. How many pounds of tea were re- quired ? Outline for Review I. Common Fractions : 1. Definition. 2. Fractional unit. 3. Terms: Denominator. Numerator. 4. Kinds : Proper. Improper. Simple. Compound. Complex. Mixed number. 5. Value of a fraction. 6. Principles of fractions. II. Decimals : 1. Definition. 2. A decimal. 3. The decimal sign. 4. Kinds of decimals: Pure decimal. Mixed decimal. 5. Reduction of decimals. 7 . Reduction of fractions : To higher terms. To lower terms. To an improper fraction. To whole or mixed numbers. To a common denominator. 8. Addition of fractions. 9. Subtraction of fractions. 10. Multiplication of fractions. 11. Division of fractions. 12. To reduce complex frac- tions to simple. 6. Addition of decimals. 7. Subtraction of decimals. 8. Multiplication of decimals. 9. Division of decimals. 10. Circulating decimals. Decimal Currency 199. Money is any stamped metal or other substance legally used as a medium of commerce. 200. Currency is the money of a country. 201. Coin is stamped metal used as currency. 202. A Decimal Currency is a currency based upon the decimal system of notation. 203. The United States, Canada, France, and Germany have each adopted a more or less imperfect decimal system. United States Money 204. United States Money is the legal currency of this country. The system was adopted in 1786, and has been changed several times by acts of congress. 205. The Coins of the United States are made of gold, sil- ver, nickel-copper, and bronze. Gold and silver are mixed with a base metal, called alloy, nine parts pure metal and one part alloy. 206. The Gold Coins of the United States are : The Double Eagle, value $20, weight 516 grains. The Eagle, value $10, weight 258 grains. The Half Eagle, value $5, weight 129 grains. NOTE The THREE DOLLAR piece, the QUARTER EAGLE, and the ONE DOLLAR piece are no longer coined. The weight of the $1 piece is 25.8 grains. 207. The Silver Coins of the United States are : The Standard Dollar, value $1, weight 412.5 grains. The Half Dollar, value 50^, weight 192.9 grains. The Quarter Dollar, value 250, weight 96.45 grains. The Dime, value 10^, weight 38.58 grains. 70 MODERN BUSINESS ARITHMETIC 208. The Nickel- Copper Coin of the United States is the Five Cent piece, value 5^, weight 77.16 grains. NOTE The FIVE CENT piece (silver) and- the THREE CENT piece ( nickel-copper ) are no longer coined. The NICKEL is composed of 25 parts nickel and 75 parts copper. 209. The Bronze Coin of the United States is the One Cent piece, value 1^, weight 48 grains. NOTE The ONE CENT piece is composed of 95 parts copper and 5 parts alloy. 210. Money is called a Legal Tender when the law re- quires that it be received in payment of a debt. 211. United States Gold Coins of standard weight are legal tender for all debts in the United States. 212. Standard Silver Dollars are legal tender for all debts not under special contract to the contrary. The other silver coins are legal tender in sums not exceeding ten dollars. 213. The Nickel and One Cent piece are legal tender in sums not exceeding twenty-five cents. 214. The Paper Money of the United States consists of Treasury Notes ( Greenbacks ), Gold Certificates, Silver Certifi- cates, and National Bank Notes. 215. Greenbacks, or treasury notes, are issued by the gov- ernment, and are legal tender for all debts except duties on im- ports and interest on government bonds payable in gold. 216. Gold Certificates and Silver Certificates are is- sued by the government to represent coin in the treasury. They are principally used to facilitate the handling of large amounts of cash. 217. National Bank Notes are furnished by the govern- ment and issued by National Banks which are required to deposit an equal amount of U. S. bonds with the government as security for their redemption. They are not legal tender but on account of the security given, circulate without question. DECIMAL CURRENCY 71 218. Table for United States Money: 10 mills = 1 cent ^, or ct. 10 cents 1 dime d. 10 dimes = 1 dollar.... $. 10 dollars = 1 Eagle.... E. 219. The Unit of measure is the dollar, and sums of money are spoken of as dollars and cents. The Eagle and dime are sel- dom mentioned in business transactions. 220. To reduce United States money to higher denomina- tions, move the decimal point to the left ; to lower denomina- tions, move the decimal point to the right. Thus : $80. = 8. Eagles; $35. = 350. dimes; $25. = 2500. cents. Addition and Subtraction 221. To Add or to Subtract United States money. Write units of like denomination in same columns. Add or subtract as in simple numbers. 222. Solve the following : 1. Add 35 dollars, 148 dollars and twenty-five cents, 7 dollars and seventeen cents, and one hundred dollars and 52 cents. 2. From eight hundred forty dollars and five cents, subtract three hundred four dollars and thirty cents. 3. Monday's sales were $517. 62; Tuesday's, $478.25 ; Wed- nesday's, $524.88; Thursday's, $495.35; Friday's, $392.07; Saturday's, $812.22. Find the total sales for the week. 4. Jones's checks for the month of January were as follows : $28.75, $32.80, $105.40, $75.25, $1250, $35.95, $67.20. Find the total amount withdrawn. 5. Brown deposited the following sums to his credit : $750, $250, $325.50, $18.40, $926.05, $38.55; and withdrew as fol- lows: $32.75, $42.80, $91.25, $10.35, $18.75, $31.25, $48, $82.15. What was his balance in bank ? 72 MODERN BUSINESS ARITHMETIC Multiplication and Division 223. To Multiply or to Divide United States money, pro- ceed as in multiplication or division of decimals. .224. Solve the following : 1. Multiply $125.75 by 47 6. $25.625 X 11 -*- 25 = ? 2. Multiply $204.05 by 308 7. $142.50 + 12 X 65 *= ? 3. Divide $625.75 by 15 8. $87.75 X 14 $54 == ? 4. Divide $1875.50 by 12i 9. $271.25 + .33J + $71 = 5. Divide $274.50 by 16f 10. $95.40 X 48^ $172 = ? PRACTICAL PROBLEMS Solve the following : 1. . Bought 1248 pounds of prunes at 4 cents per pound, 590 pounds of pears at 5 cents per pound, 1892 pounds of peaches at 3/4 cents per pound, and 636 pounds of plums at 6 cents per pound. Find the total amount of the bill. 2. Jones's income was $1250 per year. He spent $17 per month for board, $135 for clothes, $17 for shoes, $3 per month for lodge dues, 75 cents per week for washing, and $95 for sun- dries. How much did he have left to place in the bank? 3. Henry's salary for January was $35 ; this was increased $5 every month in the year. What was his total earnings for the year ? 4. If it cost 7 cents per pound to raise hops, what will be the profit on a hop crop of 250 bales, weighing 275 pounds each, sold at 13/4 cents per pound? 5. A merchant bought corn at 55 cents per bushel, wheat at 90 cents per bushel, and barley at 75 cents per bushel. If he bought two bushels of wheat to every one of barley, and two bushels of corn to every one of wheat, what was the number of bushels of each if he paid $522.50 for the whole? Simple Interest 225. Interest is the sum paid for the use of money cr other value. . . 226. Principal is the money or value for the use of which interest is paid. 227. Rate is the number of cents paid for the use of $1 for one year, and is called rate per cent. 228. Bank Discount is the amount charged by banks on promisory notes or other commercial paper bought by the bank. 229. Interest and Bank Discount are estimated at a cer- tain rate on the $1. 230. To Find Interest or Bank Discount by the Cancellation Method. Write the principal, time, and rate at the right of a vertical line; at the left of this line write a year in the same denomination in which the time is expressed. Cancel and reduce. The result will be the interest for the given time and rate. EXAMPLE : Find the interest on $720 for 7 months at 6%. 360 \ mo. 7 mo. .00 rate $25.20 = Interest EXAMPLE : Find the interest on $960 for 63 days at 8%; also on $1200 for 1 year 3 months 24 days at 7 % $00 ds. 192 $000 7 ds. X$ mo. rate 100 15.8 mo. .07 rate $13.44 = Interest $110.600 == Interest 1 year = 12 months. 24 days = .8 of a month. Every 3 days .1 of a month. NOTE In the above examples it will be noticed that the 7 months, the 63 days, and the 15.8 months are ^, /A, and V/ of a year respectively, and that we are only taking those fractional parts of a whole year's in- terest which is always found by multiplying- the PRINCIPAL by the RAT E. For further discussion of the subject of interest see main topic. 74 MODERN BUSINESS ARITHMETIC 231. Find the interest on the following : 1. $840 for 30 ds. at 6% 6. $150 for 4 mo. at 6% 2. $1230 for 54 ds. at 6% 7. $750 for 7 mo. at 1% 3. $1350 for 37 ds. at 8% 8. $1050 for 11 mo. at 7\-% 4. $2700 for 93 ds. at 7% 9. $325. 50 for 1 yr. 2 mo. al 5. $3500 for 17 ds. at 9% 10. $4500 for 5 mo. 12 ds. at 10% PRACTICAL PROBLEMS 232. Solve the following : 1. Find the interest on a $630 note for 1 year 4 months 15 days at 6 % . 2. Find the proceeds of a note sold at the bank ; face of note, $420 ; time to run, 3 months ; money worth 7%. 3. Find the discount at 8 % on a note for $960 sold at bank 7 months 21 days before maturity. 4. What were the proceeds of a note for $720 discounted at bank for 105 days at 7% ? 5. A $500 note, with interest at 6%, is given for 2 years 8 months 27 days. How much is due at maturity ? 6. Find the proceeds of a note for $600, due in 1 year, at 6% interest, discounted at bank 4 months before due at 10%. NOTE Discount the AMOUNT of the note at MATURITY for the time yet to run. 7. How much would be due at maturity on Boyd's note for $1000 given for 2 years 4 months 27 days at 6% ? 8. What would be the proceeds of the above note if sold at a bank and discounted 1 year 2 months 15 days before maturity at 10%? 9. After holding a note of $1000, due in 2 years with inter- est at 7%, for 6 months, I sell it to the bank at a discount of 9% for time yet to run, paying a collection fee of /^%. How much should I receive? ( Collection is charged on face of note.) 10. The following note was discounted at the bank July 25, 1907 ; rate of discount, 8%: $524.50 San Francisco, Cal., December 10, 1906. One year after date I promise to pay A. L. Ward, or order, Five Hundred Twenty -four 5 %oo Dollars, with interest at six per cent per annum. fohn W. Wilson. If a collection fee of ^ % is charged, what should be the net proceeds of the above note on date of discount ? SIMPLE INTEREST 75 HOME WORK No. 9 1. Add 10 Eagles, 540 dimes, 350 cents, 182 mills, 6 dollars, 135 Eagles, 25 dimes, 5235 cents, 9840 mills, 400 mills, 1725 cents and 3 Eagles. 2. From 1847.5 dimes take 15740 mills. 3. If John received 1 dime, 2 cents, and 5 mills per hour for his labor, and works 11 months, of 26 days each, at that rate; how much will he earn if he averages 8.5 hours each day ? 4. Find the net proceeds of the following note, sold to bank November 16, 1907, at 8% discount: 5. Find the net proceeds of the following note, discounted at bank April 26, 1908. Rate of discount, 10% ; collection, *4% : NOTE The cancellation method of calculating- interest and bank dis- count here given will enable students to work out all ordinary problems occuring in their business practice. 76 MODERN BUSINESS ARITHMETIC 6. A note for $1272 dated July 5, 1907, and drawing 7% in- terest, is paid September 1, 1908. What amount will be re- quired to make settlement in full ? 7. Jones owed $7800 unpaid amount on his farm which he agreed to pay in three equal yearly installments as follows : $2600, at 8% interest, due in 1 year ; $2600, at 7% interest, due in 2 years; and $2600, at 6% interest, due in 3 years. What was the total amount paid ? 8. Matthews & Co. owed their jobber as follows : Jan. 1, Mdse., $480 bought on 3 mo. time. Feb. 1, " 600 1 Mar. 1, 900 ' 2 ' If this account is all paid on May 1 , how much cash will be required, money being worth 8% ? 9. Having on hand a note for $1845 due in 1 yr. 4 mo. 18 ds. with interest at 6%, I sell it at the bank 7 mo. 24 ds. before due. If the bank charges me 8% discount and #% for collec- tion, how much should I receive for the note ? 10. Ross gave his note as follows : $1254.60 Oakland, Cal.,July 25, 1908. Sixtv days after date I promise to pay A. B. Glenn, or order, Twelve hundred fifty -four 6 %oo Dollars, without interest. Value received. KEMP ROSS. What is due on this note December 23, 1908 ? NOTE The legal rate in California, when no rate is agreed upon, is seven per cent. Aliquot Parts 233. The Aliquot Parts of a number are the fractional parts of it. Thus, 2, 3, 4, 6, 9, 12, and 18 are aliquot parts of the number 36. 234. All composite numbers contain aliquot parts. The ali- quot parts of 100 and of 360 are those most commonly used. 235. Aliquot Parts of 100 : 50 i of 100 81 == ! ! 2 of 100 33J i of 100 6J == iV of 100 25 t of 100 6t = T V of 100 20 i of 100 5 = ^VoflOO 16| J of 100 4 = A of 100 14? = | of 100 3J == uV of 100 124 i of 100 2i == -?V of 100 Hi i of 100 2 = A of 100 10 - -A of 100 If == ^ of 100 9-iV = IT of 100 1J = V of 100 236. Multiples of the Aliquot Parts of 100 : 66==4oflOO 87i= | of 100 75 = | of 100 18} =; A of 100 40 =fcflOO 31t==AoflOO 60 = | of 100 43f == T V of 100 80 = | of 100 56t.= =AoflOO 83i = | of 100 68f = -H of 100 37i = I of 100 81t == II of 100 62^ == f of 100 93f == if of 100 237. An Aliquot Part More or Less than 100: 150 = i more than 100 95 = A less than 100 133i == t more than 100 90 -- ^ less than 100 125 = t more than 100 83 i = ) less than 100 120 = t more than 100 80 t less than 100 ll(>;i = i more than 100 75 = t less than 100 78 MODERN BUSINESS ARITHMETIC = t more than 100 66| = t less than 100 110 = T V more than 100 62^ = f less than 100 108t = IT more than 100 37i = f less than 100 238. Aliquot Parts of 360: 180 = i of 360 40 = t of 360 120 = t of 360 36 == T V of 360 90 = i of 360 30 = iV of 360 72 = t of 360 24 = T V of 360 60 = t of 360 . 20 T V of 360 45 = t of 360 18 == T V of 360 NOTE The aliquot parts of 360 days are much used when computing interest 239. To Find the Cost when the Price or Quantity is an Aliquot Part of 100. Take such a part of the quantity or price as the price or quantity is a part of 100. EXAMPLE : What will be the cost of 887 yards of cloth at 33J cents per yard ? At $1.00 per yd. 387 yds. would cost $387. At 33J cents per yd. the cost will be i of $387 = $129. 240. Find the cost of the following invoices, making all ex- tensions mentally : 1. 480# Cocoa 50^ 2. 368 yds. Cabot A 270# Japan Tea 33i^ 711 yds. Cabot W 325# Sugar 5^ 515 yds. Muslin 840# Rice 12^ 948 yds. Linings 918# Raisins 16f^ 425 yds. Gingham 385# B. Powder 20^ 432 yds. Cambric 3. 24 bxs. Soap 87i# 4. 6 doz. cans Corn 120# Starch 20^ 4 doz. cans Beans 48 gals. Molasses 37^^ 10 doz. cans Peas " 32 gals. Vinegar 18|^ 15 doz. cans Oysters 320# Salt lj^ 7 doz. cans Clams 28# Pepper 25^ 2 doz. cans Lobsters 16# Spice 12i^ 2 doz. cans Shrimps ALIQUOT PARTS 79 5. 12 doz. qts. Peaches 10^ 6. 240 sks. Flour $1.12* 8 doz. qts. Pears 8^ 80 sks. Graham .37$ 6 doz. qts. Plums 12-J^ 72 sks. Corn Meal .62| 6 doz. qts. Apricots 150 48 sks. Rye Flour .83{ 12 doz. qts. Cherries 16^ 48 sks. Buckwheat 1.081 10 doz. qts. Blackbrs. 6|^ 24 sks. Hominy 1.25 10 doz. qts. Loganbrs. 8\0 36 sks. Potatoes 1.15 12 doz. qts. Strawbrs. 12|f 18 sks. Beans 3.50 241. To Find the Price or Quantity when the Quantity or Price is an Aliquot Part of 100. Divide the cost by the quantity or price by dividing it by the Al- iquot part the the quantity or price is of 100. EXAMPLE : At 12^ cents per yard, how many yards of cloth can be bought for $60 ? 12i = i of 100. 60 -f- i = 60 X 8 = 480, No. of yards. 242. Find the price or quantity of each of the following by multiplication only : 1. At 25 cents per yd., how many yds. of flannel can be bought for $35 ? 2. At 33j cents per bushel, how many bushels of oats can be bought for $127 ? 3. At 16| cents per lb., how many Ibs. of cheese can be bought for $52.50? 4. Bought 12| yds. of cloth for $17.75. What was the price per yd. ? 5. At 8j cents per doz., how many doz eggs can be bought for $4.50? 6. At $1.25 per yd., how many yds. of silk can be bought for $37. 50? 7. Bought 62^ bushels of millet for $225. What was the price per bushel ? 8. At 83J cents per yd., how many yds. of carpet can be bought for $120? 9. At .14 1 cents each, how many books can be bought for $88? 10. Sold my farm of 66 acres for $7500. What was the price per acre ? 80 MODERN BUSINESS ARITHMETIC HOME WORK No. 10 Extend and foot the following 1. 2. 3. 75 yds. @ $.50 96 Ibs. @ $.01} 189 yds. @ $.66} 88 yds. @ .09^ 56 Ibs. @ .02} 256 yds. @ .18f 91 yds. @ .14f 76 Ibs. @ .05 528 yds. @ .75 72 yds. @ .12} 75 Ibs. @ .06| 728 yds. @ .87} 78yds. @ .16} 84 Ibs. @ ' .08} 616 yds. @ .62} 96 yds. @ .25 90 Ibs. @ .01| 775 yds. @ .60 84 yds. @ .33} 80 Ibs. @ .06} 952 yds. @ .37} 99yds. @ .11} 87 Ibs. @ .03} 648 yds. @ .83} 4, 5. 6. 176 yds. @ $.31} 1424 prs. < g $1.50 1656 gal. @ $ .13} 432 yds. @ .81} 2562 prs. is 26 years." What was her age ? 8. The sum of two numbers is 35 ; their difference is l /2 the less number. What are the numbers? 9. What part of 3 is % of 2 ? 10. A boy lost Vs of his kite string and then added 60 feet more, when he found he had % as much as at first. What was the original length ? 249. Partnership Problems. 1. If A invests $200, and B $500, and their total gain is $210, how much of the gain should each receive? ANALYSIS : If A invests $200, and B $500, their total investment is $700, of which A's share is f , and B's share is \. Their total gain is $210, and since their gain is in proportion to their capital, A's share is \ of $210, or $60, and B's share is f of $210, or $150. 2. A invests $3000, B $4000, and C $5000. If their total loss is $840, what should be each one's share? 3. Jones invests $300 for 5 months; Brown, $400 for 4 months ; and Smith, $700 for 2 months. If their total gain is $405, how much should each receive? 4. The total gain of a firm was $770. White puts in % the capital for 7 months, Green Vs the capital for 12 months, and Black the remainder for 10 months. How much was each one's share of the gain ? 5. Hill, Cooper, and Sullivan are partners in business. Hill puts in $400 for 7 months and gains a certain sum ; Cooper puts in $700 for a certain time and gains $105 ; Sullivanputs in a cer- tain sum for 2 months and gains $90. If the total gain of the firm is $335, what is Hill's gain, Cooper's time, and Sullivan's capital ? 250. Labor Problems. 1. If A can do a piece of work in 3 days and B in 5 days, how long will it take them to do it working together ? 84 MODERN BUSINESS ARITHMETIC ANALYSIS : If A can do the work in 3 days, he can do of it in 1 day. If B can do it in 5 days, he can do J of it in 1 day. Both working to- gether can do the sum o and I, or T 8 f of it in 1 day, and to do f, or all the work, will require as many days as T 8 S is contained in |f, or 1| days. 2 . Lambert can saw a certain pile of wood in 8 days ; Lewis in 12 days, and Lucien in 6 days. How long will it take all three to do it? 3. Two men can dig a ditch in 15 days. The first can dig it alone in in 25 days. How long will it take the second to dig it alone ? 4. A, B, and C can do a job of work in three days. A can do it in 9 days ; B in 12 days. How long will it take C to do the job ? 5. Ralph can mow a field in 4 days, 'and Lewis can mow it in 6 days. How long will it take Ralph to finish the work after they have both worked together 1 day ? 251. Time Problems. 1. What is the time of day, if the time past noon equals Vs the time to midnight ? 2. What is the time of day if % the time to noon equals the time past midnight ? 3. What is the time of day if Vs the time past midnight equals the time to midnight again ? 4. What is the time of day if % the time past noon equals Vs the time to midnight ? 5. What is the time of day if % of the time past midnight equals % the time to midnight again ? 252. Clock Problems. 1. How many minute spaces does the minute hand gain on the hour hand every hour ? ANALYSIS : If the minute hand travels 60 minute spaces in 1 hour, and the hour hand travels 5 minute spaces in the same period, the min- ute hand will gain 55 minute spaces every hour. ANALYSIS 85 2. At what time between 1 o'clock and 2 o'clock are the hour and minute hands together ? 3. At what time between 5 and six o'clock are the hour and minute hands together ? 4. At what time between 3 and 4 o'clock are the hour and minute hand in a straight line ? 5. At what time between 7 and 8 o'clock are the hands of a clock at right angles ? 253. Fish and Pole Problems. 1 . The head of a fish is 9 inches long ; the tail is as long as the head and half the body, and the body is as long as the head and tail together. How long is the fish ? ANALYSIS : If the tail is as long as the head ( 9 inches ) and \ the body, the head any tail together are 9 inches and 9 inches and \ the body ; since the body is as long as the head and tail together, the length of the head and tail equals \ the length of the fish, and 18 inches equals \ the length of the body or J the length of the fish, 72 inches. 2 . The head of a fish is 6 inches long ; the tail is as long as V2 the head and 1 A the body, and the body is twice the length of the head and tail together. How long is the fish ? 3. A pole stands 6 feet in the water; Vs of its length is in the mud, and four times as much is in the air as in the mud and water together. What is the length of the pole ? 4. A pole is in four sections ; the first is 2 feet long ; the second is as long as the first and half the third, and the third is as long as the first and second, while the fourth is as long as the first, second, and third together. How long is the pole? 5. A liberty pole was broken off i of its length plus 3 feet from the top ; the part left standing was found to be 12 feet longer than three times the length of the part broken off. What was the original length of the pole ? 254. Age Problems. 1. George is 8 years old and his father is 32. How long be- fore George will be one-half the age of his father ? 86 MODERN BUSINESS ARITHMETIC ANALYSIS: If George is 8 years, and the father 32 years, the differ- ence of their ages is 24 years. If George is to be \ the age of his father, his age will be equal to the difference of their ages, or 24 years. If he is now 8 years, it will be 16 years before he is 24 years old. 2. One-third .of A's age equals three-fourths of B's; and the sum of their ages is 52 years. How old is each ? 3. Two-thirds of three-fifths of Jones's age is four-fifths of five-sixths of Smith's. If the difference of their ages is 28 years, how old is each? 4. John is three times as old as Jack, but in 5 years he will be only twice as old. What is the age of each? 5. Twelve years ago Glover was one-fourth the age of his uncle. Now he is one-half as old. How old is each ? 255. Miscellaneous Problems. 1. A, B, and C take luncheon together. A furnishes 4 loaves, B 3 loaves, and C pays 35 cents for his share. If all eat equal amounts, how should the money be divided between A and B? 2. How far can a person ride in an automobile, traveling at the rate of 20 miles an hour, and return on his bicycle at the rate of 10 miles an hour, if he is gone six hours ? 3. A hound is 60 yards behind a fox. How far will the hound have to run to catch the fox if he runs 10 yards to every 8 of the fox, and one leap of the hound equals two of the fox's? 4. I sold a bill of goods and gained 20%. Had they cost me $45 more, I would have lost 10%. What was the cost of the goods ? 5. A and B meet at a butcher shop and together buy 80 pounds of beef, the price of which is 10 cents per pound. A takes 50 pounds of the better quality, and agrees to pay one-half cent more per pound than B does for the remainder. How much shall each one pay ? ANALYSIS 87 HOME WORK-NO. 11 NOTE Students should take much pride in making out a full set of problems, together with solutions, as indicated by the following outline : 1. Give original examples, with .solutions, illustrating the different steps in simple analysis. 2. Give original examples, with complete analyses, showing the different steps in compound analysis. 3. Originate a problem in the comparison of whole numbers, using not less than five integers. 4. Originate a problem in the comparison of fractional num- bers, using not less than two fractions and as many whole num- bers as necessary. 5 . Refer to Article 249 and then write out a partnership prob- lem in which the capital and time of each partner are different. 6. Write a labor problem entirely unlike those given in Arti- cle 250. 7. Originate a time problem, using time past noon and time to noon similar to those in in Article 251. 8. Originate a clock problem, giving in degrees the angle des- cribed by the hands of the clock. 9. Originate a fish and pole problem. 10. Write an original age problem. Bills, Invoices, and Statements 256. A Bill or Invoice is an itemized statement of goods bought or sold. The term Bill is also applied to any itemized statement of material furnished, labor performed, or services rendered. 257. The term Invoice is usually applied to bills of consider- able value, and containing several or many items. 258. A Bill should contain the following : 1. The place and date. 2. The name and address of the buyer. 3. The name and address of the seller. 4. The terms of sale. 5. The quantity, price, and extension of each item. 6. The total amount, or footing. INTEREST CHARGED AT 1O PER CENT. PER ANNUM ON ALL ACCOUNTS AFTER MATURITY HOOPER & JENNINGS Importers and Wholesale Grocers 462-464 Bryant Street San Francisco, Cal., July 20, 1908. Sold to W. E. GIBSON, Oakland, Cal. TERMS 60 DAYS 2ff ff 259. Bills may be receipted in full, or credits given for partial payments. BILLS, INVOICES, AND STATEMENTS 89 260. To Receipt a Bill is to write upon it an acknowledg- ment of payment signed by the seller. TERMS 30 days SAN FRANCISCO CAL., Feb. 4, 1908. Bowen & Goldberg WHOLESALE GROCERS Main Office: No. J732 Market Street SOLD TO E. K. ISACCS, Los Angeles, Cal. SUBJECT TO SIGHT DRAFT WHEN DUE. INTEREST CHARGED AFTER MATURITY. CORRECT PROPORTIONS PERFECT FINISH THOROUGH WORKMANSHIP UNION MADE C. J. HBBSEMAN Makers of Workingmen's Best Garments FACTORY I 1107-9-11-13 WASHINGTON STREET PHONE MAIN 678 Sold to KEEGAN BROS. TERMS NET 30 DAYS Oakland, Cal., March 29, 1908. 45 1 doz. Com. Suits 9 00 12 1 ' Plasterers' Overalls 6 50 31 1 ' White Aprons 6 50 21 2 ' Coats 9.50 19 00 20 4 ' Eng. Overalls 9.50 38 00 42 1 ' Blk. Golf Shirts 6 00 85 00 ) - 90 MODERN BUSINESS ARITHMETIC 261. To Discount a Bill is to make an allowance from the list price either to obtain the selling price or to induce the buyer to pay the bill before it is due. F. 0. GARDINER, Stockton, Cal. Chicago, May 2, 1908 BOUGHT OF The Gregg Publishing Company 1512 WABASH AVENUE TERMS CASH. Remittances must be made in postal or express money order, or in bank draft. Personal checks upon local banks not received unless exchange rates are added. 262. Several discounts are some times offered on one bill, the terms being indicated on the bill head. TERMS : 60ds.net; 30 ds. 5%; 10 ds. San Francisco^ April 4, '08 L. B, LAWSON & CO. China, Glass, and Earthenware Chicago, Illinois* Sold to A. P. ARMSTRONG, Portland, Oregon fe**> S3- .^r^^L^>^ -~tL^^^^ /^ -^ ^X/ 3- *-S 7s ^^A^JUM^ 4S^f~ JH SI ^^^^^rtS^'tt**^ ^/ *SJ rj9^>. iC //^5L^^/ HB^^_ 13- f-J /i ^^A/^X ^^^ Z~^ //* >* Lstt-*. *^X^- x /2-/(^-S fr 7* TzZ&^sSZ*^ M^jft^ ^^j ^~ ~^~-~ BILLS, INVOICES, AND STATEMENTS 91 263. A Statement is a summary of invoices sold, together with any credits allowed, and showing the balance remaining unpaid. STATEMENT April 1, 1908 2?il?rbarlj $Iap?r (Eompattg J. S. Sweet Publishing Co., Santa Rosa Cal. 264. A Credit Memorandum is given when goods are re- turned or when a claim against a bill for some cause is allowed. CREDIT MEMORANDUM American Type Founders Co. 820 Mission Street, SAN FRANCISCO, April 13 1908 J. S. Swe et Pub. Co., Santa Rosa Rebate on bill April 1, '08 3 15 92 MODERN BUSINESS ARITHMETIC 265. To Extend the items of a bill is to multiply the price of one by the number and to write the result in the first money column. 266. Short Extension is the placing of several items on the same line, extending only their sum to the money column. San Francisco. Feb. 5, 1908. A. M. GROUSE, Santa Rosa TO SMITH'S CASH STORE DR Country Trade Solicited Retail Grocers QaatZ. h? J*-~^yj " ^L^^^y ** ^fc^^.y^ to I /? /si, ^d^/" r " ^L^^,^^' &L Y v -^ (ZjC il x^^J^r^y ^-^ j^ ^/ x ^ / -r f -<~ 6 -T&y/^^y *" ^2^ 2J ~ ^^f^^jt^.^ 7 *" / n?'<7 (^ + tj^ (/ S 3 "^^! ^ 2 " rX a a 7/ ^^a^Lf^^,^ ^"^ /3^, ^~ s ^^ ^^L~^ x ~ A s 7 -^ ' 267. Commercial Signs and Abbreviations : Acct., or %, account. @, at or per. Ami., amount. BaL, balance. Ex., Bxs., box, boxes. Bo't, bought. TD / /L, bill of lading. %> in care of. Co.y company. Ctg., cartage. Coin., commission. Contra., against. Exch., exchange. C. O. D., collect on delivery. For 'd, forward. Cr. , credit, or creditor. Dr. , debit, or debtor. E. and O. E. , errors and omis- sions excepted. F. O. B., or /. o. 6., free on board. Mdse., merchandise. Net., without further discount. Sunds., sundries. Rec'd, received. #, number. #, pounds. , cent. $, dollars. ;, pounds sterling. % , per cent. 3 1 is read 3 1 A. 3 2 is read 3 l /2. 3 3 is read 3%. (), degrees. O, foot, feet. ( r/ ), inch, inches. Pkg., package. L. P., ledger folio. BILLS, INVOICES, AND STATEMENTS HOME WORK No. 12 268. Find the cash cost of each of the following bills : 1. 93 Oakland, Cal., May 18, 1908. M KETTERLIN BROS., Santa Rosa, Calif/ TO i!r2Ctttla-fkrkttts dompattg * MANUFACTURERS AND IMPORTERS OF PAINTS, OII,S, VARNISHES, COLORS, ETC. SAN FRANCISCO 707-9-11 SANSOME STREET OAKLAND 1 7TH AND CAMPBELL STS. 1 10 300 100 bbl. Paris White-357 Ibs. .15 gal. XX White-5's 1.00 Ibs. MPC Lead-50's .06 2 ' -15 's .06 ] Chicago, ILL, March 15, '08. HART, SCHAFFNER & MARX SHAKERS OF FINE CLOTHES &OR MEN Van Buren and Market Streets SOLD TO KEEGAN BROS. , Santa Rosa, California SHIPPED VIA Milw., viaU. P. TERMS: June 1, '08. 7% 10 ds., 5% 30 ds, STOCK NO. 26552 7 Suits 8.50 26873 5 " 15.00 32738 5 " 18.00 30777 5 " 15.50 29800 1 t 16 00 27374 5 " 14.00 26606 1 t ( 15 50 27011 8 12.00 26762 8 Pants 3.75 27049 7 " 3.50 27073 4 " 3.50 -? 94 3. MODERN BUSINESS ARITHMETIC Jfatttterg 010. 816-820 Mission St., San Francisco Date [ March, 5, '08. ] J. S. SWEET PUBLISHING CO., Santa Rosa, Cal. Shipped. Designer and Maker of Fashionable Styles in TYPE World's Largest Seller Everything for Printers Your Order No. 51260 QUAN- TITY POINT DESCRIPTION TYPE SUPPLIES PER CENT DISCOUNT TOTAL 45# 5 f 1 10 10 10 10 Lin. Ronaldson #551 .60 Quads .45 Lin. Ronaldson Slope #2 I.e. " " 2 1 50 15 list 1 18 Lin. " Clarendon 3 25 1 12 t ( it it 2 75 1 8 ft 1 1 i ( 2 25 12# 10 Mod. #510 Figures .60 10# 10 Spaces & Quads .50 4 Yankee Job Cases .75 10 1 Quarter Cases 3 00 list 1 Harris Rule Case 4 65 ii Less discount Freight allowance 25. Total 4. SAN FRANCISCO SACKAMKNTO Los ANGELES NEW YORK Bought of BAKER & HAMILTON Reg. NO. - Shipping NO. San Francisco, Apr . 5 , ' 08 Sold to KETTERLIN BROS. Santa Rosa 2 Sensible Twine Holders .20 3 1 4 AAA J Wrenches #15 doz. Atkin Excel Saw Tools .45 6.50 ' ' Bolts & Nuts-8i Shears 4.50 2 Coil Gal. Fence Wire #16 3.65 1 ' Tarred Lath Yarn-93 Ib. .101 i doz. Reload Outfits 2.80 2 Ibs. Brass Pins f - 16 .78 1 > > > i > | - 18 .94 9 Denominate Numbers 271. A Denominate Number is a concrete number whose unit is a measure ; as, 5 inches, 10 pounds, 20 hours. 272. A Simple Denominate Number has but one de- nomination ; as, 6 yards. 273. A Compound Denominate Number contains two or more denominations ; as 6 yards 2 feet 8 inches. 274. A Measure is the unit of computation. 275. A Quantity is measured by the number of times it contains the unit of measure. 276. The Classification of measures is as follows : 1. Value or Money 4. Extension 2. Weight 5. Time 3. Capacity 6. Arcs and Angles Measures of Value UNITED STATES MONEY 277. United States Money is the legal currency of this country. The system was adopted in 1786, and has been changed several times by acts of congress. 278. 'The Unit of measure is the dollar, and sums of money are spoken of as dollars and cents. The Eagle and dime are sel- dom mentioned in business transactions. TABLE : 10 mills = 1 cent ^, or ct. 10 cents = 1 dime d. 10 dimes 1 dollar.... $. 10 dollars == 1 Eagle.... E. NOTE In business transactions, dollars and cents are used with the decimal point between; as, $17.50. NOTE For further discussion of this subject, see page 69. , 96 MODERN BUSINESS ARITHMETIC CANADA MONEY 279. Canada Money is the legal currency of Canada, and has about the same values as the United States money. Its unit is the dollar. TABLE : 10 mills = 1 cent, ^ or ct. 100 cents = 1 dollar, $. 280. The Silver Coins are the fifty cent, twenty-five cent, twenty cent, ten cent, and five cent pieces. 281. The Copper Coin is the cent piece. 282. There are no Canadian gold coins. The larger denomi- nations consist of paper currency and the gold coins of England and the United States. ENGLISH MONEY 283. English or Sterling Money is the legal currency of Great Britain. Its unit is the pound sterling. TABLE : 4 farthings (far.) =1 penny, d. 12 pence = 1 shilling, s. = P und ' ' 20 shilling sovereign, sov 284. The intrinsic value of the pound or sovereign in United States money is $4.8665. 285. Sterling coins are made 925 parts pure gold or sil- ver and 75 parts alloy. 286. The Gold coins are the sovereign and half sovereign. 287. The Silver coins are the crown (5s), half crown, shil- ling, and the six and three penny pieces. 288. The Copper coins are the penny, half penny, and far- thing. FRENCH MONEY 289. French Money is the legal currency of France. The unit is the franc. TABLE : 10 millimes (m) = 1 centime, ct. 10 centimes = 1 decime, dc. 10 decimes = 1 franc, fr. 290. The intrinsic value of the franc in United States money is $.193. DENOMINATE NUMBERS 97 291. The Gold coins of France are the 100, 40, 20, 10, and 5 franc pieces. 292. The Silver coins are the 5, 2, and 1 franc, and the 50 and 25 centime pieces. 293. The Bronze coins are the 10, 5, 2, and 1 centime pieces. GERMAN MONEY 294. German Money is the legal currency of the German Empire. The unit is the mark. TABLE : 100 pfennigs 1 mark. 295. The intrinsic value of the mark in United States money is $.2385. 296. The Gold coins of Germany are the 20, 10, and 5 mark pieces. 297. The Silver coins are the 2 arid 1 mark pieces, and the 20 pfennig piece. 298. The Nickel coins are the 10 and 5 pfennig pieces. Measures of Weight 299. Weight is the measure of the earth's gravity. 300. The unit of weight is the Troy pound as registered at the United States mint. It contains 5760 grains. 301. Measures of Weight are of four kinds: Troy Weight, Avoirdupois Weight, Apothecaries' Weight, and Diamond Weight. TROY WEIGHT 302. Troy Weight is used in weighing gold, silver, and other precious metals ; in philosophical experiments, and is the standard at the United States mint. TABLE : 24 grains (gr.) = 1 pennyweight, pwt. 20 pennyweights = 1 ounce, oz. 12 ounces = 1 pound, Ib. 98 MODERN BUSINESS ARITHMETIC AVOIRDUPOIS WEIGHT 303. Avoirdupois Weight is used in weighing all kinds of merchandise, farm produce, and metals, except the precious metals. 304. Its unit is the pound, which contains 7000 Troy grains. TABLE : 16 sixteenths = 1 ounce, oz. 16 ounces = 1 pound, Ib. 100 pounds = 1 hundredweight, cwt. 20 cwt., or 2000 Ibs. = = 1 ton, T. 305. The Long Ton used in estimating duties on imported goods, and in weighing coal and iron at the mines, contains 2240 avoirdupois pounds. TABLE : 16 ounces = 1 pound, Ib. 28 pounds = 1 quarter, qr. 4 quarters = 1 hundredweight, cwt. 20 cwt. or 2240 Ibs. == 1 ton, T. OTHER AVOIRDUPOIS MEASURES : 100 pounds of grain = 1 cental. 100 pounds of fish = 1 quintal. 100 pounds of nails = 1 keg. 196 pounds of flour = 1 barrel. 200 pounds of pork or beef = 1 barrel. 280 pounds of salt = 1 barrel. 240 pounds of lime = 1 barrel. 306. Gross Weight is the total weight, including box, barrel, crate or other covering. 307. Net Weight is the gross weight less the weight of the box, barrel, crate, or other covering. 308. In California nearly all grains, vegetables, fruits, and seeds are bought and sold by the avoirdupois pound or cental. ' 309. In many States the bushel is the standard of weight in buying and selling such commodities, the weight of a bushel de- pending upon the law or custom of each State. DENOMINATE NUMBERS 99 310. The following table gives the weight of a bushel in California and about the average weight in other States : OTHER OTHER CAL. STATES CAL. STATES Barley 50 Ibs. 48 Ibs. Flaxseed 56 Ibs. 56 Ibs. Beans 60 Ibs. 60 Ibs. Oats 32 Ibs. 32 Ibs. Blue Grass, seed 14 Ibs. 14 Ibs. Onions 50 Ibs. 57 Ibs. Buckwheat 40 Ibs. 48 Ibs. Potatoes 60 Ibs. 60 Ibs. Corn, shelled 52 Ibs. 56 Ibs. Rye 54 Ibs. 56 Ibs. Corn, ears 68 Ibs. 68 Ibs. Wheat 60 Ibs. 60 Ibs. APOTHECARIES' WEIGHT 311. Apothecaries' Weight is used by druggists in weighing dry medicines for filling prescriptions. Most drugs are bought at wholesale by avoirdupois weight. 312. Its Unit is the pound, containing 5760 troy grains. TABLE : 20 grains (gr.xx) = 1 scruple, sc., or 9. 3 scruples (9iij) = 1 dram, dr., or 3. 8 drams (Sviij) = 1 ounce, oz., or g. 12 ounces (gxij) = 1 pound, lb., or tb. 313. The pound, ounce, and grain are identical with Troy weight. NOTE Physicians usually write prescriptions in Roman notation, using small letters. Thus, 7 ounces is written 5 y iJ (the final "i" being written " j " ) ; 8 drams, 5 v iiJ > 12 scruples, 9xij, etc. 314. SIGNS USED IN PRESCRIPTIONS : fy = recipe. P = small part aa = equal quantities. P. aeq = equal parts. ss = half q. p = as much as you please. gr. = grain misce = mix. DIAMOND WEIGHT 315. Diamond Weight is used in weighing diamonds and other precious stones. TABLE : 2 sixty-fourths = 1 thirty-second of a carat. 2 thirty-seconds = 1 sixteenth of a carat. 2 sixteenths = 1 eighth of a carat. . , , _ ( 1 fourth of a carat, or " { 1 carat grain = .792 Troy grains. 4 carat grains = 1 carat = 3.168 Troy grains. 100 MODERN BUSINESS ARITHMETIC 316. The word carat is also used to express the proportion of pure gold in a mixture, 24 carats representing pure gold. Thus, " 18 carats fine," means that in the mixture there are 18 parts of pure gold and 6 parts alloy, or base metal. Measures of Capacity 317. Measures of Capacity are those used in estimating the contents of a given space. 318. Measures of capacity are divided into two classes liquid measures, and dry measures. LIQUID MEASURE 319. Liquid measure is used in measuring liquids of all kinds. TABLE : 4 gills (gi.) = 1 pint, pt. 2 pints = 1 quart, qt. 4 quarts = 1 gallon, gal. 31i gallons = 1 barrel, bbl. 2 barrels = 1 hogshead, hhd. NOTE The term BARREL is applied to casks of various sizes which contain 31 1 gallons or over. Under 31 \ gallons they are called KEGS. 320. The Unit of liquid measure is the gallon^ which con- tains 231 cubic inches. NOTE In estimating the contents of cisterns, reservoirs, etc., 7| gal- lons are allowed to each cubic foot. APOTHECARIES' FLUID MEASURE 321. Apothecaries' Fluid Measure is used by drug- gists in measuring liquids for filling prescriptions. 60 minims (ffl) =1 fluid drachm, f3 8 fluid drachms = 1 fluid ounce, f. 16 fluid ounces = 1 pint, O. 8 pints = 1 gallon, cong. NOTE Cong., abbreviation of the Latin CONGIUS, for gallon; O., for OCTARIUS", is Latin and means ONE-EIGHTH. NOTE The MINIM is equivalent to one drop of water. The gallon is the same as in liquid measure, and contains 231 cubic inches. DENOMINATE Xr.MBKRS 101 322. As in Apothecaries' Weight the symbols are written be- fore the numbers to which they refer. Thus, O4 f7 is read 4 pints 7 fluid ounces. DRY MEASURE 323. Dry Measure is used in measuring grain, fruits, veg- etables, and other dry articles. 324. The Unit of dry measure is the bushel, which contains 2150.42 cubic inches. TABLE : 2 pints (pt.) == 1 quart, qt. 8 quarts = 1 peck, pk. 4 pecks = 1 bushel, bu. NOTE In some places the DRY GALLON of 4 quarts is used in measur- ing berries and small fruits. It contains 268.8 cubic inches. NOTE In estimating the contents of bins, boxes, etc., f of the num- ber of cubic feet will give the number of bushels, sticken measure, and | of this number of bushels will give the number of heaped bushels. Measures of Extension 325. Extension has one or more of the dimensions, length, breadth, and thickness. It may be a line, a surface, or a solid. 326. A I/ine has only one dimension length. 1 inch 2 inches 4 inches NOTE An inch may be divided into halves, quarters, or eighths, or any other fractional part. 327. I^inear Measure is used in measuring lines and dis- tances. It is also called long measure. UNBAR MEASURE TABLE : 12 inches (in.) = 1 foot, ft. 40 rods = 1 furlong. 3 feet = 1 yard, yd. 8 furlongs, or 5i yards, or \ _ A A 320 rods, or =1 mile. 16i feet j 5280 feet 328. The U. S. Standard Unit of extension is the yard of 3 feet, or 36 inches. 102 MODERN BUSINESS ARITHMETIC SURVEYORS' I/INEAR 329. Surveyors' Linear Measure is used by surveyors in measuring distances on land. 330. The Unit is the chain, the measure of which is as fol- lows : TABLE : 7.92 inches = 1 link, 1. 1 chain = 4 rods. 1 chain = 22 yards. 1 chain = 66 feet. 1 chain =100 links. 1 chain = 792 inches. 25 links = 1 rod, rd. 4 rods 1 chain, ch. 80 chains '== 1 mile, mi. Therefore, 4 rods = 22 yards = 66 feet = 100 links = 792 inches. SQUARE MEASURE 331. Square Measure is used in computing the areas of plane surfaces. 332. Surface has two dimensions, length and breadth. 333. Area is the number of square units in a given surface. 334. A Rectangle is a plane figure bounded by four sides and having four right angles. 335. A Square is an equilateral (equal sides) rectangle. TABLE : 144 square inches == 1 square foot, sq. ft. 9 square feet = 1 square yard, sq. yd. 301 square yards = 1 square rod, sq. rd. 160 square rods = 1 acre, A. 640 acres = 1 square mile, sq. mi. 36 square miles = 1 township, Tp. 336. The area of a rectangle is found by taking the product of the two dimensions. NOTE In computing the square units in a given surface where the length and breadth are given, the product of these two dimensions equals the number of square units in a row multiplied by the number of rows. Thus, instead of 3 feet, the width, times 5 feet, the length, the analysis is 3 times the five square" feet in a row, or 15 square feet. DENOMINATE NUMBERS 103 SURVEYORS' SQUARE MEASURE 337. Surveyors' Square Measure is used in computing the area of land. 338. The Unit of land measure is the acre. TABLE : = 1 square rod, sq. rd. = 1 Square cham ' Sq - ch " 625 square links 16 square rods jr 10000 square links 10 square chains, 160 square rods 640 acres 36 square miles . = 1 square mile. = 1 township, Tp. 339. A Principal Meridian is an imaginary line extend- ing north and south, from which government surveys are made. 340. A Base Isine is an imaginary line extending east and west, crossing the meridian at a fixed point. DIAGRAM : T4N R4W - I z < Q T3N R1E T3N R4E T2N R2W K u 5 BASE LINE Tl S R3 E T2 S R 4W CIPAL Z E 0. T4 S R3W T4 S R2E 341. Townships are located north and south of the Base Line by numbers, and east and west of the Principal Meridian by the number of the range or row. 104 MODERN BUSINESS ARITHMETIC NOTE The foregoing are read : Township 4 North, Range 4 West ; Township 3 North, Range 1 East ; Township 2 North, Range 2 West ; etc. 342. In Regular Surveys, townships are six miles square and contain 36 square miles. Irregular townships contain dif- ferent areas. 343. Regular Townships are divided into sections or square miles which are numbered as follows : DIAGRAM OF A TOWNSHIP : NORTH 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 DIAGRAM OF A SECTION : NE i 160 A W| 320 A NW i of SEi 40 A E i of SE \ 80 A SOUTH 344. A Section is one mile square and contains 640 acres. Sections may be subdivided into halves and quarters ; quarters into quarter-quarters, etc. In cities and towns, land is described by giving the number of the lot, the number of the block, and the addition, or the original plat of the city as re- corded on the official survey. The 40 acre portion of the above diagram would be read, "the northwest quarter, of the southeast quarter, of section No. 16. DENOMINATE NUMBERS 105 CUBIC MEASURE 345. Cubic Measure is used in X measuring the contents of solids. 346. A Rectangular Solid is one bounded by six rectangular surfaces. 347. A Cube is a rectangular solid whose surfaces are equal squares. 348. The Volume, or solid contents, are found by taking the product of the three di- mensions. TABLE : 1728 cubic inches = 1 cubic foot, cu. ft. 27 cubic feet = 1 cubic yard, cu. yd. 1 cubic yard = 1 load. 349. Wood Measure is used in measuring wood. TABLE : 16 cubic feet = 1 cord foot. 8 cord feet or 128 cubic feet = 1 cord. 350. Rough stone is sometimes reckoned by the perch', which contains 24 J cubic feet. Time Measure 351. Time is a measured portion of duration. 352. The revolution of the earth upon its axis causes day and night. Its revolution around the sun requires one year of 365 days 5 hours 48 minutes 49.7 seconds. 353. In reckoning time, 365 days are called a common year. This being almost one-fourth of a day less than the exact year, every fourth year is given one more day, and is called leap year. As this method is not absolutely accurate, the centennial years are not leap years unless divisible by 400. 106 MODERN BUSINESS ARITHMETIC 354. The Unit of time measure is the day of 24 hours. TABLE : 60 seconds = 1 minute, min. 60 minutes = 1 hour, hr. 24 hours = 1 day, da. 7 days = 1 week, wk. 4 weeks = 1 lunar month, lu. mo. 365 days 1 common year. 366 days == 1 leap year. 12 months = 1 year, yr. 100 years = 1 century, C. 355. The Months and Seasons of the year are as follows: MONTH ABBREVIATED SEASON WINTER SPRING SUMMER AUTUMN WINTER 356. The number of days in each month may be kept in mind by memorizing the following rhyme : "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." NOTE In business computations, 30 days are usually called a month. In reckoning time, the prevailing custom is to count years and months by dates only, and the extra days as days. Thus, from February 10th to March 31st, the time is 1 month ( from February 10th to March 10th ) and 21 days (from March 10th to March 31st), instead of 49 days, or 1 month and 19 days. January February February (leap yr, ) Jan. Feb. March April May Mar. Apr. May June July August June July Aug. September October November Sept. Oct. Nov. December Dec. DENOMINATE NUMBERS 107 Circular Measure 357. Circular or Angular Measure is used in measur- ing angles, arcs, directions, elevations, etc. 358. The Unit is the degree, the ^fa part of the circumfer- ence of a circle. 359. A Circle is a plane figure bounded by a curved line, every point of which is the same distance from its center. 360. The Circumference of a circle is the line that bounds it. 361. An Arc is a part of a circle. 362. An Angle is the divergence of two lines from a common point. 363. A Right Angle is formed by lines drawn perpendicular to each other from a common point. 364. A circle may be divided into 360 degrees. A semi-circle into 180 degrees. A quadrant into 90 degrees, etc. 365. A Diameter of a circle is a line passing through the center and terminating in its circumference. 366. A Radius is one-half a diameter. 367. To measure an arc is to ascertain the number of degrees between the radii joined by the arc. TABLE : 60 seconds ( " ) = 1 minute, ( ' ) 60 minutes = 1 degree, ( ) 30 degrees = 1 sign, ( s. ) 12 signs ) ' 1 . . / c x 360 degrees \ 368. One degree on a meridian or on the equator is equal to about 69.16 common or statute miles. 108 MODERN BUSINESS ARITHMETIC COUNTING TABLE : PAPER TABLE : 12 units = 1 dozen, doz. 24 sheets = 1 quire, qr. 12 dozen ==1 gross, gro. 20 quires 1 ream, rni. 12 gross = 1 great gross, G. gro. 2 reams 1 bundle, bdl. 20 units = 1 score. 5 bundles = 1 bale. BOOKS : A sheet folded into 2 leaves is called a folio. A sheet folded into 4 leaves is called a quarto. A sheet folded into 8 leaves is called an octavo. A sheet folded into 12 leaves is called a 12 mo. A sheet folded into 16 leaves is called a 16 mo. Comparison of Weights 369. The Unit of Troy weight and of Apothecaries' weight is the pound which contains 5760 grains. 370. The Unit of Avoirdupois weight is the pound which contains 7000 grains. 371. The Troy ounce and the Apothecaries' ounce each con- tain i^ of 5760 grains = 480 grains. 372. The Avoirdupois ounce contains T V of 7000 grains = 437^ grains. COMPARATIVE TABLE: 1 pound Troy or Apothecaries' weight =5760 grains. 1 pound Avoirdupois weight = 7000 grains. (Avoirdupois the greater by 1240 grains). 1 ounce Troy or Apothecaries' weight = 480 grains. 1 ounce Avoirdupois weight = 437^ grains. (Troy and Apothecaries' the greater by 42| grains.) 373. In changing from one kind of weight to another, the quantities must first be reduced to grains. Reduction of Denominate Numbers 374. Reduction of Denominate Numbers is the pro- cess of changing their denominations without altering their values. 375. Reduction Ascending is to reduce the given num- ber to a higher denomination. Thus, 36 pence reduced to shil- lings = 3 shillings. 376. Reduction Descending is to reduce the given num- ber to a lower denomination. Thus, 4 reduced to shillings = 80 shillings. 377. To reduce to a higher denomination, divide by the number of units required to make the higher denomination. 378. To reduce to a lower denomination, multiply by the number of units of the lower denomination required to make one the higher. 379. Reduction Ascending. EXAMPLE : Reduce 1250 farthings to . 4 farthings = 1 penny 4 ) 1 2 5 far. 12 d. = 1 s. 12 ) 3 1 2 d. and 2 far. remainder. 20 s. = l. 20 ) 26 s. and d. remainder. l and 6 s. remainder. Answer, l 6s. Od. 2 far. 380. Reduction Descending. EXAMPLE : Reduce 3 7s. 3 d. to farthings. 20s. = l. 804 d. 3 , 3 d. added. 60 s. 807 d. _]_ s. added 4 far. = 1 d. 67 s. 1628 far., Answer. 12 d. = 1 s. 804 d. 110 MODERN BUSINESS ARITHMETIC ENGLISH MONEY 381. Solve the following : 1. Reduce 4 5s. 7d. to pence. 2. Reduce l4 10s. 9d. 2 far. to farthings. 3. Reduce 721 pence to higher denominations. 4. Reduce 47 lid. to farthings. 5. Reduce 37425 far. to higher denominations. 6. In %2 of a how many pence ? 7. In .725 of a ; how many farthings? 8. Reduce 845.75 pence to s. d. and far. 9. A traveler from England lands in New York with /50 10s. 6d. which he exchanges for U. S. money at intrinsic value. How much does he receive ? 10. An American traveling in England has $8273.05 changed to English money. How much did he receive ? FRENCH AND GERMAN MONEY 382. Solve the following : 1. How many francs in 3240 centimes ? 2. Reduce 42 francs to centimes. 3. How many dollars U. S. money in 2123 francs? 4. How many francs in $2123 U. S. money? 5. An Englishman lands in France with ^200 and exchanges it for French money. How much should he receive on the in- trinsic basis ? 6. How many marks in 4280 pfennigs ? 7. Reduce 75 marks to pfennigs. 8.' How many dollars U. S. money in 260.5 marks? 9. How many marks in $2623.50 U. S. money ? 10. A Frenchman traveling in Germany desired to change his 477 francs for marks. How many should he receive ? TROY WEIGHT 383. Solve the following : 1. . Reduce 5 Ibs. 7 oz. to pennyweights. DENOMINATE NUMBERS 111 2. Reduce 3 Ibs. 4 oz. 15 pwt. 10 gr. to grains. 3. Reduce 17 Ibs. 18 pwt. 22 gr. to gr. 4. Reduce 5760 gr. to ounces. 5. Reduce 8880 pwt. to Ibs. 6. Reduce 35179 gr. to higher denominations. 7. What will be the cost of a gold medal weighing 11 pwt. 16 gr. at 5 cents per grain ? 8. How many spoons weighing 1% oz. each can be made from a bar weighing 5 Ibs. 10 oz. 1 9. A miner wishing to have a watch case made, sent to the watchmaker 2 oz. 8 pwt. 9 gr. of gold 9 Ao pure. If the watch- maker charged $17.50 for his labor, and $22.50 for the works, what was the total value of the watch ? 10. What is 5 Ibs. 10 oz. 15 pwt. 12 gr. of gold dust worth, at 84 cents a pwt. ? AVOIRDUPOIS WEIGHT 384. Solve the following : 1. Reduce 5 cwt. 75 Ibs. 12 oz. to ounces. 2. Reduce 2 T. 16 cwt. 48 Ibs. to pounds. 3. Reduce 2560 oz. to hundredweights. 4. Reduce 587650 oz. to higher denominations. 5. Reduce 29120 Ibs. to long tons. 6. An importer received a shipload of 540 long tons of coal costing $3 per ton, freight 25 cents per ton, and duty 75 cents per ton. If he sell it at $5 per standard ton, what will be his gain? 7. What will be the cost of 7 carloads of wheat, each car containing 20 tons, at $1.15 per cental? 8. In building a house, I used 2 kegs of six penny nails at 3% cents per pound, 5 kegs of 8's at 3V2 cents per pound, 7 l /2 kegs of spikes at 3 1 /4 cents per pound, and l l /2 kegs of shingle nails at 4 cents per pound. What was the total cost of the nails ? 9. What is the capacity of the smallest car that will exactly carry either barley, flaxseed, wheat, or oats, whole bushels, Cali- 112 . MODERN BUSINESS ARITHMETIC fornia weights; and how many bushels of each kind would be re- quired for a load ? 10. Find the total cost of the barley, flaxseed, wheat, and oats in the above, if the cost of the flaxseed was Vs more than the wheat, the cost of the wheat 1 A more than the barley, the cost of the barley Vs more than the oats, and the oats was worth 30 cents per bushel. APOTHECARIES' WEIGHT 385. Solve the following : 1. Reduce 3 Ibs 58 35 to drams. 2. Reduce 1 Ib. 57 33 92 gr.15 to grains. 3. Reduce 4245 grains to higher denominations. 4. Reduce 12560 scruples to pounds. 5. How many 2 -grain capsules can be made from Si 3l 9l of quinine.? 6. A druggist made 4200 four-grain capsules of a certain kind of medicine. Allowing one grain for the weight of each shell, what was the total weight ? 7. If the above medicine cost $1 an ounce, and retailed for 25 cents per dozen capsules, what would be the gain ? 8. Medicine bought for $12 a pound, Apothecaries' weight, is sold for 10 cents a scruple. What would be the gain on 11 pounds ? 9. An ounce of medicine will make how many doses, if each dose requires Vw of a grain? 10. How many 3-grain pills can be made from 2 Ibs. 52 32 92 gr.2 of drugs, and what will be the cost at 15 cents a dozen ? Comparison of Weights 386. Solve the following : 1. Reduce 10 Ibs. Troy to Avoirdupois pounds. 2. Reduce 10 Ibs. Avoirdupois to Troy pounds. 3. Reduce 10 Ibs. Avoirdupois to Apothecaries' weight. DENOMINATE NUMBERS 113 4. Reduce 10 Ibs. 10 oz. 10 pwt. 10 gr. Troy to Apothecaries' weight. 5. Reduce 17 Ibs. 12 oz. Avoirdupois to Troy weight. 6. Which is the heavier and how much, a pound of gold or a pound of feathers ? 7. Which is the heavier, an ounce of gold or an ounce of feathers, and how much ? 8. A man bought a bar of silver weighing 125 pounds, Avoir- dupois weight, for 60 cents an ounce, and sold it for 60 cents an ounce, Troy weight. Did he gain or lose, and how much ? 9. A druggist bought 5 pounds of quinine at $12 per pound, avoirdupois weight, and sold it in 2-grain capsules at 10 cents per dozen. What was his profit ? 10. A grocer uses an Apothecaries' scales in selling bicarbon- ate of soda. Out of how much does he cheat his customers in selling a 48-pound box, the selling price being 45 cents per pound? LIQUID MEASURE 387. Solve the following : 1. Reduce 5 gal. 3 qts. 1 pt. to pints. 2. Reduce 3 bbls. 22 gal. 2 qts. 1 gi. to gills. 3. Reduce 4 hhds. 28 gal. 1 pt. to gills. 4. Reduce 2268 pts. to barrels. 5. Reduce 14271 gills to higher denominations. 6. How many barrels in a tank that will hold 1055 gallons 1 quart? 7. How many 1^ pint bottles can be filled from a cask of wine containing 45 gallons ? 8. How many pint, quart, and half -gallon bottles of each an equal number can be filled from a cask holding 42 gallons ? 9. A grocer bought 5 bbls. of vinegar at $6 a barrel and sold it at 10 cents a quart. What was his gain ? 10. A grocer's gal. measure was 1 gi. short of correct measure. How much would he profit in selling a 45 gallon cask of molas- ses at 62 cents per gallon by using the short measure ? 114 MODERN BUSINESS ARITHMETIC APOTHECARIES' FI/UID MEASURE 388. Solve the following : 1. Reduce cong.7 O5 fSl2 to fluid drachms. 2. Reduce O3 fS6 f57 11145 to minims. 3. Reduce cong.18 fS7 0135 to minims. 4. Reduce U143456 to higher denominations. 5. Reduce 516382 to higher denominations. 6. How many ounce bottles can be filled from a tankard con- taining cong.ll ? 7. A druggist fills 124 doz. fS2 bottles with perfume. What quantity was required ? 8. Brown bought 3 gills of a tincture at 25 cents per gill and sold it at 15 cents a fluid drachm. What did he gain ? 9. By buying alcohol at $4 per gallon, liquid measure, and selling it at 10 cents a fluid ounce, what would be the gain on five gallons ? 10. A druggist had 3 ounce, 5 ounce, and 8 ounce bottles, and wished to use twice as many of the 3 ounce as of the 5 ounce, and twice as many of the 5 ounce as of the 8 ounce. How many bottles would be required to hold the contents of 4 barrels each containing 33f gallons ? DRY MEASURE 389. Solve the following : 1. Reduce 5 bu. 3 pk. 5 qt. to quarts. 2. Reduce 17 bu. 1 pk. 3 qt. 1 pt. to pints. 3. Reduce 17 bu. 7 qt. to pints. 4. Reduce 128 pints to bushels. 5. Reduce 57631 pt. to higher denominations. 6. What will 4 bu. 2 pk. of nuts cost at 8 cents per quart ? 7. Cranberries bought for $5 per barrel of 2^ bushels are sold at 10 cents per quart. What is the gain on a barrel ? 8. If one horse requires 12 quarts of oats per day, how many bushels will it take to feed 6 horses 8 days ? DENOMINATE NUMBERS 115 9. A grain dealer's bushel measure is too small by 1 pint. What does he make dishonestly in selling 12 tons of wheat at 90 cents a bushel ? 10. A dealer bought 2 bu. 6 qt. of berries at 40 cents a pk., dry measure, and sold them at 10 cents per qt., liquid measure. What did he gain ? IVINEAR MEASURE 390. Solve the following : 1. Reduce 8 rd. 5 yd. 2 ft. 7 in. to inches. 2. Reduce 1 mi. 4 ch. 2 rd 20 1. to inches. 3. Reduce 4 leagues 2 mi. 7 fur. 4 yd. 1 ft. to inches. 4. Reduce 71364 inches to higher denominations. 5. Reduce 35824 links to higher denominations. 6. If it costs $16000 per mile to build a railway, what will be the cost to build 5 fur. 23 rd. 5 yd. 1 ft. 6 in. ? 7. How many linear feet of boards will it take to fence a field 25 rods wide by 40 rods long, the fence to be five boards high? 8. If a steamer travels 20 miles an hour, how far will she go in 5 days 10 hours and 30 minutes ? 9. What will it cost to fence a field 140 rods long, 80 rods wide, at $.37 l /2 per rod for posts, and 3 cents per linear foot for the wire fencing ? 10. An automobile wheel is 100 inches in circumference. How many times will it revolve in going from San Francisco to Los Angeles, a distance of 484 miles ? SQUARE MEASURE 391. Solve the following : 1. Reduce 5 sq. yd. 4sq. ft. 72 sq. in. to square inches. 2. Reduce 12 A. 48 sq. rd. 21 sq. yd. to square yards. 3. Reduce 2 A. 64 sq. rd. 140 sq. ft. to square feet. 4. Reduce 14285 sq. in. to higher denominations. 116 MODERN BUSINESS ARITHMETIC 5. Reduce 7235 sq. rd. to acres. 6. What will it cost to lay a walk 8 feet wide around the outside of a block 300 feet square, at 16% cents per square foot ? 7. Find the cost of flooring a room at 5 cents per square foot, the distance around it being 280 feet, and the width % the length. 8. What will be the cost of plastering the walls and ceiling of a room 40 feet wide by 60 feet long and 16 feet high at 33 1 /ij cents a square yard, allowing for a 4-foot wainscoting, but no allowance to be made for doors or windows ? 9. A city lot containing VB of an acre is sold at $100 per front foot. If the lot is 90 feet deep, what is the total selling price? 10. Find the cost of carpeting a lodge room the floor of which is 36 feet wide, and 54 feet long ; the carpet to be regular 27 in. tapestry $1.55 per linear yard ; strips to run lengthwise the hall, and 9 inches allowed on each strip for matching. SURVEYORS' SQUARE MEASURE 392. Solve the following : 1 . How many acres in 4 sections ? 2. Reduce 640 sq. ch. to acres. 3. Reduce 2 A. 5 sq. ch. 12 sq. rd. to square links. 4. Reduce 17342 sq. 1. to higher denominations. 5. Reduce 5760 sq. rd. to square chains. 6. How many acres in a field 23^6 chains wide, and 27 l /2 chains long ? 7. Hill owns the S. E. x /4 of the N. W. % of a section of land. How many acres has he ? 8. The E. % of the S. W. *4 of a section of land was bought for $75 per acre and sold at $110 per acre. How much was gained ? 9. A sold the N. V 2 of the S. W. % and the S. 2 of the N. W. X of a section of land at $62.50 per acre. How much did he get for his land ? Draw diagram and locate the property. DENOMINATE NUMBERS 117 10. What is the cost of a farm bought at $125 an acre and des- cribed as follows : The E. Y* of the N. W. # of the S. E. # of the N. E. # of the S. W. Y of section 16, Tp. 2 N. Range 3 W. ? Draw diagram of section 16, and locate the farm. CUBIC MEASURE 393. Solve the following : 1. Reduce 17 cu. ft. 132 cu. in. to cubic inches. 2. Reduce 25 cu. yd. 22 cu. ft. to cubic feet. 3. Reduce 12 cords to cubic feet. 4. -Reduce 51840 cu. in. to cubic feet. 5. Reduce 18 cd. ft. to cubic inches. 6. What will it cost to dig a cellar 16 feet wide by 24 feet long and 9 feet deep at 60 cents a cubic yard ? 7. How many cords in a pile of wood 48 feet long, 6 feet high, and 4 feet wide ? 8. What will be the cost of building a wall 132 feet long, 4 feet 6 inches high, and 18 inches wide, at $2.40 a perch ? 9. Allowing 7 bricks to the square foot for ^ach tier of bricks, how many bricks will it take to build the sides and one end of a store building 27 feet wide, 120 feet long, the walls be- ing 22 feet high, no allowances for openings or corners, and the walls three bricks thick ? 10. A railway tunnel is ^ of a mile long, 20 feet wide, and 18 feet high. If it cost $1.40 per cubic yard to excavate it, $2.75 per linear yard to timber it, and $28 per rod to lay the track ; what was the total cost when finished ? TIME MEASURE 394. Solve the following : 1. Reduce 12 yrs. 7 mos. 15 ds. to days. 2. Reduce 7 wks. 1 da. 12 hrs. 20 min. to minutes. 3. Reduce 1620 hours to higher denominations. 4. Reduce 1342782 seconds to higher denominations. 5. How many minutes in February, 1908 ? 6. How many more seconds in July than in June? 118 MODERN BUSINESS ARITHMETIC 7. Find the exact time from March 15th to August 23d. 8. How many times will a clock that ticks 3 times in every 2 seconds tick in a day ? 9. A note given September 15, 1907, is due April 2, 1910, How long has it to run ? Give answer in years, months, and days. 10. A note dated July 1, 1907, is written, "one year after date I promise to pay, etc." If this note is discounted at bank December 21, 1907, what is the term of discount? CIRCULAR MEASURE 395. Solve the following : 1. Reduce 7 24' 30" to seconds. 2. Reduce 45 50' 54" to seconds. 3. Reduce 21485' to higher denominations. 4. Rednce 457864" to higher denominations. 5. Reduce 145 to statute miles. 6. New York is 74 3' west of Greenwich. How many sec- onds are they apart. 7. San Francisco is 122 26' 45" west of Greenwich. How many geographic miles is San Francisco from New York ? 8. A dial of a clock represents a circle. How many degrees from 12 M. to 8 p. M. ? 9. How many statute miles around the earth on its greatest circle ? 10. The earth revolves on its axis once every 24 hours. How many degrees, minutes, and seconds will it revolve in 4 hours 24 minutes 30 seconds? 396. Solve the following : 1 . What will be the cost of a great gross of lead pencils at 30 cents per dozen ? 2. Brown sold 5 gross of penholders at 5 cents each. What did they bring ? DENOMINATE NUMBERS 119 3. In a crate containing f\ of a G. gro. of eggs, 1 out of every 18 was broken ; the remainder were sold at 25 cents per dozen. What did they bring ? 4. A is 2 score years of age ; B is as old as A and C, and C is \ the age of A. What is the age of each ? 5. John is 12 years old ; James is as old as John, plus -J- of Henry's age, and Henry is as old as John and James together. Find the age of James and Henry. 6. How many sheets of paper in 2 reams ? 7. What will 15 reams of 20# 14x17 Queen Bee flat paper cost at 9 cents per Ib. ? 8. Bought 2 bundles of 16# folio linen typing paper (500 sheets 17 x 22) at 12 cents per Ib., and after cutting the same into letter size (fourths), sold it at 60 cents per 500 sheets. What was my gain ? 9. How many sheets of paper 28x42 will it take to print 1000 16 mo. books of 320 pages each? 10. Ten reams of paper will make how many octavo booklets, reckoning 500 sheets to the ream ; and how many pages in each allowing one sheet to each booklet ? HOME WORK No. 13 1. Which has the greater intrinsic value, ^20, 400 marks, or 500 francs, and by how much in U. S. money? 2. Which is the heavier, a 10-pound steel sledge, or a 10- pound sack of silver, and how much ? 3. Which is the heavier, a 4-ounce gold watch case or a 4- ounce boxing glove, and how much ? 4. How many 10-grain powders can be made from Ibl, Svij, 5iv, 9ij of drugs ? 5. How many pint, quart, and two-quart bottles, of each an equal number, can be rilled from a keg containing 10 gal. 2 qts. of cider ? 120 MODERN BUSINESS ARITHMETIC 6. A farm is 60 chains long and 124 rods wide. How many acres does it contain ? 7. Draw a map and locate Tp. 2 N. and R. 3 E., also locate the N. % of the S. W. X of the N. E. X of Section 21. How many acres ? 8. How many perches of stone in a wall 66 ft. long, 15 ft. high, and 2 ft. 6 in. thick? 9. How many more seconds in January than in February 1908? 10. A grocer's scales is /^ oz. short in every pound. Out of how much does he cheat his customers in selling a 310-pound barrel of sugar worth 6 cents per pound ? Longitude and Time 397. A Meridian is any imaginary line extending from pole to pole on the earth's surface. 398. There are three First Meridians : 1. The Meridian of Greenwich the one passing through Greenwich, a suburb of L,ondon, England. 2. The Meridian of Washington, D. C. the one passing through the observatory at Washington. 3 . The Meridian of Paris the one passing through Paris, France. 399. Longitude is the distance east or west of a first meridian. 400. Using the Meridian of Greenwich as the first mer- idian, Washington is 77 0' 15" west longitude, and Paris is 2 20' east longitude. 401. Standard Time in the United States, for conven- ience, has been established as follows : 1. Eastern time, taken when the sun is on the meridian 75 west of Greenwich. 2. Central time, taken when the sun reaches the meridian of 90 west. 3. Mountain time, taken when the sun reaches the meridian of 105 west. 4. Pacific time, taken when the sun reaches the meridian of 120 west. 402. It will be noticed that the difference of longitude of the above is 15 each. The difference of time is one hour, the same time being used in all territory of 7i east and west of each stan- dard meridian. 403. The Earth makes one revolution in 24 hours. Its circumference is 360. 360 -r- 24 = 15 the distance passed in 1 hour. 122 MODERN BUSINESS ARITHMETIC 404. If a point on the earth passes 15 in 1 hour or 60 min- utes, in 1 minute it will pass -fa of 15 or 15'. In 1 minute or 60 seconds it passes 15'; in 1 second it will pass ^ of 15' or 15". 405. Another analysis is : If a point on the earth passes 15 in 60 minutes, to pass 1 would take iV of 60 minutes or 4 minutes. If it passes 15' in 60 seconds, to pass l' would take iV of 60 seconds or 4 seconds. 406. To Find the Difference in Time when the Difference in Longitude is Given. Divide the difference of longitude by 15, and the result will be the difference in time ; or multiply the difference in longitude by 4, .and the result will be minutes and seconds. EXAMPLE : Find the difference of time between New York and Chicago. Chicago is 87 27' 45" west New York is 74 3 west Dif . of Long. 15) 13 24 45 hr. 53 min. 39 sec. Or, Dif. in Long. 13 24' 45" 4 Dif. in Time 53 min. 39 sec. rem. 407. To Find the Difference of I/ongitude when the Difference of Time is Given. Multiply the difference in time by 15, and the result will be the difference in longitude ; or divide the difference in time expressed in minutes and seconds by 4, and the result will be the difference in longitude. EXAMPLE : Find the difference of longitude between Boston and San Francisco, the difference of time being 3 hours 25 min- utes 33 seconds. Dif. in Time 3 hr. 25 min. 33 sec. 15 51 23' 15" Dif. in Longitude- Or, 3 hr. 25 min. 33 sec. Reduce hr. to min. 4) 205 min. 33 sec. 51 23' 15" Dif. in Longitude. LONGITUDE AND TIME 123 408. The following table gives the longitude of some of the principal cities of the world : Albany 73 44' 50" W. New Orleans 90 3' 0"W. Astoria, 124 0' 0" W. Omaha 95 56' 14" W. Boston 71 3' 30" W. Paris 2 20' 0" E . Berlin 13 23' 45" E . Philadelphia 75 9' 3"W. Bombay 72 54' 0" E . Rome 12 27' 0" E . Cincinnati 84 29' 32" W. Rio Janeiro 43 20' 0"W. Chicago 87 37' 45" W. San Francisco 122 26' 45" W. Detroit 83 3' 0" W. St. Paul 95 4' 55" W. Honolulu 157 52' 0" W. St. Louis 90 15' 15" W. Mexico 99 5' 0" W. Salt Lake City 111 53' 47" W. New York 74 3' 0" W. Washington 77 0' 15" W. 409. In finding the difference of the longitude of two places, subtract if both are east or west longitude ; add if one is east and the other west. 410. Solve the following : 1 Find the difference in the time of Boston and Chicago. 2. Between Detroit and Omaha. 3. When it is noon at Washington what time is it in San Francisco ? 4. When it is noon at Philadelphia, what time is it at Paris ? 5. When it is 6:30 P. M. in Rome, what time is it in San Francisco ? 6. In traveling from Chicago west, my watch gained 2 hours 15 minutes 30 seconds. What was my longitude ? 7. Since starting on my journey, my watch has lost 1 hour 32 minutes 45 seconds. Which way did I travel and what was the difference of longitude ? 8. I started from Salt Lake City at 9:15 A. M., and after traveling two days found my watch had lost 1 hour 49 minutes 37 seconds. What direction had I traveled, and what large city has the same longitude as my destination ? 9. What is the difference of time between Bombay and Hon- olulu ? 10. In sailing from San Francisco to Bombay, will a chro- nometer gain or lose time, and how much ? 124 MODERN BUSINESS ARITHMETIC HOME WORK-NO. 14 NOTE Questions should be answered in writing. 1. Why multiply by 15 in reducing longitude to time, and why does this number hold good as regards minutes and seconds. 2. Why add in some instances and subtract in others in find- ing the difference of longitude between two places ? 3. What is the longitude and latitude of your home city from London ? From Washington ? 4. What is the difference of time between your home city and London ? Your home city and Washington ? 5. What is the difference of time between New York and San Francisco ? 6. In traveling west from Boston, Mass., I find my watch to vary from correct time by 1 hr. 6 min. 17 sec. What large city has the same longitude as my destination ? 7. When it is noon in Philadelphia, what time is it at St. Louis, Mo.? 8. When it is 4 P. M. in St. Paul, what time is it in Wash- ington, D. C. ? 9. Will a chronometer gain or lose and how much in travel- ing from Rome to Omaha ?. 10. The great earthquake at San Francisco occurred April 18, 1906, at 5:15 A. M. Had the news been telegraphed to New York without loss of time at what hour should it have been re- ceived ? Denominate Fractions 411. Denominate Fractions may be reduced from one denomination to another by the same operations and principles which apply to denominate numbers. 412. To Reduce a Denominate Fraction or Deci- mal to Lower Denominations. Multiply by the number of units of the next lower denomination required to make one of the given fraction or decimal. If there be a fractional remainder, treat it 'in the same manner. EXAMPLE : Reduce of a > to lower denominations. EXAMPLE: Reduce ,.190625 to lower denominations. . 190625 .8125s. .75d. _ 20 _ 12 _ 4 3.812500s. 9.7500d. 3.00 far. Answer, 3s. 9d. 3 far. 413. Solve the following : 1. Reduce %2 to lower denominations. 2. Reduce ..31875 to lower denominations. 3. Reduce %2 of a rod to lower denominations. 4. Reduce .245 mi. to lower denominations. 5. Reduce .54375 Ibs. Troy to lower denominations. 6. Reduce .365375 T. Avoirdupois to lower denominations. 7. How many acres in .375 of a section? 8. How many gills in %e of a gallon ? 9. A sold Vs of % of .75 of a ton of coal for $5. What was the selling price per cwt. 10. How many sq. 1. in .012345 of an acre? 126 kODERN BUSINESS ARITHMETIC 414. To Reduce a Denominate Fraction or Deci- mal to a Higher Denomination. Divide by the number of units required to make one of the higher denomination. EXAMPLE : Reduce ^ minute to days. I X -sV X T = TsVo days. EXAMPLE : Reduce .64 quarts to bushels. .64 -f- (8 X 4) = .02bu. 415. Solve the following : 1. Reduce % pt. to gallons. 2. Reduce % ft. to yards. 3. What fraction of a bushel is % of a quart ? 4. What fraction of a mile is %2 of a rod? 5. What decimal of a ton is 45 Ib ? 6. What decimal of a day is 10.8 minutes? 7 . What part of a mark is % pfennig ? 8. Reduce .33% of a shilling to the fraction of a . 9. Three-fourths of a Ib. Avoirdupois is what fraction of a bushel of wheat ? 10. One-third of B's age equals % of A's. If the sum of their ages is .75 of 52 years, what is the age of each ? 416. To Reduce a Denominate Number to a Deci- mal or Fraction of a Higher Denomination. Reduce the denominate numbers by dividing the lowest first, and successively the others, annexing the fractional part at each change in denomination. EXAMPLE : Reduce 13 hours 30 minutes to the fraction of a day. To decimal of a day. FRACTION : DECIMAL : 30 min. X 6 V = \ hr. 60) 30 min. 13i hrs. = -V- hrs. .5 hr. -V- hrs. X 2 1 !- = A da. Ans. 13. hr. 24) 13.5 hr. Ans., .5625 days. DENOMINATE FRACTIONS 127 417. Solve the following : 1. Reduce 2 yd. 2 ft. 6 in. to the fraction of a rod. 2. Reduce 87 Ib. 12 oz. to the decimal of a cwt. 3. Reduce 2 pk. 5 qt. 1 pt. to the fraction of a bushel. 4. Reduce 2 sq. ft. 117 sq. in. to the decimal of a sq. yard. 5. What part of 4 hours is 42 minutes 30 seconds? 6. What part of a hhd. is 10 gal. 2 qt. 1 pt. 2 gi. ? 7. What part of a f 5 are f 35 R136 ? 8. What decimal part of a cwt. is Vi of 22% Ibs. ? 9. What decimal part of a circle are 18 deg. 20 min. 15 sec.-? 10. What decimal part of a ream are 12 qr. 18 sheets of paper ? Addition of Denominate Numbers 418. To Add denominate numbers is to unite them into one sum whether simple or compound. 419. To Add Denominate Numbers. Write like denominations in the same columns ; add and reduce each sum to higher denominations when possible. EXAMPLE: s. d. far. 4382 7 8 2 10 9 3 2 24 24 21 11 sums of each column . Reduced = 25 5 11 3 Ans. 420. Solve the following : 1. Add 5 cwt. 46 Ib. 12 oz., 12 cwt. 9 Ib. 8 oz., 2 cwt. 25 Ib., 21 Ib. 10 oz. 2. Add 4 da. 21 hr. 36 min. 10 sec., 14 hr. 24 min. 15 sec., 2 da. 22 min., 3 da. 12 hr. 40 sec. 3. Add 8 yd. 2 ft., 5 yd. 1 ft. 3 in., 2 ft. 9 in:, 3 yd. 2 ft. 6 in., 2 ft. 10 in., 7 yd 1 ft. 8 in. 4. Add 2% hhd., 36 gal. 3 qt. 1^4 pt., % gal., 12 qt. % pt., 1 bbl. 3 gal. 3 gi., % qt. 1 gi. 5. Add R)5 57 33, Ibl2 SlO 35 92, 32 34 9l gr.15, tblO 37 gr. 12, 36 92V2. 128 MODERN BUSINESS ARITHMETIC Subtraction of Denominate Numbers 421. To Subtract denominate numbers is to find their dif- ference . 422. To Subtract Denominate Numbers. Write like denominations in the same columns ; subtract as in simple numbers, taking a unit of the next higher denomination when necessary to increase the minuend. EXAMPLE : bu. pk. qt. pt. 4260 1821 2331 Ans. 423. Solve the following : 1. From 25 rd. 2 yd. 2 ft. 6 in., take 14 rd. 4 yd. 1 ft. 10 in. 2. From 4% bu. take 3Vs bu. 3. From 44 cd. 4 cd. ft. 10 cu. ft. take 18 cd. 6 cd. ft. 14 cu. ft. 4. From a cask of cider containing 44 gal., 12 gal. 3 qt. 1 pt. 1 gi. was drawn off. How much remained ? 5. A sold from his farm, containing 320 A., two lots of land; the first contained 72 A. 32 sq. rd.; the other 112 A. 4 sq. ch. How much did he have left ? Multiplication of Denominate Numbers 424. Multiplication is a short method of making addi- tions of the same number. 425. To Multiply a Denominate Number. Multiply as in simple numbers. Reduce to higher denomina- tions when necessary. EXAMPLE : Multiply 3 mo. 10 ds. 5 hrs. 20 min. 30 sec. by 5. mo. ds. hrs. min. sec. 3 10 5 20 30 5 15 50 25 100 150 product. Reduced = 16 21 2 42 30 Ans. DENOMINATE FRACTIONS 129 Solve the following : 1. Multiply 32 rd. 1 yd. 2 ft. 5 in. by 10. 2. Multiply 4 bu. 3 pk. 5 qt. by 9. 3. Multiply 2 gal. 2 qt. 1 pt. 3 1 /i gi. by 64. 4. If an acre of land will produce 35 bu. 3 pk. 6 qt. 1 pt. of grain, how much will a farm of 1 A section produce? 5. What will be the cost of 8 casks of vinegar, each cask containing 42 gal. 3 qt. 1 pt. at 22 cents per gallon? Division of Denominate Numbers 426. Division is the process of finding one of the equal parts of a number. 427. To Divide a Denominate Number. Divide as in simple numbers. Reduce remainder to lower denom- inations when necessary. EXAMPLE : Divide 47 bu. 2 pk. 7 qt. 1 pt. by 5. 5)47bu. 2pk. 7qt. 1 pt. 9211 Answer. ( Dividing and reducing each remainder.) 428. Solve the following : 1. Divide 426 A. 123 sq.rd. 25 sq. yd. 7 sq. ft. by 12. 2. Divide /44 8s. lOd. by 8. 3. Divide 320 gal: 3 qt. 1 pt. 3 gi. by 42. 4. How many boxes holding 1 bu. 1 pk. 7 qt. each can be filled from 356 bu. 3 pk. 5 qt. of berries? 5. A township 6 miles square is divided into farms each containing 153 A. 6sq. ch. How many farms were there? Areas or Surfaces 429. A Straight Line is one whose points all lie in the same direction. A strht L,n. NOTE A straight line is the shortest distance be- tween two points. 430. A Curved Line is one that changes its direction at every point. 431. Parallel Lines are equidistant in their entire length. 432. An Angle is the divergence of two lines from a common point. 433. A Right Angle is formed where one straight line meets another straight line making two equal angles. 434. An Acute Angle is less than a right angle. 435. An Obtuse Angle is greater than a right angle. 436. A Quadrilateral is a plain figure having four sides and four angles, 437. A Parallelogram is a quadrilater- al whose opposite sides are parallel. 438. A Rectangle is a right-angled par- allelogram. 439. A Square is an equilateral rect- angle. 440. A TrapeZOid is a quadrilateral having only two sides parallel. 441. A Trapezium is a quadrilateral whose opposite sides are not parallel. AREAS OR SURFACES 131 442. A Triangle is a plane figure hav- ing three sides and three angles. 443. An Isosceles Triangle is one having two equal sides and two equal angles. 444. An Acute-Angled Triangle is one all of whose angles are acute. 445. An Obtuse - Angled Triangle is one having one obtuse angle. 446. The Base of a figure is the side upon which it is supposed to rest. 447. The Altitude is the perpendicular distance between the base line and the highest point opposite. 448. The Hypothenuse of a right- angled triangle is the side opposite the right angle. 449. The Diagonal of a quadrilateral is a line connecting two opposite angles. 450. A Rhomboid is an oblique-angled parallelogram. 451. A Rhombus is an equilateral rhomboid. 452. A Polygon is a plane figure bound- by straight lines. NOTE Polygons are named from their number of sides. Thus, one of five sides is called a PENTA- GON ; of six sides, a HEXAGON ; of seven, a HEPTA- GON ; of eight, an OCTAGON ; etc. 453. The Perimeter of a polygon is the total length of its boundary lines. Pentagon. Hexagon. Heptagon. Octagon. Nonagon. Decagoc. 132 MODERN BUSINESS ARITHMETIC Surface Measure 454. A Surface has two dimensions, length and breadth. NOTE A square inch is a rectangular surface whose length and breadth are each ONE inch. 455. The Area of a surface is the num- ber of square units within its perimeter. NOTE Thus a rectangle 3 inches wide and 5 inches long has three rows of square inches with four square inches in a row, or 15 square inches in all. 456. To Find the Area of a Rectangle. Multiply the length by the breadth expressed in the same linear units. 457. Solve the following and draw diagram for each : 1. Find the area of a garden 15 l /2 rods long by 7 l /2 rods wide. 2. A floor is 42 ft. 6 in. long by 20 ft. wide. What is the area? 3. Ten windows are each 9 ft. by 3 ft. 4 in. What is their entire area in square yards ? 4. A walk extends around the outside of a court 20 yds. wide by 80 ft. long. If the walk is 3 yds. wide, what is its area? 5. What is the area in square yards of a tennis court 10 rods long by 60 feet wide ? 458. To Find the Area of a Triangle. Multiply the base by one-half the altitude ; or, multiply the alti- tude by one-half the base. NOTE Every rectangle may be divided into two equal triagles ; there- fore the area of a triangle is one-half the area of its rectangle. 459. Solve the following and draw diagram for each : 1. Find the area of a triangle whose base is 12 ft. and whose altitude is 17 ft. 2. What is the area of a triangle whose base is 25 ft. and whose altitude is 32 ft? AREAS OR SURFACES 133 3. The gable of a house is 20 ft. wide and 8 ft. high. How many square feet ? 4. A triangular field is 15 chains on one side and the perpen- dicular distance from the opposite angle is 15 rods. How many acres in the field ? 5. At $90 per acre, what will be the cost of a farm bounded as follows : Starting at a certain point and measuring 73.54 ch. north, thence 44.82 ch. west, thence southeasterly in a direct line to the starting point ? 460. To Find the Area of any Parallelogram. Multiply its base by its altitude. NOTE Since any quadrilateral may be divided by its DIAGONAL into two triangles, the sum of the areas of those triangles will be the area of the quadrilateral. 461. Solve the following and draw diagram for each : 1. Find the area of an oblique angled parallelogram whose base is 21 ft. and whose altitude is 16 ft. 2 . Find the area of a trapezoid whose opposite sides are respect- ively 18 ft. and 24 ft., and whose altitude is 7 ft. 3. One side of a field is 64 chains long, the opposite and parallel side is 36 chains long, and the nearest distance between these sides is 25 chains. How many acres in the field? 4. The diagonal of a trapezium is 44 feet. The perpendicu- lar distances from this diagonal to the angles opposite are 17 ft. and 14 ft. What is its area? 5 . From a California Redwood tree a plank 72 ft. long, 72 in. wide at one end and 54 in. wide at the other is sawed. How many square feet in its surface ? 462. To Find the Area of a Circle. Multiply the circumference by one-fourth the diameter; or, square the diameter and multiply by .7854 ; or, square the radius and multiply by 3.1416. NOTE In mathematics, a circle is considered to be composed of an infinite number of triangles with their vertices at the center, and the circumference the total sum of their bases. One-fourth the diam- eter equals one-half the altitude of the triangles. The circumference is always 3. 1416 times the length of the diameter. 134 MODERN BUSINESS ARITHMETIC 463. Solve the following : 1. Find the area of a circle whose circumference is 314.16 ft. and whose diameter is 100 ft. 2. How many sq. yds. in a circle 60 ft. in diameter? 3. The circumference of a circle is 636.174 ft. What is its area ? 4. How many acres in a circular field surrounded by a race course 1 mile long ? ^^^^^^^^^^m 5. A plaza 400 ft. in diameter is sur- rounded by a walk 20 ft. wide. How many J ; square feet in the walk ? |J; 464. To Find the Lateral Area of I a Prism or Cylinder. Multiply the perimeter of the base by the length. 465. To Find the Lateral Area of a Pyramid or Cone. Multiply the perimeter of its base by one- half its slant height. 466. To Find the Lateral Area of a Frustum of a Pyramid or Cone. Multiply one-half the sum of the perimeter of both bases by the slant height. 467. To Find the Area of a Sphere. Multiply the diameter by the circumference; or, square the diameter and multiply by 3.1416. 468. Solve the following and draw diagram for each : 1. What is the total area, including base, of a pyramid 12 ft. square' and 20 ft. slant height ? 2 . Find the lateral surface of a frustum of a cone whose low- er base is 10 in., and whose upper base is 4 in. in diameter, the slant height being 24 inches. AREAS OR SURFACES 135 3. How many square feet in a length of stove pipe 24 inches long and 6 inches in diameter ? 4. A sphere 15 inches in diameter requires how many square inches of gold leaf to cover it ? 5. A State capitol has a dome 60 feet in diameter. What would be the cost to gild it at $2.50 per square foot if it is a per- fect hemisphere ? Volumes or Solids 469. A Solid or Volume is anything that has length, breadth, and thickness. 470. A Rectangular Solid is one whose lateral surfaces are rectangles. 471. A Cube is a rectangular solid whose surfaces are equal squares. 472. A Prism is a volume whose upper and lower bases are equal polygons and whose sides are quadrilaterals. 473. A Cylinder is a vol- ume whose upper and lower bases are equal circles and whose lateral surface is curved. 474. The Altitude of a solid is the perpendicular distance from its highest point to its base. Triangular Prism Rectangular Prism Pentangular Prism Cylinder 475. The Unit of Measure for solids is the cube, the edge of which is a unit of some known length. 136 MODERN BUSINESS ARITHMETIC 476. A Frustum of a pyramid or cone is that part of the solid between the lower base and any other plane parallel to the base. 477. A Sphere is a volume bounded by I a curved surface every point of which is equi- W distant, from the center. 478. A Pyramid is a volume having a polygon for its base and its sides triangles meeting at a point called the vertex. Pyramid Frustum of a Pyramid Cone Frustum of a Cone 479. A Cone is a volume having a circle for its base and tapering uniformly to a point called the vertex. 480. To Find the Contents of a Rectangular Solid. The product of the length, breadth, and thickness expressed in the same denominations will give the number of cubic units. 481. Solve the following : 1. What are the solid contents of a block of granite 8 ft. long, 3 ft. wide, and 2 ft. thick? 2. Find the solid contents of a cube whose length is 33 inches. 3. What are the solid contents of a cube whose superficial area is 726 square inches? 4. A watering trough is 11 ft. long, 21 in. wide, and 18 in. deep. How many gallons will it hold? 5. Reckoning a cubic foot equal to % bushels, how many bushels of wheat will a bin 12 ft. long, 8 ft. wide, and 5 ft. deep hold? AREAS OR SURFACES 137 481. To Find the Volume of a Prism or Cylinder. Multiply the area of the base by the altitude. 482. Solve the following : 1. A column of stone is 2 ft. 6 in. square and 16 ft. high. What are its solid contents ? 2. What is the volume of a shaft 12 ft. by 15 ft. and 90 ft. high, and what would it cost at $.3lM* per cubic ft. to erect it? 3. A mining shaft was 300 ft. deep and 6 ft. square. What was the cost of excavating and timbering, excavations costing $3.50 per cu. yd., and timbering 45 cents per sq. ft. of lateral area? 4. A triangular prism is 25 in. high; its base is right angled, 4 in. by 3 in. by 5 in. What are its contents? 5. What are the solid contents of a hollow cylinder 4 ft. long and 20 inches in diameter, the hollow being 10 inches in diam- eter? 483. To Find the Volume of a Pyramid or Cone. Multiply the area of the base by l /s the altitude. 484. Solve the following : 1. What are the solid contents of a pyramid 5 ft. square at the base and 9 ft. high? 2. What are the solid contents of a rectangular pyramid the base of which is 20 ft. by 30 ft. and whose altitude is 104 ft. ? 3. Find the volume of a cone whose base is 24 ft. in diam- eter and whose height is 60 ft. 4. A pyramid 75 ft. high and 20 ft. square at the base is cut off 25 ft. from the top. What are the solid contents of the re- maining frustum ? 5. Reckoning 144 cu. in. to a board foot, how many board feet of timber in a telegraph pole 8 in. square at the base, 4 in. square at the top and 30 ft. high ? 138 MODERN BUSINESS ARITHMETIC 485. To Find the Volume of a Sphere. Multiply its superficial area by 1/3 its radius ; or, multiply the cube of its diameter by .5236. 1. Find the solid contents of a solid shot 4 in. in diameter. 2. What are the contents of a sphere whose diameter is 10 feet? 3. An orange is 15.708 in. in circumference. How many cu. in. in its contents? 4. The earth is 8000 miles in diameter. How many cubic miles in its solid contents ? 5. A spherical cannon shell is 9 in. in diameter and 1 in. thick. How many cubic inches of solid metal in it ? HOME WORK No. 15 1. How many acres in a rectangular farm 72 rods wide by 72 chains long ? 2. A park is in the form of a rightangled triangle, the base being 40 rods and the altitude 30 rods. How many acres ? 3. A piece of cardboard is cut so that its opposite sides are parallel. Their lengths are 21 in. and 25 in., and the perpen- dicular distance between them is 15 in. What is its area? 4. How many square yards in a circular garden 200 feet in diameter ? 5. Find the number of square feet of radiation of a 2-inch steam pipe 32 feet long. 6. How many cubic feet in a column of granite, 5 ft. square and 24 ft. high ? 7. A cistern is 4 ft. by 5 ft. 6 in., and 6 ft. deep. How many gallons of water will it hold ? 8. How many feet of lumber in a 40-foot telegraph pole 10 in. square at the bottom, and 4 in. by 10 in. at the top? 9. A liberty pole is 150 ft. high, 12 in. in diameter at the base, and tapers to a point. What is its weight at 30 Ibs. per cubic foot ? 10. What is the weight of a leaden casket 12 in. long, 6 in. wide, and 4 in. thick, the lead on all six sides 1 in. thick and weighing 1 Ib. to every 3 cubic inches? MODERN BUSINESS ARITHMETIC 139 Relation of Measurements 486. Similar Lines, Areas, and Volumes have relation according to the following principles : NOTE For full discussion of the subject of proportion see page 148. PRIN. I. Corresponding lines of similar figures are in pro- portion. EXAMPLE : What is the width of a rectangle 42 feet long if a similar one is 5 feet by 14 feet ? Length : Breadth :: Length : Breadth 42 ft. : ( ) ft. :: 14 ft. : 5 ft. 42 times 5 divided by 14 equals 15, No. ft. in width. PRIN. II. Similar areas are in proportion as the squares of their like dimensions. NOTE The square of a number is its product when used twice as a factor. As, 3 times 3 equals 9. EXAMPLE : If a rectangle whose base is 18 feet contains 162 square feet, what will be the area of a similar rectangle whose base is 12 feet? Area : (Base) 8 :: Area : (Base) 3 162 sq.ft. : (18) 8 :: ( ) : (12) 8 162 times (12) 2 divided by (18) 8 equals 72, No. sq. ft. in area. PRIN. III. Similar volumes are in proportion as the cubes of their like dimensions. NOTE The cube of a number is its product when used three times as a factor. As, 3 times 3 times 3 equals 27. EXAMPLE : If a rectangular solid 6 inches long contains 60 cubic inches, what will be the contents of a similar volume 12 inches in length ? Volume : (Length) 3 :: Volume : (Length) 3 60 cu. in. : (6) 3 :: ( ) : (12) 3 60 times (12) 3 divided by (6) 3 equals 480, No. cu. in. in volume. PRACTICAL PROBLEMS 1. If a block of granite 4 ft. thick weighs 2 tons, what will a similar one 8 ft. thick weigh? 2. If the diagonal of a rectangular garden whose area is 12 sq. rd. is 82 ft. 6 in., what is the area of a similar one whose diagonal is 15 rds. ? 3. If a leaden shot 2 in. in diameter weighs 2 Ibs., what should be the weight of one 4 in. in diameter? 4. If a reservoir can be emptied by a 3 in. pipe in 12 hours, how long will it take a 4 in. pipe to empty it? 5. If a man 5 ft. tall weighs 150 Ibs., what will be the weight of one of similar build who is 6 ft. tall ? Practical Measurements Plastering, Painting, Papering, Carpeting, Etc. 487. Plastering is computed by the square yard ; painting by the square yard, or by the square of 1000 square feet ; paving by the square yard, or square foot ; carpeting by the square yard, or by the lineal yard, and papering by the roll, which is usually 8 yards long and 18 inches wide. 488. In computing the cost of materials, make allowances for openings, but in computing the cost of labor, make no such allowances, except when called for in the contract. EXPLANATION : This diagram represents the plan of the first floor of a house whose extreme outside measurements are 36 feet by 42 feet. ROOMS : The dimen- sions of the rooms are given on the diagram ; the height from floor to ceilings is 12 feet. OPENINGS: The open- ings will average two square yards each, ex- cept the archways be- tween the Jhall and re- ception room and be- tween the hall and li- brary, which are four square yards each. SECOND STORY : The dimensions of the four rooms of the second story are given on the diagram for the second floor plan. The height from floor to ceilings on this floor is 10 feet. 489. Solve the following : 1. Find the cost of plastering the reception room in the fore- going diagram, walls and ceiling, at 30 cents a sq. yd., deduct- ing one-half the area of the openings. FIRST FLOOR PRACTICAL MEASUREMENTS 141 2. Find the cost of plastering the library walls and ceilings, at 30 cents a sq. yd., deducting one-half the area of the open- ings, and allowing for 3-foot wainscoting. 3. Find the cost of plastering and paneling the dining-room, the paneling to be 7 ft. high and to cost 12^2 cents per sq. ft., the top of the walls and the ceiling to be plastered and stuccoed at 50 cents per sq. yd., allowing a reduction of one-half of area of openings, all in the paneling. 4. Find the cost of hardfinishing the kitch- en and serving room at 40 cents per sq. yd., and providing for a four foot tile wainscoting, costing 25^ per sq. ft., no allowances for open- ings in plastering, but 100 sq. ft. allowed for openings in tiling. 5. Find the cost of plastering the four chambers of the second story at 35 cents per sq. yd., deducting one- half of the area of the SECOND FLOOR OpCllingS. 6. Find the cost of flooring the second story of this building (35 ft. x 35 ft.) with Oregon pine costing $42 per M., allowing one- fourth for matching and waste, and no deductions made for walls. 7. . Find the cost of flooring with eastern oak at 15 cents per sq. ft., actual measurement, of reception room, library, dining- room, and hall ( 200 sq. ft ). 8. Find the cost of tinting library and reception room at 15 cents per sq. yd., allowing for wainscoting in library and 12 in. base-boards in reception room. 142 MODERN BUSINESS ARITHMETIC 9. What will be the cost of papering the walls and ceilings of the four chambers with wall paper costing 55 cents per roll and the ceiling paper 35 cents per roll, no allowance to be made for openings ? 10. What will be the entire cost of carpeting the house as fol- lows : Reception room rug, 9 x 12 , costing $2.25 per sq. yd. ; library rug, 12 x 18, costing $2.50 per sq. yd. ; dining-room rug, 11 x 16 , costing $1.80 per sq. yd. ; kitchen linoleum, cov- ering entire floor, costing $1.50 per sq. yd. ; four hall rugs, costing $7.50 each ; 34 yards stair and hall carpet, costing $1.50 per yd. ; carpet for all four chambers, covering entire floors, 27 in. wide, strips to run longest way of the room, and costing $1.20 per lineal yard? No allowance to be made for waste. Brick, Stone, Concrete, and Excavations 490. Brick Work is estimated by the number of bricks re- quired to build the walls. If the wall is only one brick or four inches thick, seven common sized brick are required for each square foot of superficial area , fourteen bricks are required if two bricks thick; twenty-one, if three bricks thick, etc. 491. Stone is estimated by the perch which is 16% feet long 18 inches wide, and 1 foot thick, containing 24% cubic feet.. Cut stone is sometimes estimated by the surface square foot. 492. Concrete pavements are estimated by the square foot; solid walls by the cubic foot, or by the perch. 493. When material alone is to be estimated, allow for all corners and openings. When labor alone is to be estimated, make no allowances unless by special contract. When a gen- eral estimate on material and labor together is to be made, use exterior measurements and allow one-half for openings. PRACTICAL PROBLEMS 494. Solve the following : 1. What will be the cost of a 6-foot concrete sidewalk across the front of a 50-ft. lot, at 17 cents per sq. ft. ? PRACTICAL MEASUREMENTS 143 2. What will be the cost of a concrete foundation 24 in. wide across the base, 12 in. across the top, and 18 in. deep, for a house 36 ft. square, at 12V2 cents per cu. ft. ? NOTE Estimate the length of wall to be the same as the perimeter of the building, 144 feet. 3. How many common bricks in a 13-in. fire wall 92 ft. long and 30 ft. high ? 4. What will be the cost of building a brick smoke-house 12 ft. square and 8 ft. high, the walls to be two bricks thick? No allowances ; material and labor to cost $24.50 per M. ? 5. What will be the cost of the basement walls to rest on the concrete foundation in problem No. 2 above, walls to be three bricks thick, 5 ft. high, and 36 ft by 36 ft. full size of the build- ing; the brick to cost $15 per M. ; allowance made for corners, also 7 openings 3ft. by 4 ft. ; the labor to cost $5. per M. with no allowances ? 6. Find the cost of excavating a cellar, 18 ft. by 36 ft. and 6 ft. deep, at 60 cents per cu. yd. 7. Fiud the cost of building the four walls to the above cel- lar, walls to be 12 in. thick, at $2.25 per perch. 8. At 17 cents per sq. ft. for concrete floor, and 30 cents per sq. yd. for cement walls, what would be the cost of finishing the . above cellar ? 9. Find the cost of digging and walling the cellar of a house whose length is 41 ft. 3. in. and whose width is 33 ft.; the cel- lar to be 8 ft. deep, and the wall l^ft. thick. The excavating will cost $.50 a load, and the stone and mason work $3.75 a perch. 10. How many common bricks will it take to build the four exterior walls of a house 36 ft. by. 36 ft.; the walls to be 20 ft. high and 3 brick thick, allowing for 28 openings averaging 3 ft. by 7 ft., also for the four corners ; and what would be the total cost at $18 per thousand bricks ? 144 MODERN BUSINESS ARITHMETIC Wood and I/umber 495. A Cord of wood is 8 ft. long, 4 ft. wide, 4 ft. high, and contains 128 cu ft. 496. Lumber is measured by the board foot which is 12 in. square and 1 in. thick. 497. Iy umber less than 1 in. thick is estimated as though an inch in thickness. If more than 1 in. thick, a proportionate in- crease is estimated. 498. To Find the Number of Board Feet in any Piece of I/umber. Multiply the length infect by the width and thickness in inches and divide by 12. PRACTICAL PROBLEMS 499. Solve the following : 1. Find the number of cords of wood in a pile 4 ft. wide, 6 ft. high, and 24 ft. long. 2. How many cords of wood in a pile 48 ft. long on the ground, 36 ft. on the top, 4 ft wide, and 6 ft. high? 3. How many feet of lumber in a board 16 ft. long, 10 in. wide, and 1 in. thick? 4. How many feet of lumber in 60 boards 14 ft. long, 8 in. wide, and 1 in. thick? 5. Find the contents of a board 18 ft. long, 20 in. wide at one end and 14 in. at the other, and 1 in. thick. 6. Find the cost of 180 planks 24 ft. long, 14 in. wide, and 3 in. thick, at $27 per M. 7. Find the cost of flooring a two-story house, 36 ft. by 36 ft., at $30 per M., the flooring to be 1^ in. thick, allowing % for matching and waste. PRACTICAL MEASUREMENTS 145 8. Find the cost of the following bill of lumber : 120 pcs. 15 ft. by 10 in. @ $21 per M. 240 14 ft. 12 in. 22 64 18 ft. " 2x4 in. 18 88 12 ft. " 2x12 in. 20 160 18 ft. " 2x6 in. 20 9. A field 16 ch. long by 8 ch. wide is enclosed by a board fence 5 boards high ; the boards are 16 ft. long and 6 in. wide, supported by posts every 8 feet. The lumber for fencing cost $20 per M., and the posts $10 per C. What was the cost of lumber and posts to fence the field? 10. How many shingles will it take to shingle a roof 60 ft. long, the girt from eaves to eaves over the ridge of the roof be- ing 48 ft. ; the shingles laid 4 in. to the weather, and the eave rows doubled.. NOTE A shingle is 4 inches wide or 3 to the lineal foot. Capacity of Bins, Cisterns, Etc. 500. To find the Exact Contents of a bin in bushels, re- duce the contents to cubic inches and divide by 2150.42, the number of cubic inches in a bushel. 501. To find the Approximate Contents of a bin in bushels, reduce the contents to cubic feet and take % (or .8 ) of the result for stricken measure. For heaped measure, take % of the number of bushels of stricken measure, or .64 of the number of cubic feet. NOTE Corn in the ear, potatoes, roots, and coarse articles are usually measured by heaped measure; grains and fine articles by stricken measure. 502. To find the Exact Capacity of a tank or cistern in gallons, reduce the contents to cubic inches and divide by 231, the number of cubic inches in a gallon. 503. To find the Approximate Contents of a tank or cistern in gallons, reduce the contents to cubic feet and multiply by 7%, the number of gallons in a cubic foot. 146 MODERN BUSINESS ARITHMETIC PRACTICAL PROBLEMS 504. Solve the following : 1. Find the exact number of bushels in a bin 8 ft. 4 in. long, 6 ft. 8 in. wide, and 4 ft. 2 in. deep. 2. Find the approximate contents of a bin 24 ft. long, 18 ft. wide, and 10 ft. deep. 3. What must be the depth of a bin that is 6 ft. 4 in. long by 4 ft. 6 in. wide, that will hold 72% bushels, approximate mea- sure? 4. What is the length of a wagon box 3 ft. 4 in. wide, and 18 in. deep that will hold 32% bu. of corn in the ear, heaped measure. 5. A corn crib 75 ft. long, 10 ft. wide, and 10 ft. deep, is filled \vith corn in the ear. What should it bring at 60 cents per bushel, if 2 bushels of corn in the ear are equal to one bushel of shelled corn ? 6. What is the exact contents in gallons of a tank 4 ft. square and 5 ft. 3 in. deep? 7. Find the number of barrels a cistern 6 ft. square and 8 ft. deep will hold, exact measure. 8. Find the approximate number of gallons in a watering trough 12 ft. long, 24 in. wide, and 18 in. deep. 9. How many barrels will a circular cistern 7 ft. 6 in. deep and 6 ft. in diameter hold, approximate measure ? 10. What must be the depth of a reservoir that will hold 3,000,000 gallons of water, its length being 200 ft. and its width 100 ft. ? Ratio and Proportion Ratio 505. Ratio is the relation between two numbers. 506. The Terms of a ratio are the numbers compared. 507. The Antecedent is the first term, the dividend. 508. The Consequent is the second term, the divisor. 509. The Sign is the colon (:) and is read " is to" 510. The Value of a ratio is the quotient obtained by divid- ing the antecedent by the consequent. Thus, the ratio of 18 to 3 is 6, or 18 : 3 = 6. 511. A Simple Ratio is the ratio between two numbers only; as 14 : 7. 512. A Compound Ratio is the ratio of two sets or groups of simple ratios whose products must be taken. Thus, -JQ \ t \ = 60 : 10 == 6, value of the compound ratio. 513. Solve the following : 1. What is the ratio of 42 to 7 ? Of 96 to 12 ? 2. The antecedent is 324; the consequent 9. What is the ratio ? 3. The antecedent is 5 ; the consequent is 45. What is the ratio ? 4. The antecedent is 243 ; the ratio is 27. What is the con- sequent ? 5. The consequent is 35 ; the ratio is 7. What is the ante- cedent ? 6. What is the ratio of 25 bu. to 10 pks. ? 7. What is the ratio of 25 Ib. 11 oz. 4 pwt. to 19 Ibs. 5 oz. 8 pwt. ? 8. What is the ratio of to * f 148 MODERN BUSINESS ARITHMETIC 9. Find the value of the compound ratio, (10 : 35) X (4 : 28) X (7 : 15). 10. Find the value of the compound ratio, (:) X (f:f) Proportion 514. Proportion is an equality of ratios. Thus, 12 : 4 = 21 : 7, the ratio of each couplet being 3. 515. The Sign of proportion is the double colon ( :: ), and is read '#.?," and expresses the equality of the ratios. Thus, 3 : 21 :: 5 : 35 is read 3 is to 21 as 5 is to 35. 516. The Terms of a proportion are the two antecedents and the two consequents of the equal ratios. 517. The Extremes are \hzfirst and fourth terms. 518. The Means are the second and third terms. 519. PRINCIPLE : The product of the means of any propor- tion is equal to the product of the extremes. 520. To Find any Term of a Proportion. Divide the product of the means by the given extreme. Or, di- vide the product of the extremes by the given mean. 521. Solve the following : 1. Find the fourth term of the proportion, 17 : 85 :: 6 : ( ? ). 2. Find the third term, 6 : 15 ::(?): 75. 3. Find the second term, 12 :(?):: 42 : 294. 4. Find the first term, ( ? ) : 56 :: 19 : 14. 7 Q ) ( ?8 '18 5. Find the missing term, 4 ! 10 J :: j (?) j 40. 6. Find the missing term, $5 : $17 :: 35 Ib. : ( ? Ib. ) 7. Find the missing term, 10 horses : 45 horses :: ( ?bu. ) : 25 bu. 8. Find the missing term, 7 da. : (? da.) :: 98 bu. : 56 bu. 9. Find the missing term, ( ? ) : 28 men :: 10 T. : 140 T. 10. Find the missing term, n ; :: 15 A. : 45 A. RATIO AND PROPORTION 149 CAUSE AND 522. Every Problem in proportion may be resolved into Causes and Effects. EXAMPLE : If 4 men earn $72 in 1 week, what will 10 men earn at the same rate ? Here the 4 men are a cause, the $72, the money earned, the effect. The 10 men will be a second cause, and the second effect is the number of dollars required. Thus, 1st Cause : 1st Effect :: 2d Cause : 2d Effect 4 men : $72 :: 10 men : (?). 72XO 4 NOTE Proportions in Cause and Effect may be written : ' ' 1st Cause : 2d Cause : : 1st Effect : 2d Effect -4 Men : 10 Men :: $72 : $180. 523. Study the conditions of each problem. Causes are like quantities. Effects are like quantities. Thus, if men, horses, time, money, etc., belong to the first cause they will also be found in the second cause. Effects usually include the object and all its qualities and measurements. 524. In Compound Proportion there may be several elements in each cause and also in each effect. PROBLEMS IN PROPORTION 525. Solve the following : 1. If 32 Ib. of sugar cost $1.92, what will 75 Ibs. cost? 2. If 12 horses consume 36 bu. of oats in a given time, how many horses will consume 288 bu. at the same rate ? 3. If 15 sheep can be bought for $62.25, how many sheep can be bought for $398.40? 4. What will a pile of wood cost, 40 ft. long, 4 ft. wide, and 4 ft. high, if a pile 12 ft. long, 4 ft. wide, and 8 ft. high cost $28.50? 5. If a certain capital earn $1500 in 1 yr. 8 mo., in what time will double the capital earn $1200 at the same rate ? 150 MODERN BUSINESS ARITHMETIC 6. If 12 men in 48 da., working 10 hr. to the day, can build a wall 120 rods long, how many rods can 22 men build in 60 da., working 8 hr. to the day? 7. If 10 rms. of paper are required to print 600 copies of a book containing 240 pages each, 32 lines to the page, averaging 10 words to the line, and 5 letters to the word, how many books can be printed from 24 rms. of paper, 200 pages to the book, 36 lines to the page, 12 words to the line, averaging 4 letters to the word ? 8. If it takes 33600 bricks to build a wall 80 ft. long, 20 ft. high, and 3 bricks thick, each brick 8 in. long, 4 in. wide, and 2 in. thick, how many bricks 12 in. long, 5 in. wide, and 2-Vfc in. thick will it take to build a wall 120 ft. long, 30 ft high, and 2 bricks thick? 9. If 4 men in 7 da., working 9 hr. per day, can dig a ditch 14 rods long, 3 ft. wide, and 32 in. deep, how many men would have to be added to the crew in order to dig it in 3 da., if the ditch was widened to 5 ft. and the men worked 10 hr. per day ? 10. If 8 men can do a piece of work in 12 da. how many men must be added after the work is % done that it may be com- pleted in 2 days more ? PERCENTAGE 526. Percentage embraces those subjects in arithmetic which use 100 as the basis of computation. 527. There are "Two classes of subjects in Percentage : 1. Those in which time is not a factor. 2. Those in which time is a factor. 528. The subjects of the First Class are : 1. Profit and Loss. 2. Trade Discount. 3. Commission. 4. Stocks and Bonds. 5. Taxes. 6. Duties or Customs. 7. Insurance. 529. The subjects of the Second Class are : 1. Simple Interest. 2. Periodic Interest. 3. Compound Interest. 4.. Partial Payments. 5. Bank Discount. 6. True Discount. 7. Domestic and Foreign Exchange. * 530. Per Cent, is a contraction of per ( by ) centum ( hun- dred ) and means " by the hundred." 531. The Sign of Percent is % , and is read per cent. 532. Per cent is usually expressed as hundredths. Thus, 5% may be written .05, or VOTF- 533. At least Three Essential Elements are considered in all applications of percentage. 534. The Base is the number or quantity upon which the percentage is computed. 535. The Rate expresses the number of hundredths of the base to be taken. 152 MODERN BUSINESS ARITHMETIC 536. The Percentage is the number or quantity which is a certain number of hundredths of the base. 537. The Amount is the sum of the base and percentage. 538. The Difference is the base less the percentage. 539. The Amount Per Cent, is 100% plus the rate. 540. The Difference Per Cent is 100% minus the rate. 541. The Unit of Percentage is 100%, or the whole; therefore any rate that is an aliquot part of 100 may be reduced to its lowest terms, and the fractional part taken. Thus, if the rate is 25%, iVV reduced equals \. TABLE OF ALIQUOT PARTS OF 100% 50% = $ 1H% = i 33i%=i 80% = 33i% = J 10% = T V 66|% = | 16|% = 25% =i 9^%= A: 25% =i 83i% = f 20% = i 8i% = A 75% = 20% = i 37i% = | = | 6i% = T V 40% = | 62i% - = i 5% = A 60% = f 87i% = | CASE I 542. Given, the Base and Rate to find the Percentage. Multiply the base by the rate ; or, take such a part of the base as the rate is a part of 100. FORMULA : Base X Rate = Percentage. 543. Solve the following : 1. What is 6% of $400? 12% of 900 Ibs. ? 2. What is 25% of 720 bu. ? 33i% of 840 tons? 3. What is 12|% of 936 hrs. ? 16f % of $1554 ? 4. Bonds's salary of $1250 per year was increased 24% ? What is his monthly salary ? 5. Jones's income the first year was $2500 ; the second year it increased 20% ; the third, it decreased 33|% ; the fourth year it increased 35%. What was his income the fourth year? PERCENTAGE 153 6. Prindle had $18400 invested ; 12|% in bonds, 20% in in bank stock, 15% in city lots, 30% farm property, and the remainder in merchandise. What was his merchandise invest- ment ? 7. A failed for $12400. The assignee was able to pay three installments, the first of 20%, the second of 25%, and the third of 30% . What was B's loss if A was indebted to him $3200 ? 8. A man owned % of a business. He sold % of his share for $3000. The firm's gain for the year was 25% of the capital stock. Find the total gain. 9. Cushman on Jan. 1st had $4200 in the bank. On April 1st he drew out 33%% of it; on May 1st he drew out 14 2 /7%, and on July 1st he drew out 37%%. How much had he left in the bank ? 10. Olson bequeathed his entire estate of $50000 as follows : 20% to his eldest son, 25% of the remainder to his second son, 33%% of the remainder to his daughter, 10% of the remainder to charity, and the remainder to his wife. How much did the wife receive? CASE II 544. Given, the Percentage and Base to find the Rate. Divide the percentage by the base ; or, take such a part of 100 per cent, as the percentage is a part of the base. FORMULA : Percentage H- Base = Rate. 545. Solve the following : 1. What % of 300 is 150 ? Of $900 is $225 ? 2. What % of 720 mi. is 18 mi. ? Of 4500 oz. is 900 Ib. ? 3. What % of 24 is 96 ? Of $750 is $2250 ? 4. What % of % is % ? Of % is 9 /i6 ? 5. A farmer raised 40 bu. of oats from 1 bu. of seed. What % of the crop was the seed ? 6. A merchant sold from a barrel of molasses containing 48 gallons, % .of the contents the first week, and X. tne second week, and 12%% the third week. What % of the original con- tents remained ? 154 MODERN BUSINESS ARITHMETIC 7. A boy had 6 doz. marbles. He lost 25% of them the first day; 33%% of the remainder the second day, and 16% of the remainder the third day. What % of the original number did he then have ? 8. My stock of goods increased in value 10% ; then de- creased 20% ; then increased 50%. If the original value was $1200, what is it now worth, and what is the % of increase? 9. A firm begins business with $18750 capital. The first year they gain 33%%, which amount is added to their capital; the second year they lose 10%, which is charged to investment; the third year they gain $4500. What is their % of gain the third year ? 10. Green finding himself deeply in debt, made an assignment in favor of his creditors. If his total assets amounted to $7945, and his total liabilities, including $280, assignee's costs, were $10500;, what rate % could he pay his creditors ? CASE III 546. Given, the Percentage and Rate to find the Base. Divide the percentage by the rate; or take as many times the per- centage as 100% is times the rate. FORMULA : Percentage -=- Rate = Base. 547. Solve the following : 1. Of what is 72 12%% ? Is 143 33%% ? 2. Of what are $420 16%%? Are $343 25%? 3. James lost 120 ft. of his kite string and then had 37%% left. What was its original length ? 4. A drew out 20% of his money from the bank on July 10th; 25% on Aug. 1st, when he had $605 left in bank. What was his original amount on deposit ? 5. Smith owned 66%% of a business ; he then sold 25% of his share for $1250. What was the total value of the business? 6. A merchant paid $75 for platform scales, which was 62%% of the cost of his wagon, and the cost of the wagon was 75% of the cost of his horse. What was the total cost of his chattels ? PERCENTAGE 155 7. A young man spends 25% of his income for board, 15% for clothes, and saves 45%. The remainder, $225, he spends for charity, lodge dues, and sundries. What is his total income? 8. The Surplus Fund of a bank is 200% of its Circulation ; its Circulation is 50% of its Capital Stock, and its Capital Stock is 300% of the Cash on Hand. If the Surplus Fund is $150000, what is the Cash on Hand ? 9. In a cask of vinegar 7 gallons of water was added. This was 14^7% of the total contents. How many gallons of pure vinegar in the cask at first ? 10. Hardin lost 25% of his stock in a blizzard, 20% of the re- mainder died before spring; he then sold 33%% of the remain- der, and found that he had 280 head left. How many did he have at first ? CASE IV 548. Given, the Amount or Difference and the Rate to find the Base. Divide the amount by 100% plus the rate to find the base. Di- vide the difference by 100% minus the rate to find the base. FORMULA : Amount 7*- 100% + Rate = Base. Difference -*- 100% Rate = Base. 549. Solve the following : 1. What number increased by 10% of it self will equal 88? By 12%% of it self will equal 108? 2. What amount decreased by 6% of itself will equal $188 ? By 16%% of itself will equal $300? 3. After increasing his flock of sheep 33%%, Jones found he had 728. How many had he at first? 4. John lost 20% of his marbles on Monday, and 10% of the remainder on Tuesday, when he had 54 remaining. How many had he at first ? 5. A bookkeeper's salary was increased 30% of 90% and was then $1016 per year. What was it before the increase? 156 MODERN BUSINESS ARITHMETIC 6. A manufacturer's profits were 20% less the second year than the first ; 25% less the third year than the second when they amounted to $8100. What were the profits the first year? 7. Taylor had 1008 acres of wheat after increasing his acre- age 20% each year for two years. How many acres had he to begin with ? 8. An assignee paid the creditors 70 cents on the dollar. What was A's loss if he received $1330? 9. I sold a piano for $425 and gained 25%. Had I paid $50 more for it would I have gained or lost, and how much ? 10. A city's population increased 25% the first year, 20% the second year, 33% the third, 40% the fourth, and 50% the fifth, when it was found to be 46200. What was the population at the beginning of the first year ? HOME WORK No. 16 1. I drew out 33>i % of the $5220 I had in the bank ; I then drew out 20% of the remainder ; then deposited 15% of what I drew out. How much had I then in the bank ? 2. Twenty per cent, of A's money equals 30% of B's. If they together have $1250, how much has each? 3. I sold two pieces of land, each for $6480. On one I lost 10%, on the other I gained 12^ %. Did I gain or lose on the whole transaction, and how much ? 4. Brown sold his automobile for $1980 which was 10% less than his asking price, and his asking price was 10% more than the cost. What did it cost him ? 5. A, B, and C are partners in business. A invests tw 7 ice as much as B, and B invests twice as much as C. If A's gain is 20% of his capital, B's 25% of his, and C's 33/^% of his, and their total gain and capital together is $7770, what did each in- vest ? Profit and Loss 550. Profit and Loss treats of the gains and losses in bus- iness. 551. Gains and Losses are usually estimated at a certain rate per cent., therefore the principles of Percentage apply to this subject. 552. The Elements of Profit and Loss are : The Cost, the Rate of Gain or Loss, the Gain or Loss, and the Selling Price. 553. The Cost is the base of percentage and represents the investment. 554. The Rate is the profit or loss per cent. 555. The Profit or 1/OSS is the percentage. 556. The Selling Price is the amount if there be a gain, or difference if their be a loss. 557. In solving the problems of Profit and Loss, note the elements given and apply the principles of Percentage. CASE I 558. Given, the Cost and Rate to find the Gain or Loss. FORMULA : Cost X Rate = Gain or Loss. 559. Solve the following : 1 . What is the gain on a piano bought for $400 and sold at a profit of 25%? 2. Bought potatoes at 40 cents per bushel and sold them at 371/2% gain. Find the profit. 3. Find the gain on goods bought for $1500 and sold at an advance of 16%%. 4. I bought 50 bales of hops, averaging 175 Ibs. to the bale, at 11 cents per lb., and sold them at a profit of 25%. Find my gain. 158 MODERN BUSINESS ARITHMETIC 5. How much did I receive for goods bought for $245 and sold at a loss of 15% ? 6. I bought goods for $38.50, paid freight $1.25, drayage $.75, and sold them at a profit of 33^3 % . Find the selling price. 7. Brown bought an automobile for $1250; he then sold it to Jones and gained 20% ; Jones sold it to Smith at a profit of 25% . What did Smith pay for the machine ? 8. What is the selling price of a car bought for $2650 and sold at a loss of 10% ? 9. Lambert sold 40% of his stock of produce at 20% gain; 30% at 15% gain, and the remainder at 10% loss. If his total stock cost $420, what was his total net gain ? 10. Bernardi bought goods for $16424. He sold }i of them at 20% profit, YI of the remainder at 25% profit, YZ of those yet remaining at 12>^% loss, and the remainder at 10% gain. What was his net gain ? CASE II 560. Given, the Gain or 1/oss and the Cost to find the Rate. FORMULA : Gain or L,oss -5- Cost = Rate. 561. Solve the following: 1. Goods bought for $80 on which a gain of $20 is made is a gain of what % ? 2. If the cost of a carriage is $120 and it is sold at a profit of $30, what is the rate of gain ? 3. I made a profit of $72 on a piano that cost me $400. What was the rate of profit ? 4. Smith sold a house for $2150 that cost him $1500. What was his gain % ? 5. If wheat selling for 21 cents per bushel more than cost brings 91 cents per bushel, what is the rate of gain ? PROFIT AND LOSS 159 6. What % does a grocer make who buys sugar at 4/4 cents per Ib. and sells it at 5 cents per Ib. ? 7. Wool that cost 28 cents per Ib. was damaged and then sold for 21 cents per Ib. What was the rate % of loss? 8. Find the average rate of gain on the following: Calico bought at 4 cents and sold at 5 /4 cents ; gingham bought at 8 cents and sold at 12% cents; silesia bought at 7 cents and sold at 10^ cents. 9. A contractor pays his men $3.50 per day for their labor and receives $4.20 per day. What % of profit does he make? 10. My salary was increased 20% the first month; 25% the second month; 33/3% the third month. What was the total rate of increase ? CASE III 562. Given, the Gain or I/oss and the Rate to find the Cost. FORMULA : Gain or Loss -*- Rate = Cost. 563. Solve the following : 1. My profit was $12.50 and the rate of gain was 25%. Find the cost. 2. If my gain was 18%, or $126, what was the cost ? 3. I lost 16^ by selling goods $540 below cost. Find the cost. 4. By selling hops at a gain of $320, I made 16%. I in- vested the proceeds in oranges which I sold at a loss of $40. For what did I sell the oranges ? 5. Find the cost of goods sold at $700 profit, or a gain of 14 2 / 7 %. 6. Lumber sold at a profit of $3.50 per M. is a gain of 17^2%. Find the cost. 7. My gain for the month is $385.50, or 20% on the cost. What was the cost of the goods sold ? 160 MODERN BUSINESS ARITHMETIC 8. A and B each gains 33/<3% on his investment. A's gain is $420, and B's gain is $510. How much more had B invested than A ? 9. Brown's gain is 15% of his investment; Green's is 22%% of his. If they each gain $900, how much more has Brown in- vested than Green ? 10. The profits of a bank for six months was $16500, or7 l /4% on the Capital Stock and Surplus. If the Surplus was $120000, what was the Capital Stock ? CASE IV 564. Given, the Selling Price and the Rate to find the Cost. FORMULA : Selling Price -=- 1 + Rate = Cost ; or, Selling Price *"!. Rate = Cost. 565. Solve the following : 1. Find the cost of goods sold for $27.50, the rate of gain being 10%. 2. Find the cost of a piano sold at a loss of 16^3 % and bring- ing $280. 3. Having used my automobile for 6 months, I sold it for $1000, which was 25% below cost. What did it cost? 4. I sold a carriage to Smith and gained \2%% ; Smith sold it to Jones for $132 and gained 10%. What did the carriage cost me ? 5. Some city lots increased in value each year 25% on each previous year's value. At the end of 4 years they were sold for $3906.25. What did they cost ? 6. At what price shall I mark goods that cost me $420 that I may give a 10% discount and still make a 20% profit? 7. Flour that cqst $3.60 per bbl. must be listed at what price that a reduction of 25% may be made and still leave a profit of 25%? PROFIT AND LOSS 161 8. I sold 2 pianos, each for $384 ; on one I gained 20% ; on the other I lost 20%. Did I gain or lose on the whole transac- tion, and how much? 9. Brown sold his crop of grapes at a profit of 12/4% on the cost of raising. Had the cost been $720 more, he would have lost 12% % . For what did he sell them ? 10. If I buy goods at 25% off list and sell them' at 20% above, what % do I make ? HOME WORK No. 17 1. I buy goods at 50% off and sell at 25 and 10% off list price. What per cent, profit do I make? 2. I mark goods at 33/ / 3% above cost. If I allow a discount of 10% from the marked price, what per cent, profit do I make? 3. I sold a piano at a loss of 12% % and lost $80. What would I have gained had I sold it at a profit of 1824% ? 4. Bought oranges which I sold at a gain of 16.^3%, and in- vested the proceeds in eggs which I sold at a profit of 10%. If the eggs brought $423.50, what did the oranges cost? 5. Hanson's sales for January were $5544. What was his rate of gain if his total profits were $792 ? 6. At what price shall I mark goods that cost $70 that I may discount the bill 12>^% and still make 20% ? 7. A grocer buys goods on an average discount of 20% off list price. What per cent, profit does he make if he sells at an average of 10% above list price? 8. A dealer sold two lots of land at $1012 each. On one he made a profit of 15%, and on the other he lost 12%. Did he gain or lose on both transactions, and how much ? 9. A's gain of 20% was equal to B's gain of 30%. If their total gain amounted to $675, what was the capital of each ? 10. By selling goods at a certain price a merchant gained \6 2 /3 % . Had the goods cost him $300 more he would have lost 6/ / 3 % . What was the cost of the goods ? Trade and Cash Discounts 566. Trade Discount is a deduction made from the list price of an article to fix its selling price. 567. Cash Discount is a deduction made from the selling price of an article to secure cash payment. 568. The List Price is an established price, usually pub- lished in catalogues, for the purpose of securing a basis from which trade discounts may be made. 569. The Selling Price is the contract price for which the goods are sold and is called the net amount. 570. The Terms are the conditions upon which a bill is sold and they are usually printed, stamped, or written upon the "bill heads." Thus, "Terms, 60 ds.; 30 ds., 5%; 10 ds. 10%; " etc. 571. Legal Interest may be collected on all bills over due, and when paid before maturity, a discount is usually allowed. 572. A Succession of Discounts are frequently made. Thus, 20 and 10% off == 100% 20% = 80%. 10% off 80% = 8%. 80% 8% = 72%, Ans. 573. Trade and Cash Discounts are estimated at a certain per cent., therefore the principles and cases of Percentage apply to this subject. CASE I 574. Given, the List Price and Rates of Discount to find the net amount of the Bill. FORMULA : List Price X 100% - - Rate % of Discount - Net Amount of Bill. TRADE AND CASH DISCOUNTS 163 575. If a succession of discounts are given, treat each net amount as a new list price and compute the discount as given in the above formula. EXAMPLE : Find the net amount received for a piano, listed at $800, and sold for 25% and 10% off. 100% 25% == 75%, $800 X 75% = $600. 100% - - 10% = 90%. $600 X 90% == $540, Ans. It will be noticed that the sum of 25% and 10%, or 35%, is not the same as 25% and 10% off. 576. Solve the following : 1. Find the net amount of goods listed at $500, less 25% dis- count. 2. List price $840, less 12^2 % discount. 3. List price $1250, less 20 and 10% discount. 4. List price $4320, less 16^ and 25% discount. 5. List price $1200, less 33^i, 25, and 10% discount. 6. Find the net amount of a bill for a carload of 14 tons of prunes, listed at 8 cents per lb., less 25 and 33>o% discount. 7. Pianos listed at $1200, $1000, $900, $800, and $600 were were discounted 33^i, 20, and 10% off. Find the net values of each. 8. A bill of clothing which amounted to $1420, was dis- counted 20 and 5% off, w r ith an additional discount of 2% for cash. What amount of cash would pay the bill ? 9. The "terms" of a bill were "60ds., 5% 30 ds., 10% 10 ds." If the total amount was $720, with a trade discount of 15 and 10%, what amount would settle the bill if paid in 8 days? In 20 days? In 40 days? 10. Which is better for the buyer, 50, 20, and 10% off, or 33^, 25, and 25% off, and how much? 164 MODERN BUSINESS ARITHMETIC CASE II 577. Given, the Net Amount of a bill and the Rate of Discount to find the List Price. FORMULA : Net Amount -*- 100% - - Rate of Discount List Price. 578. If a succession of discounts are made, treat each list price found as a new net amount and proceed as per formula. EXAMPLE : Find the list price of a piano sold for $540, the discounts being 25 and 10% off. 100% -- 10% = 90%. $540 -4- 90% = $600. 100% 25% = 75%. $600 -*- 75% = $800, Ans. 579. Solve the following : 1. Find the list price of goods sold for $315, the discount being 10%. 2. Selling price $551.25, discount 25%. 3. Selling price $504, discount 33^i and 10% off. 4. Selling price $612, discount 20, 33/i. and 10% off. 5. Selling price $801, discount 33M*, 25, 20, and 10% off. 6. Find the list price of gloves per dozen, which retailed at 90 cents per pair, a discount of 50 and 10% being allowed. 7. I made 25% on goods that cost me $280, by selling at a discount of 20% from marked price. Find the marked price. 8. At what price shall I mark goods that cost $208.80, that I may discount the bill 40 and 20% and still make 33/3 % ? 9. Sewing machines were sold for $45.60. If the first dis- count was 20% and the total discount 32%, what was the second discount ? 10. Smith & Co. buy shoes listed at $96 per case of 2 doz. each, at 40 and 30% off. What discount in addition to 25% shall they make in order to sell at a gain of 50% ? TRADE AND CASH DISCOUNTS 165 HOME WORK-NO, is 1. My discount on a piano listed at $800 was $160. What was the rate of discount ? 2. I paid $36 for a sewing machine, which was a discount of $9 from the list price. What was the rate of discount ? 3. Which is the greater rate of discount, and how much, $24.30 off $450, or $15.40 off $280? 4. If I buy goods marked at $900, at 33;^% and a second rate off, for $480, what is the second rate of discount ? 5. What discount is equivalent to 40, 33 >3, and 20% off. 6. Which is the cheaper, to buy goods for 25, 33^, and 10% off, or 40, 20, and 5% off, and how much on a purchase listed at $400 ? 7. A machine listed at $360 was discounted 20% and $14.40. What was the second rate of discount and the selling price ? 8. Jones paid $512 for goods after being allowed a discount of 33 :/ 3 and 20% off. What was the marked price? 9. Smith received a discount of 60, 25, 16^, and 10% on hardware that cost him $1575. What was the list price? 10. I sold a piano for 35 and 25% off list for $585, and still made 17% profit. Find the cost and the list price. COMMISSION 580. Commission is a compensation charged by an agent for buying, selling, or collectijig for another. 581. An Agent is one who transacts business for another. 582. A Commission Merchant is an agent whose princi- pal business is to buy and sell goods for others for a commission. 583. A Principal is one for whom an agent transacts busi- ness. 584. A Shipment is the merchandise sent to a commission merchant to be sold. 585. A Consignment is the merchandise received by a commission merchant to be sold. NOTE A SHIPMENT by the principal is a CONSIGNMENT to the agent. 586. The Consignor or Shipper is the one who sends the goods. 587. The Consignee is the one to whom the goods are sent. 588. Freight and Dray age are the charges paid to the railway and transfer companies for transportation. 589. Insurance and Storage are sometimes charged by a commission merchant to reimburse him for sums paid on general insurance and rent accounts. 590. Guaranty is a charge to insure against loss through bad debts. It is generally included in the commission charged. 591. A Shipment Invoice is a list of goods forwarded to be sold on commission. 592. An Account Sales is a statement rendered by a com- mission merchant to the consignor, and contains : 1. A list of goods received to be sold. 2. An itemized list of goods sold. 3. The charges in detail. 4. The net proceeds. 5. A communication stating the manner of remittance or of making the credit. COMMISSION 167 593. The Total Sales is the sum received for the goods before any charges are deducted. 594. The Net Proceeds is the sum left after deducting all charges. 595. An Account Purchase is an itemized statement of goods purchased by a commission merchant togethei with freight, commission, and other charges. 596. The Entire Cost is the total amount, including first cost of goods and all charges. 597. Since Commission is usually computed at a certain rate per cent., the cases of percentage may apply. 598. The Amount of Sale, Purchase or Collection is the Base. The Rate of Commission is the Rate. The Commission is the Percentage. The Entire Cost is the Amount, and the Net Proceeds is the Difference. CASE I 599. Given, the Amount of Sale, Purchase, or Collec- tion, and the Rate of Commission to find the Commission. ( Sale ) FORMULA : Amount of j Purchase > X Rate = Commission. ( Collection ; EXAMPLE : A commission merchant sells a consignment of eggs for $440, and charges 5% commission. What is his com- mission ? $440 X 5% = $22, commission. 600. Solve the following : 1. What is the commission on a sale of $1200 at 3% ? 2. On a purchase of goods amounting to $4260 the commis- sion charged was 2\% . Find amount of commission. 3. My agent collected bills amounting to $575, on a commis- sion of 10%. What is his commission, and what amount should I receive? 4. My agent sold 52 bales of hops, averaging 180 Ibs. each, at 15 cents per lb., and sent me a draft to cover the sales less his commission of 4%. Find face of the draft. 168 MODERN BUSINESS ARITHMETIC 5. A commission merchant was instructed to purchase 20 boxes of oranges at $2.75 each ; 15 crates of bananas at $3 each; and 12 boxes of lemmons at $3.50 each. Find the entire cost, the freight charges being $2.25, and his commsssion 6%. 6. An agent collected the following bills: J. E. Brown, $141.25; I. J. King, $78.40; H. C. Hill, $27.70; R. L. Jones, $189.25; T. E. Smith, $52.50. What did his principal receive if he paid $2.60 expenses and 12\% commission for collecting? 7. L. Ayers directed his agent to purchase $9000 worth of prunes and to ship the same to a New York agent who sold them for $13520. If the freight charges were $300, and the rate of commission for buying was 5 % , and for selling 4 % , what did he profit by the transaction ? 8. Find the net proceeds of the following : Account Sales B. S. TAYLOR & COMPANY COMMISSION MERCHANTS Received of THE MERRITT FRUIT PACKING CO. , Santa Rosa, California To be sold on their account and risk: 400 boxes Early Crawford Peaches 100 Crates Strawberries July 200 Boxes Peaches Si. 40 50 Crates Strawberries 6. 4uly 3 200 Boxes Peaches 1.25 50 Crates Strawberries 5. CHARGES : July 1 Freight 81 25 July 3 Cartage Commission, 10% on sales 14 73 Net Proceeds remitted in cash COMMISSION 9. Find the entire cost of the following : 169 Account Purchase R. J. PERKINS & COMPANY COMMISSION MERCHANTS I,os Angeles, Cal., July 28, '08, Bought for KETTERLIN BROS., Santa Rosa, California The following goods per their order of July 25, 1908. PURCHASES : 50 Boxes Navel Oranges S3. 25 40 " " " 2.75 35 " Lemons 3.50 CHARGES : Freight Cartage Commission, 3% 12 3 25 50 Amount charged - - 10. A commission merchant sells 7 tons of potatoes at 1/4 cents per lb.; 24 crates of cabbage, 120 Ibs. each, at 3 cents per lb,; 270 bbls. apples at $3.25 per bbl., and 120 cases of eggs, 36 doz. to the case, at 18^ cents per doz. His charges are $23.50 for cartage; $5.80 for storage; >^% for insurance; 1/4 % for guaranty on the sale of apples which were sold on ac- count, and 3% for his commission. What were the net pio- ceeds. CASE II 601. Given, the Amount of Sale, Purchase, or Col- lection and the Commission to find the Rate of Commission. Sale ) FORMULA : Commission H- Amount of Purchase \ = Rate. Collection ) 170 MODERN BUSINESS ARITHMETIC EXAMPLE : The commission on a sale of cotton amounting to $6440 was $225.40. Find the rate of commission, and the net net proceeds. Com. $225.40 H- Amt. of Sale $6440 = 3i%, Rate. $6440 $225.40 = $6214.60, Net proceeds. 602. Solve the following : 1. Find the rate of commission when $24.60 is charged for selling goods amounting to $1230. 2. Find the rate of commission when $16.71 is charged for buying $278.50 worth. 3. My agent sold a house and lot for $2850. His commis- sion was $71.25. Find the rate charged. 4. A lawyer collected a bill of $324.40 and charged $40.55 commission. What was the rate for collecting? 5. Find the rate of commission charged when $2 3 5. 40 is paid for buying 26750 Ibs. of wool at 32 cents per Ib. 6. If a commission merchant charged \/o for insurance, 2\% for guaranty, and the total charges on sales amounting to $1475.50 were $88.53, what was the rate of commission ? 7. I paid my Chicago agent $20.25 from a sale of $320 worth of dried fruit. If the cartage was $4.25, what was the rate of commission ? 8. An agent sent me $1072.56 as the net proceeds of a total sale amounting to $1117.25. Find the rate of commission charged. 9. The entire cost of an account purchase was $968.30. If the incidental charges were $9.20, and the cost of the goods bought $920, what was the rate of commission charged ? 10. A owed B $850. Not being able to collect the bill, B placed it in the hands of a collector who succeeded in collecting 80% of the debt. If the collector's charges were $42, including notary's fee of $1.20, what was the rate of collection, and what was B's loss? COMMISSION 171 CASE III 603. Given, the Commission and the Rate of Commis- sion to find the Amount of Sales, Purchase, or Collection. Sale FORMULA : Commission -5- Rate = Amount of Purchase Collection. EXAMPLE : An agent's commission was $41.35 at a 5% rate. Find the amount of goods sold. Com., $41.35 *- Rate, 5% ~-= Amt. of sale, $827. 604. Solve the following : 1. The commission is $210; the rate is 3%. Find the amount of goods sold. 2. The commission is $123.50; the rate 2}4%. Find the amount of purchase. 3. My agent collected a bill charging 8% commission. If his fee amounted to $19.40, how much did I receive? 4. My agent's commission on a sale was $99.40; the rate charged was 7 % . What was the amount of sale ? 5. A commission merchant charged a commission of 5%, guaranty 1%, and insurance /4%. If his total charges were $94.25, what was the amount of sale? 6. My agent charged 5% for selling and 4% for buying. What w r ould be the net proceeds of a sale, and the entire cost of a purchase if his commissions were $135.25 and $123.40 respect- ively ? 7. An agent collected a bill on a commission of 6% and re- mitted the proceeds less his commission of $38.40. What was the amount remitted ? 8. A collection agent's charges, including notary's fees of $2.75, and $1.50 for recording, were $33.27 ; his rate of collec- tion was 4%. What amount did his principal receive? 9. A commission merchant sold a consignment of cotton at 11 cents per Ib. and charged a commission of 3/4%, guaranty !>%, insurance #%, freight $128.44, and cartage $34.60. If his total charges amounted to $454.80, how many pounds of cot- ton did he sell ? 172 MODERN BUSINESS ARITHMETIC 10. My agent sold a consignment of goods at 33/^, 25, and 10% off list price, charging me 6% commission. If his com- mission was $76.95, what was the list price? CASE IV 605. Given, the Net Proceeds or Entire Cost and the Rate of Commission to find the Amount of Sale, Purchase, or Collection. FORMULA: Net Proceeds -*- 100% - - Rate = Amount of Sale or Collection ; or, Entire Cost -*- 100% + Rate = Amount of Purchase. EXAMPLE : The net proceeds of a sale of hams and bacon was $695.52. If the agents commission was 4%, what was the value of the goods sold ? Net Proceeds, $695.52 -*- 100% Rate, or 96% = Amt. of Sale, $724.50. 606. Solve the following : . 1 . I received $502 . 20 from my agent as the net proceeds of a sale. His commission was 7 %. Wnat was the total amount of sale? 2. Smith & Co., directed their agent to purchase lumber, the entire cost of which was $17757.20. If the agent's commission was 3 % , what was the net price of the lumber ? 3. The Goodyear Rubber Company received a New York draft for $876.28 as the net proceeds of a collection upon which a commission of 5% had been charged. What amount was collected ? 4. What was an agent's commission at 6% on a collection the net proceeds of which were $324.30 ? 5. Fairbank & Co., of Chicago, sent their N. Y. agent a consignment of canned goods to be sold on a 2>^% commission. The net proceeds, after paying freight $32.50, drayage $41.25, storage $12.60, and the commission, was $12159.65. What was the amount of sale ? 6. I sent my St. Louis agent a car load of oranges to be sold on a commission of 5%, and directed him to invest the proceeds COMMISSION 173 in flour after deducting his commission of 3% for buying. If the oranges brought $2140, what was the cost of the flour? 7. A. L. Bagley & Co. sent their agent $930. 75 with instruc- tions to purchase potatoes after deducting his commission of 2%, and to sell the same as soon as the market price advanced 10%. If the agent's commission for selling was 4%, did they gain or lose by the transaction, and how much ? 8. Zimmerman & Co. received $402.33 as the net proceeds of a sale of butter after deductions were made as fallows : Freight, $4.38; cartage, $1.25 ; insurace, ^ % ; guaranty, 2^4% ; and a commission of 3%. How many pounds of butter were sold, if the price paid was 28 cents per pound ? 9. A commission merchant received $49043.27, and was di- rected to invest one-half in Island cotton at 12 cents per pound, the remainder he invested in Southern Alabama cotton at 10 cents per pound, after deducting 2% for buying each kind. How many pounds of each kind of cotton did he purchase ? 10. I sent a commission merchant a shipment of wine and di- rected him to sell the same and invest the proceeds in sugar after deducting his commission of 5% for selling and 4% for buying. If his total commission was $450, what was the selling price of the wine, and the cost of the sugar? HOME WORK No. 19 1. A commission merchant bought goods costing $38450 on a commission of 2 % . What was the entire cost of the goods ? 2. The net proceeds of a sale, after deducting $152.25 ex- pense and a commission of 5%, was $6820.75. \Vhatwasthe amount of the sale ? 3. A commission merchant retained $22.25 to defray the charges for selling a piano for $350. If the cartage was $4.75, what rate of commission did he charge ? 4. A sale of $940 netted me $902.40 after paying insurance 1% and a commission. What was the rate of commission? 5. My agent remitted me $258 in cash after paying storage $11.40 and retaining his commission of 10%. What was the amount of sale, and his commission ? 6. I bought goods on a commission of 6%. If the entire cost of the purchase w r as $1847.05, what was my commission? 174 MODERN BUSINESS ARITHMETIC 7. An agent sold a consignment of wool for $7210 and was instructed to invest the proceeds in structural steel, after deduct- ing his commission of 5% for selling and 3% for buying. What was his total commission, and what w r as the price paid for the steel ? 8. I sent my agent $1440.40 in cash and directed him to in- vest in flour, after deducting his commission of 4% for buying. He then sold the flour at a gain of 20% on the cost price. What was his rate for selling, if his total commission amounted to $138.50? 9. The net proceeds of a sale of dried fruits consisting of 8400 Ibs. of prunes sold at 3i cents, 4200 Ibs. peaches sold at 4| cents, and 12500 Ibs. apples sold at 4 cents per Ib. were $905.40. If the charge for storage was $7.50, and for insurance $10.12, what was the commission and rate of commission ? 10. I sent my agent a consignment of hops to be sold on com- mission and directed him to invest the proceeds in wheat, after deducting 7% commission for selling and 3% for buying. If if his total commission was $400, what was the selling price of the hops, and the cost price of the wheat ? Outline for Review J. Percentage : III. Trade and Cash 1. Definitions. Discounts: 2. Classes of Subjects : 1. Definitions. First. 2. List Price. 3. Selling Price. 3. bign. ^ Terms etc. 4. Kssential Elements : c r^ Base. 5 - Cases ' unt - IV. Commission: Difference. 1- Definitions: Percentage. 2. Agent. Principal. 5. Unit of Percentage. 3. Commission Merchant. 6. Cases. 4. Shipment, Consignment. -rr T* jz+ ^ T 5. Consignor, Consignee. II. Profit and Loss: 6. Freight, Drayage. 1. Definitions. 7. Insurance, Storage, Guar- 2. Elements: anty. C s t ^- 8. Acct. Sales, Acct. Purchase. Profit or Loss. 9. Total Sales, Net Proceeds, Selling Price. Entire Cost. 3. Cases. 10. Cases. Stocks and Bonds 607. A Corporation is an association of individuals char- tered by law to transact business. 608. The Articles of Incorporation are the regulations governing the organization of the association. 609. The Articles must contain the following : 1. The name of the corporation. 2. The purpose for which it is organized. 3. Its principal place of business. 4. The term of its existence. 5. The number and names of the directors. 6. The amount of capital stock and the par value of each share. 7. The amount of capital stock actually subscribed. 610. The Capital Stock is the total amount of all the shares that may be issued at their par value. 611. Stocks is a general term applied to shares of capital stock of all kinds. 612. Stocks are at par when they sell for their face value ; above par when they sell for more, and below par when they sell for less than their face value. 613. Certificates of Stock are issued by the officers of the corporation to these who contribute to the capital stock, and are usually transferable. 614. The Market Value of stock is the amount for which it can be sold. 615. Premium and Discount are terms used to indicate the difference between the par value and the market value. 616. Brokerage is the percentage charged by a broker for buying or selling stocks. It is usually %% or }&% on the par value of the stocks. 176 MODERN BUSINESS ARITHMETIC 617. A Stock Broker is one who buys and sells stocks. 618. An Installment is a portion of the capital stock paid in by the subscribers. 619. An Assessment is a sum required of the stockholders to meet current losses or needs of the company. 620. A Dividend is a. percentage paid to the stockholders from the profits of the business. 621. Bonds are the promissory notes of a government, state, municipality, or corporation. 622. Stock Quotations are the published prices for which stocks are selling. 623. Bonds like Stocks may sell at a premium or at a discount. 624. Bonds are of two kinds, Registered and Coupon. 625. Registered Bonds are those payable to the owner as registered on the books of the company. 626. Coupon Bonds have certificates of interest attached, which when due may be cut off and presented for payment. 627. Treasury Stock is that portion cf the Capital Stock which has not been subscribed. It is usually reserved for the future needs of the corporation and may be sold to increase its working capital, 628. Preferred Stock is stock issued usually to rehabili- tate a corporation in a weakened condition, and takes precedence in the matter of drawing dividends. Thus, preferred stock may receive a certain per cent, dividend from the profits cf a business and the remainder, if any, may be distributed as dividends on the common stock. 629. Watered Stock is stock issued for which no con- sideration is received. The issuing of watered stock is usually for the purpose of either inflating the value of the stock of a corporation or for reducing the high rate per cent, of profit which in some states is forbidden by law. 630. Bonds are sometimes designated by the rate of interest they bear. As " Missouri 5's " = Missouri bonds drawing 5%. STOCKS AND BONDS 177 631. Since the Premium, Discount, and Brokerage are esti- mated at a certain rate per cent., the cases of Percentage apply to the subject of Stocks and Bonds. 632. The Quantities considered in Stocks and Bonds are ; Par Value = Base ; Rate of Premium, Discount, Dividend, or Brokerage = Rate; Premium, Discount, Dividend, Assessment, or Brokerage = Percentage ; Market Value = Amount or Dif- ference. NOTE The par value of the stock in the following: problems is $100, and the rate of brokerage is \ per cent, unless otherwise specified. Brokerage is always estimated on the par value. CASE I 633. Given, the Par Value of the Stocks and the Rate to find the Premium, Discount, Dividend, Assessment or Broker- age. ( Premium or Discount FORMULA : Par Value X Rate = < Dividend or Assessment ( Brokerage. EXAMPLE: I sold 44 shares of S. P. R. R. stocks at 12% premium. How much was the premium ? 44 shares at $100 each = $4400. $4400 X 12% $528. 634. Solve the following : 1. What w r as a broker's commission on 120 shares of N. Y. Central's sold at 5% discount? 2. Chicago and Rock Island shares are selling at 8% discount. What is my broker's commission on 82 shares sold at that price? 3. I received an 8% dividend on 128 shares of B. & O. stock. How much cash did I receive ? 4. My profit on a sale of 32 shares of Union Pacific's was l2 l /2% less brokerage. What was my gain? 5. A bank whose capital stock is $150000 declares a dividend of 3%. What is the total dividend, a*nd how much does Jones receive who owns 25 shares ? 178 MODERN BUSINESS ARITHMETIC 6. Lake Shore stocks are selling for $107 1 /. What would be the premium on 46 shares ? 7. Amalgamated Copper is 12% below par. How much would I receive for 96 shares after paying brokerage ? 8. Anaconda Copper Co.'s stocks ($50) are paying a 2% quarterly dividend. What annual income should Green receive who owns 77 shares ? 9. I buy 140 shares of Canadian Pacific's at 167 X and sell the same at 171%, paying brokerage both for buying and selling. What is my profit ? 10. Goldfield Consolidated levied an assessment of 5% upon its stock ($50) for development purposes, 2% for current ex- penses, and 4% for machinery. What would be the total assess- ment on 1000 shares, and how much would be required of A who owns 45 shares ? CASE II 635. Other Quantities being given to find the Rate of Premium, Discount, Dividend, Assessment or Brokerage. FORMULA: Prem., Dis.,.Div., Ass., or Brok. -*- Par Val. = Rate. EXAMPLE : A dividend of $128 was received as a dividend on 64 shares of Bank Stock. What was the rate ? .Div.. $128 -H Par Val., $6400 = 2% Rate. 636. Solve the following : 1. The par value of stocks is $800; the dividend is $60. What is the rate of dividend ? 2. Par value, $1200 ; dividend, $132. Find the rate. 3. Brokerage, $14.50; par value, $5800. Find the rate of brokerage. 4. I sold 42 shares of Bait. & Ohio at a discount of $189. What was the rate of discount ? 5. A broker's commission is $3.50. What rate does he charge if the sale is 56 ( $50 ) shares ? STOCKS AND BONDS 179 6. Stock received at par was sold at a net gain of $608. If 76 shares were sold and brokerage charged, what was the rate of premium? 7. An electric power company with a capital of $500000 has gross earnings amounting to $82000, and its total expenses are $43250. What whole rate of dividend may it declare, and what surplus would remain ? 8. The net earnings of the Bullfrog Mining company for the year were $275000. The capital stock consists of 5000 shares of preferred stock, guaranteed 4% semi annual dividends, and 10000 shares of common stock. What annual rate of dividend can be declared on the whole stock after paying preferred stock divi- dends ? 9. A National bank with a capital of $150000 has net earn- ings of $21345.20. If 10% of this is placed in a reserve fund, what is the greatest whole per cent, of dividend that it may de- clare, and what will be the remaining undivided profits ? 10. A gas company is able to declare a dividend of 18% on its capital stock of $200000. If it waters its stock by the addi- tion of 3000 shares, what rate of dividend may it declare on the same income and still place $1000 in the reserve fund ? CASE III 637. Other Quantities being given to find the Par Value, Market Value > or the Rate of Investment. FORMULA : Prem., Dis., Div., Ass., or Brok., -s- Rate = Par Value. Par Val. X 100% + Rate = Market Value. Div. -*- Market Val. = Rate of Investment. EXAMPLE : Stocks sold at a premium of $135 yields a prem- ium of 9% . What is the par value of the stocks ? Prem., $135 -* Rate, 9% = $1500, 'Par Val. EXAMPLE : The par value of electric railway stock is $4500 ; the rate of discount is 10%. Find the market value. Par Val., $4500 X 90% = $4050, Market Value. ISO MODERN BUSINESS ARITHMETIC EXAMPLE: School bonds bought at 120 yield 6% interest. What is the rate of income ? Div., $6 *- Market Val., $120 = 5%, Rate of Investment. 638. Solve the following : 1. Brown receives a 3% semi annual dividend of $480. How many ( $50 ) shares does he own ? 2. What will be the cost of 270 shares of N. Y. Central Ry. stock at 11 024 ; brokerage /8% ? 3. My broker sold 115 shares of Southern Pacific's at 77 l /2 charging brokerage at 1 /i%. What did I receive for my stock? 4. I invested $5120 in Northern Pacific's at 127 &, paying brokerage. If a dividend of 8% is declared, what rate of in- vestment do I receive ? 5. How many shares of stock bought at IIO 1 /^ and sold at 116%, brokerage 1 A% for buying and V% for selling, will gain $690 ? 6. What amount must be invested in ( $50 ) stock at $62.50 per share, paying brokerage /^%, to yield an income of $720, the stock paying 12% dividend? 7. Which is the better investment, Union Pacific 5's at 110 or Rock Island 6's at 120, and how much on an investment of $39600 ? 8. I directed my agent to sell 200 shares of preferred ?tock at 97%, yielding 3% semi-annual dividends, and directed him to buy Edison Electric's at 208 which yield 15% annually. Did I increase or diminish my income, and how much, and what sur- plus was left, paying brokerage both ways? 9. Glenn & Co. sold through a broker 500 shares of United Fruit ( $100 ) stock at 107, paying annual dividends of 6%, and directed him to invest the proceeds in U. S. Rubber ($50) at 35% and paying 2 % semi-annual dividends. Did they increase or decrease their income and how much, and what surplus was left ; brokerage /^ % both for selling and buying ? STOCKS AND BONDS 181 10. J. A. McDonald & Co., through their broker, invested a sum of money in Mich. 6's at 109^, and twice as much in Ohio 5's at 98 3 /i I brokerage in each case %%. The annual income from both investments was $2772. How much did they invest in each kind of stock ? HOME WORK No. 20 1. The Western Railway Company with a capital stock of $500000 declares a 2% quarterly dividend. What will be A's annual income on 420 shares ? 2. A mining company with a capital of $250000 has net earnings amounting to $14275. What is the highest whole rate per cent, of dividend that may be declared, and what surplus would remain ? 3. What per cent, of income does stock paying 6% dividend yield when bought at 120 ? 4. What will be the cost of 240 shares of the Wright Bros. Aerial Navigating Company quoted at 84 X ; brokerage X% ? 5. My broker bought 320 shares of S. P. ($50) stock at 62% which yielded a semi-annual dividend of 2%%. What was my annual rate of income on my investment ; brokerage 6. I directed my broker to sell 80 shares of Ohio 6's at and to buy Pennsylvania 5's at 79^. Did I increase or dimin- ish my income, and how much ? What was the surplus ? 7. What price must be paid for stocks paying 4% dividends to yield 5% on the investment? 8. Which is the better investment, stocks bought at and paying 5%, or stocks bought at 88 paying 4%, and how much on an investment of $19800 ? 9. My income from an investment in Wabash ($50) 6's was $114. If I paid 66% and brokerage V% , what amount did I invest ? 10. I sold through my broker 54 shares in Consolidated Vir- ginia ($100) stock at 148^ paying 3% quarterly dividend, and directed him to purchase Bakersfield Oil Stock ( $50 ) at 94^ paying 8% semi-annual dividends. Did I increase or de- crease my income ; how much, and what was the surplus ; brok- erage X % ? TAXES 639. A Tax: is a certain sum levied on the person, property, or income of a person, firm, or corporation for the purpose of defraying the expenses of the government. 640. Property Tax is a tax on property. Property is of two kinds, Real Estate or Personal Property. 641. A Poll Tax is a tax on every male citizen of the State. 642. Real Estate is land and permanent improvements thereon. 643. Personal Property consists of all kinds of movable property, called chattels. 644. An Assessor is the person who prepares the assess- ment rolls and estimates the values of property. 645. The Tax Collector receives the taxes and gives re- ceipts for the same. 646. Collection is a sum paid to a collector for collecting taxes. 647. The Assessment Roll is the list of the taxable prop- erty together with its assessed valuation. 648. Taxes are levied for different purposes ; as, county, state, school, library, street, highways, etc. 649. Since taxes are estimated as a certain per cent, of the assessed value of the property, the cases of Percentage may ap- ply. 650. To find the Tax, Rate of Taxation, and Assessed Value of taxable property. FORMULA : Assessed Value X Rate =- Tax. Tax -r- Rate = Assessed Value. Tax - Assessed Value = Rate. TAXES 183 651. Solve the following : 1. The assessed valuation of the city of Santa Rosa, Cal., is $6,000,000, and the rate of taxation for state and county pur- poses is 1.42%, and for municipal purposes 1.25%. What is the total tax ? 2. If a collection fee is 1%, how much must be the total tax in order to raise sufficient funds to build a courthouse to cost $321750? 3. A tax on a store building assessed at $27500 was $68.75. At the same rate, what would be the value of another building taxed for $92 ? 4. The assessed value of the property of a town is $1420000. The total tax to be raised is $31950. What would be A's tax who is assessed for $8400 ? 5. What is Brown's tax in a city whose rates are as follows : 1% for improvements, 5 mills on the dollar for library, 75 cents on the $100 for county tax, 14 mills on the dollar for State tax, if he is assessed at $1200 and one poll at $2 ? 6. How much will be a person's tax who has property as- sessed for $10540, if he pays 1^4% city tax, .54% State tax, 2 mills on the dollar school tax ? 7. A special tax was levied on a town for the purpose of building a bridge the net cost of which was to be $1370.85. If the collector's commission was 2M}% and the rate of taxation 2 l /2 mills on the dollar, what was the assessed valuation of the town? 8. The assessor's roll footed up $17235850. The expenses of the county for roads was 7 mills on the dollar ; for salaries, 4 mills on the dollar ; for jail, county farm, and other charities, l l /2 mills on the dollar ; for schools, 25 cents on the $100 ; for state tax, 60 cents on the $100. If there are 12000 polls at $2 each, what is the entire tax of the county ? 9. What is my total tax if the assessed value of my property is $7200 and the rates are as follows : Schools, 4 mills ; general purposes, 5 mills ; library, .5 of a mill; state tax, 3.5 mills; hospital, 1 mill; other expenses, 3 mills; and I pay road tax and poll tax $2 each ? U. S. Customs or Duties 652. Customs or Duties are taxes levied upon imported goods for the purpose of raising funds for the government and to protect home industries. 653. A Custom House is the place where duties are col- lected . 654. A Port of Entry is the city in which a custom house is located. 655. The Collector of the Port is the officer who col- lects duties for the government. 656. A Manifest is a statement in detail of a ship's cargo. 657. A Clearance is the certificate given by the collector of port that a vessel has complied with the requirements of law and is allowed to depart. 658. A Tariff is a schedule of the rates of duty required by law to be paid en imported goods. 659. Ad Valorem Duty is the duty estimated upon the entire cost of the goods in the country from which they are ex- ported. 660. Specific Duty is the duty estimated upon the weight or quantity of the goods imported without regard to their value. 661. Allowances are made for the tare, leakage, breakage, etc., before the duties are computed. 662. Tare is an allowance made for the box, crate, or cov- ering containing the goods. 663. Leakage is an allowance made for waste of liquids imported in casks, barrels, etc. 664. Breakage is an allowance made en account of waste of goods shipped in glass or other breakable material. 665. Gross Weight or Gross Value is the entire weight cr value before any deductions are made. UNITED STATES CUSTOMS OR DUTIES 185 666. Net Weight or Net Value is the weight or value after all deductions are made. 667. Since duties are estimated at a certain rate per cent., the cases of Percentage will apply. 668. To find the Duty, Rate of Duty, or Value of Goods im- ported. FOMUL, : Net Value X Rate = Duty. Duty -8- Rate = Net Value. Duty -*- Net Value = Rate. EXAMPLE : What is duty on 540 yds. cf silk, invoiced at 3 francs per yd.; boxing and cartage, 5 francs; the specific duty being \2\ cents per yd., and the ad valorem duty 33| % ? 540 yds. X 3 fr. == 1620 fr. 1620 fr. + 5 fr. = 1625 fr., total invoice cost. 1625 fr. X 19.3 cents = $313.63. $314 X 33i% = $104.67, ad valorem duty. 540 yds. X 12| cents = $67.50, specific duty. $104.67 + $67.50 = $172.17, total duty. NOTE The LONG TON of 2240 Ibs. is used in weighing goods at the custom house. The VALUE of the is $4.8665, The franc, $.193. The mark, $.2385. ' A BONDED WAREHOUSE is a place where goods on which duty has not yet been paid may be stored. Duties are computed on WHOLE DOLLARS only. If the fraction is 50 cents or more, it is counted as a whole dollar ; if less than 50 cents, it is dropped. PRACTICAL PROBLEMS 669. Solve the following : 1. What is' the duty on 720 yds. of carpet invoiced at 10 s. 6 d. per yd., the duty being 25% ? 2. Find the specific duty on 38080 Ibs. of tool steel at $58.50 per ton. 3. What is the entire duty on an invoice of 40 doz. pairs of kid gloves, costing 1420 francs ; boxing and cartage, 30 francs ; specific duty, $1.80 per doz. pairs, and ad valorem duty, 20% ? ^86 MODERN BUSINESS ARITHMETIC 4. An invoice of goods from Germany was billed at 7240 marks. What was the duty at 35% ? 5. Find the duty on 13200 yds. of China silk, imported from Shanghai, invoiced at 2 s. 6 d. per yd. Ad valorem duty 16l%, and specific duty 8 cents per yd. 6. A merchant imported 240 pieces of carpet, each piece con- taining 96 yds., invoiced at 2/^ marks per yd. The ad valorem duty was 12/^%, and the specific duty 8^i cents per yd. What was the entire cost of the carpet ? 7. What is the rate of duty on an invoice of goods, the en- tire cost -of which was $1095.35, including boxing and cartage $22.50. and an ad valorem duty of $182.60? 8. A New York jobber imported from England 10 cases of English broadcloth ; gross weight, 1240 Ibs.; value ^550. What was the cost of the cloth after being allowed 5% tare on weight, the duties charged being 40 cents per lb., and 37^% ad val- orem? 9. A wine merchant imported 200 doz. bottles of champagne invoiced at $15 per doz., and 20 casks of port wine, each con- taining 30 gals., invoiced at $2.25 per gal. A breakage of 10% and a leakage of 20% is allowed by the custom officers. What is the duty at 33 /^% ad valorem on the champagne, and 20% on the port ? 10. I imported two kinds of watches ; on the first I paid a duty of 33>i%, on the second 35%. Including duty, I invested twice as much in the second kind as in the first. If the total duty paid w y as $1660, what was the total cost of each kind ? TAXES AND DUTIES 187 HOME WORK 21 1. The assessed value of a town is $4750000, and the rate of taxation is as follows: General purposes, 80 mills; hospital, 4 mills ; school, 24 mills ; road, 27 mills, and library, 10 mills on the $100. Find the total tax. 2. My total rate of taxation was 2^. cents on the dollar, and my tax amounted to $229.35. What was the assessed value of my property ? 3. The county rate of taxation was $1.25, the state rate $.45. What was the school rate if my tax was $192 on an assessed val- uation of $9600 ? 4. A village school house to cost $3981.25 was paid for by a tax of lX cents on the dollar. If the collector's commission was 2 % , what was the assessed value of the property ? 5. The assessed value of the property of a town is $4,552,800. If there are 1145 polls at $2 each and a collector's fee of 1%, what rate of taxation will be required to meet a net expenditure of $77392.26? 6. What is the duty on imported goods invoiced at 3240 francs, the rate of duty being 42% ? 7. A firm imported 4800 yds. of body brussels carpet in- voiced at 5 marks per yard, a charge of 45 marks for boxing and cartage being added to the bill. What is the total duty at ad valorem, and 15 cents per yard specific? 8. What will be the total cost of an invoice of watches, im- ported from London, and billed at ^584 15s. 6d., the rate of duty being 35%, exchange being $4.88? 9. A paper company imported from Canada 500 long tons of wood pulp invoiced at 1^4 cents per Ib. What was the entire cost, if the boxing and cartage was $1.37^ per ton; freight, $1250, paid in Holyoke, Mass. ; specific duty, $2.25 per ton, and an ad valorem duty of 20% ? 10. Hall & Co imported merchandise billed at 4320 marks, on which there were prepaid charges of 150 marks. The gross weight was 7 tons, on which a tare of 20% was allowed. If the specific duty was $1.75 per ton, and the advalorem duty 25%, what was the entire cost of the goods ? INSURANCE 670. Insurance is indemnity against loss. There are many kinds of insurance, and they take their names from the nature of their risks ; as, Fire Insurance, Marine Insurance, Life Insurance, Accident Insurance, Health Insurance. NOTE Among the many special forms of insurance are : GUARANTEE COMPANIES that act as bondsmen, PLATE GLASS INSURANCE, HAILSTORM AND CYCLONE INSURANCE, STEAM BOILER INSURANCE, LIVE STOCK IN- SURANCE, etc., etc. 671. Fire Insurance is indemnity against loss or damage by fire. 672. Marine Insurance is indemnity against loss or dam- age to vessels and their cargoes. 673. Accident Insurance is indemnity against loss by accidents. 674. Health Insurance is a remuneration paid for loss of lime or for expense caused by ill health. 675. The Insurer is the party guaranteeing against loss. 676. The Insured is the party indemnified. 677. The Policy is the contract of insurance. 678. The Face of the Policy is the amount of insurance guaranteed. 679. The Premium is the sum paid for insurance. 680. The Term of Insurance is the time for which the insurance is given. 681. There are two principal kinds of insurance companies : Mutual and Non-Mutual. 682. Mutual Companies are those in which the insured share in the gains or losses. 683. The Non- Mutual Companies are those owned ex- clusively by stockholders and the insured do not share in the gains or losses. NOTE Many companies combine the mutual and non-mutual plans as above described. INSURANCE 189 Fire Insurance 684. Since the premiums paid for fire insurance are esti- mated at a certain rate per cent., the principles of Percentage will apply. 685. To find the Premium, Rate of Premium, and Face of Policy. FORMULA : Face of Policy X Rate = Premium. Premium -f- Rate = Face of Policy. Premium -H Face of Policy = Rate. EXAMPLE : A house valued at $4500 is insured for 3 years at y its value. If the annual rate charged is Y\/o, what is the premium ? y* of $4500 = $3000, face of policy. $3000 X 3 A% == $22.50, prem. for 1 year. $22.50 X 2 = $45, prem. for 3 years. NOTE Policies are issued for 1 year or for 3 years. The cost for 3 years is double that for 1 year. PRACTICAL PROBLEMS 686. Solve the following : 1. How much will it cost to insure a house for $2500, the rate of premium being %% ? 2. My house is insured for $2200, and my furniture for $800. What is my premium at 1J4% ? 3. Brown insured his house worth $6000 for Y\ its value in the Northwest National for three years at an annual rate of 70 cents on the $100. What premium did he pay ? 4. The ^Etna Insurance Company takes a year's risk of $8000 at a 90 cent rate. A fire occurs causing 25% damage. What is the company's loss? 5. A paid $29.25 for insurance on his stock of merchandise at a 65 cent rate. What was the face of his policy ? 190 MODERN BUSINESS ARITHMETIC 6. If a three years' policy at an annual rate of 70 cents cost $24.50, what is the amount of insurance? 7. As an agent my commission of 25% on insurance prem- iums amounted to $2227.86. What was the total amount cov- ered, if the average annual rate was 60 cents on the $100? 8. I insured my dwelling in the Phoenix Company for $3220 at 1 % ; my household goods and furniture in the Island Com- pany for $1200, at 90 cents ; my store building for $1800 in the Lion Company, at l/^%, and my stock of merchandise for $12000 in the Home Company, at $1.20. What was the total amount of premium paid, and what was the average rate? 9. B's property valued at $14560, is insured for Y its value at 1%% premium. A fire occurs causing a loss equal to ^ the face of the policy. What is B's loss if the insurance company pay only 90 cents on the dollar ? 10. The Hartford Insurance Company took a risk on a ware- house for 3 years at l/^% premium and reinsured Y\ of their policy in the Commercial at 1%%. A fire occurred in which the entire plant was destroyed. If the loss of the Hartford Com- pany was $2440, what was the face of the policy? I/ife Insurance 687. Jyife Insurance is a contract by which the insurer agrees to pay a beneficiary a certain sum upon the death of the insured or at a specified time. 688.. The Beneficiary is the one named in the policy to receive the benefit. 689. There are many kinds of policies written by life insur- ance companies ; among them are : Ordinary Life Policy, Lim- ited Life Policy, Endowment Policy, Annuity Policy, Midual Poli- cies, etc. 690. The Ordinary Life Policy requires regular prem- iums to be paid during life, and the benefit to be paid only upon the death of the insured. INSURANCE 191 691. The Limited Life Policy requires premiums to be paid for a stated number of years, the benefit to be paid upon the death of the insured. TABLE OF INSURANCE RATES, 1908 Premium Rates for $1000 of Insurance > c R ORDINARY LIFE 20-YR. ENDOWMENT 20-PAYMENT LIFE Annual Semi- Annual Quar- terly Annual Semi- Annual Quar- terly Annua' Semi- Ann ual Quar- terly 20 $15.50 $8.06 $1.11 $42.79 $22.25 $11.34 $23.31 $12.13 $6.18 21 15.84 8.24 4.20 42.83 22.28 11.35 23.69 12.32 6.28 22 16.19 8.42 4.29 42.89 22.31 11.37 24.08 12.53 6.39 23 16.57 8.62 4.40 42.94 22.33 11.38 24.48 12.73 6.49 24 16.96 8.82 4.50 43.00 22.36 11.40 24.91 12.96 6.61 25 17.37 9.04 4.61 43.05 22.39 11.41 25.35 13.19 6.72 26 17.80 9.26 4.72 43.12 22.43 11.43 25.80 13.42 6.84 27 18.26 9.50 ' 4.84 43.20 22.47 11.45 26.27 13.66 6.97 28 18.73 9.74 4.97 43.27 22.50 11.47 26.76 13.92 7.10 29 19.24 10.01 5.10 43.36 22.55 11.49 27.27 14.18 7.23 30 19.77 10.28 5.39 43.46 22.60 11.52 27.80 14.46 7.37 31 20.33 10.58 5.24 43.57 22.66 11.55 58.36 14.75 7.52 32 20.92 10.88 5.55 43.69 22.72 11.58 28.94 15.05 7.67 33 21.54 11.20 5.71 43.81 22.79 11.61 29.53' 15.36 7.83 34 22.20 11.55 5.89 43.97 22.87 11.66 30.16 15.69 8 DO 35 22.90 11.91 6.07 44.13 22.95 11.70 30.83 16.04 8.17 36 23.63 12.29 6.27 44.31 23.05 11.75 31.51 16.39 8.35 37 24.40 12.69 6.47 44.52 23.15 11.80 62.22~ 16.76 8.54 ' 38 25.23 13.12 6.69 44.75 23 27 11.86 32.97 17.15 8.74 39 26.11 13.58 6.92 45.00 23.40 11.93 33.76 17.56 8.95 40 27.03 14.06 7.17 45.30 23.56 12.01 34.59 17.99 9.17 41 28.01 14.57 7.43 45.62 23.73 12.09 35.46 18.44 9.40 42 29.05 15.11 7.70 45.99 23.92 12.19 36.38 18.92 9.64 43 30.16 15.69 8.00 46.40 24.13 12.30 37.35 19.43 9.90 44 31.35 16.31 8.31 46.87 24.38 12.42 38.37 19.96 10.17 45 32.60 16.96 8.64 47.39 24.65 12.56 39.45 20.52 12.17 46 33.94 17.65 9.00 47.97 24.95 12.72 40.59 21.11 10.46 47 35.36 18.39 9.37 48.63 25.29 12.89 41.81 21.75 10.76 48 36.88 19.18 9.78 49.37 25.68 13.09 43.10 22 42 11.08 49 38.50 20.02 10.21 50.19 26.10 13.30 44.47 23!l3 11.43 50 40.24 20.93 10.67 51.11 26.58 13.55 45.92 23.88 11.79 51 42.08 21.89 11.16 52.13 27.11 13.82 47.48 24.69 12.59 52 44.03 22.90 11.67 53.25 27.69 14.12 49.13 25.55 13.02 53 46.13 23.99 12.23 54.51 28.35 14.45 50.88 26.46 13.49 54 48.37 25.16 12.82 55.89 29.07 14.81 52.77 27.44 13.99 55 50.75 26.39 13.45 57.43 29.87 15.22 54.79 28.49 14.52 56 53.29 27.71 14.13 59.13 30.75 15.67 56.96 29.62 15.10 57 56.02 29.13 14.85 61.00 31.72 16.17 59.28 30.83 15.71 58 58.91 30.64 15.62 63.05 32.79 16.71 61.76 32.12 16.37 59 62.03 32.26 16.44 65.32 33.97 17.31 64.44 33.51 17.08 60 65.41 34.02 17.34 67.82 35.27 17.98 67.33 35.02 17.85 692. The Endowment Policy requires premiums to be paid for a stated number of years or until the death of the in- sured, the benefit to be paid at the end of the stated time or upon the death of the insured. 192 MODERN BUSINESS ARITHMETIC 693. Mutual Policies are those issued by mutual insur- ance companies which permit the insured to participate in the profits of the business, thereby reducing the rate of premium. 694. The Surrender Value is the amount that the com- pany will pay upon surrender of the policy. 695. To find the Annual Premium on $1000 consult the preceeding table. EXAMPLE : A man 29 years of age takes out a 20 annual pay- ment policy for $5000. What annual premium does he pay? 29 yrs. and 20 annual payments = $27.27 premium. $27.27 X 5 = $136.35, annual premium on $5000. PRACTICAL PROBLEMS 696. Solve the following : 1. What will be the annual premium on an ordinary life pol- icy for $2000 at the age of 42 years ? 2. A man takes out a 20 year endowment policy at the age of 30 years for $4000. What annual rate will he pay ? 3. What will a limited 20 payment life policy for $6000 cost me annually if taken at the age of 25 years ? 4. A, at the age of 32 years, had his life insured for $1000 under the ordinary life plan. If he had died at the age of 54 years, how much more would his heirs receive than had been paid in? 5. Wishing to take out insurance at the age of 27 years, I decided to adopt the 20 year endowment plan. If the* face of the policy was $2500, what would the total insurance cost me ? 6. What will be the excess received over that paid to the heirs of one who at the .age of 40 takes out a limited 20 pay- ment life policy for $10000, and dies at the age of 70 ? 7. What is the difference in cost of a 20 year endowment policy for $3000 at the age of 37 years, and a 20 payment policy for the same amount, at the same a^c ? INSURANCE 193 8. The Metropolitan Life Insurance Company issues an ordi- nary life policy for John Jones, aged 22 years, for $5000. If the heirs received $4433.35 more than had been paid in, how old was the insured at the time of his death ? 9. The New York Life Insurance Company issued a 20 year endowment policy to a man aged 45 years. If he dies at the age of 57 years and his heirs receive $1431.32 more than has been paid to the company, what was the face of the policy? 10. The Equitable Life Insurance Company issues a 20 pay- ment life policy for $25000 to a person who lived long enough to pay 15 annual premiums amounting to $17220. What was the age of the insured at the time of his death ? Outline for Review V. Stocks and Bonds : 1. Corporation. 2. Articles of Incorporation. 3. Capital Stock. 4. Stocks, Certificates. 5. Par Value, Market Value. 6. Premium, Discount. 7. Installment, Assessment, Dividend. 8. Bonds, Registered Bonds, Coupon Bonds. 9. Treasury Stock, Preferred Stock, Watered Stock. 10. Cases. VI. Taxes : 1. Definitions. 2. Property Tax, Poll Tax. 3. Real Estate, Personal Prop- erty. 4. Assessor, Tax Colector. 5. Collection. 6. Assessment Roll. VIL U. $. Customs or Duties : 1. Definitions. 2. Custom House, Port of Entry. 3. Manifest, Clearance. 4. Ad valorem Duty, Specific Duty. 5. Tare, Leakage, Breakage. 6. Gross Weight, or Gross Value. 7. Net Weight, or Net Value. VIII. Insurance : 1. Definitions. 2. Fire, Marine, Accident, Health. 3. Insurer, Insured. 4. Policy, Premium. 5. Mutual and Non-Mutual Companies. 6. Life Insurance. 7. Beneficiary. 8. Kinds of Policies. 9. Surrender Value. INTEREST 697. Interest is the sum paid for the use of money or other value. 698. There are three methods of computing interest : 1. By Simple Interest. 2. By Periodic Interest. 3. By Compound Interest. 699. All of these methods require the element of time in ad- dition to the regular elements of Percentage. 700. The Principal is the money or value for which inter- est is paid. 701. The Rate of Interest is the amount paid for the use of $1 for 1 year. 702. The Time is the period for which the interest is com- puted. 703. The Amount is the sum of the principal and interest. 704. Legal Interest is the rate of interest established by law. 705. Usury is a higher rate than the law allows. 706. Since interest is computed at a certain rate percent., the cases of Percentage apply, and the additional element of time is added. 707. The elements are as follows : 1. The Principal = Base. 2. The Interest = Percentage. 3. The Rate of Interest = Rate. 4. The Amount = Principal + Interest. 5. The Time. In computing Common Interest, 360 days are considered a year, and 30 days a month. In computing Exact Interest, 365 days are considered a year. Simple Interest 708. Simple Interest is interest on the principal only for the given time and rate. CASE I 709. Given, the Principal, Time, and Rate to find the Interest. 710. Three Methods of finding simple interest are given in this work. 1. Cancellation Method. 2. Six Per Cent. Meth- od. 3. Bankers' Method. For Cancellation Method turn to page 55 of this book. Six Per Cent. Method 711. In the Six Per Cent. Method, 12 months of 30 days each, or 360 days constitute a year. The analysis of the method is as follows : FOR YEARS : The interest on $1 for 1 year or 12 months at 6% = $.06. Therefore, ~to find the interest on $1 for years, multiply $.06 by the number of years. FOR MONTHS : The interest on $1 for 2 months = \ of $.06 or $.01. Therefore, to find the interest in cents on $1 for months, divide the number of months by 2. FOR DAYS : The interest on $1 for 1 month or 30 days = \ of $.01 or $.005. The interest on $1 for 6 days = of $.005 or $.001. Therefore, to find the interest in mills on $1 for days, divide the number of days by 6 . SUMMARY I $.06 X No. of years = Int. on $1 expressed in cents. No. of months -5- 2 = Int. on $1 expressed in cents. No. of days -5- 6 = Int. on $1 expressed in mills. 196 MODERN BUSINESS ARITHMETIC EXAMPLE : Find the interest on $200 for 4 years 8 months 12 days at 6%. $.06 X 4, number of years = $.24 int. on $1 for 4 years. 8 months -^-2 = .04 int. on $1 for 8 months. 12 days -*- 6 = .002 int. on $1 for 12 days. $.282 int. on $1 for whole time. $.282 X $200 = $56.40 total interest. 712. If the rate per cent, is other than 6% take J of the in- terest at 6% and multiply by the rate required. PRACTICAL PROBLEMS 713. Solve the following by 6% method : 1. Find the interest on $1 for 2 yrs. 10 mo. 15 ds. at 6%. 2. Find the interest on $400 for 1 yr. 6 mo. 24 ds. at 6%. 3. Find the interest on $750 for 5 yrs. 4 mo. 27 ds. at 6%. 4. Find the interest on $960 for 3 yrs. 3 mo. 3 ds. at 6%. 5. Find the interest on $1500 for 4 yrs. 11 mo. 23 ds. at 6%. 6. Find the interest on $3000 for 3 yrs. 8 mo. 21 ds. at 7%. 7. Find the interest on $5000 for 7 yrs. 7 mo. 7 ds. at 7%. 8. Find the amount of $720 on interest for 2 yrs. 5 mo. 12 ds. at 6%. 9. A note for $540 draws interest for 9 mo. 18 ds. at 8%. What is the amount due ? 10. My note for $1000 at 9% has been running 1 yr. 10 mo. 21 ds. If I have already paid the interest for 6 months, what amount will now be due ? Bankers' Method 714. The Bankers' Method of computing interest is based upon the fact that by pointing off two places ( dividing by 100 ) in the principal, the result will be the interest at any rate for as many days as the rate is contained in 360, the number of days in a year. INTEREST 197 715. By pointing off two places the interest on any principal is found : At 2% for 180 days, the basis of time at 2%. At 3% for 120 days, the basis of time at 3%. At 4% for 90 days, the basis of time at 4%. At 5% for 72 days, the basis of time at 5%. At 6% for 60 days, the basis of time at 6%. At 8% for 45 days, the basis of time at 8%. At 9% for 40 days, the basis of time at 9%. At 10% for 36 days, the basis of time at 10%. At 12% for 30 days, the basis of time at 12%. At 15% for 24 days, the basis of time at 15%. At 18% for 20 days, the basis of time at 18%. At 20% for 18 days, the basis of time at 20%. At 24% for 15 days, the basis of time at 24%. 716. To find the interest at 7%, increase the interest at 6% by I of itself. To find the interest at 11%, increase the interest at 10% by A of itself. 717. To find the interest for any number of days, increase or decrease the interest for the basis of time by using aliquot parts. 718. The Bankers' Method is particularly adapted to short periods of time, and is not recommended except when the time is expressed in days. EXAMPLE : Find the interest on $450 for 36 days at 6%. Pointing off two places = $4.50 interest for 60 days at 6%. \ of $4.50 = $2.25 interest for 30 days, i of $2.25 = .45 interest for 6 days. $2.70 interest for 36 days. EXAMPLE : Find the interest on $960 for 108 days at 8% . Pointing off two places = $9.60 interest for 45 days at 8%. Multiplying $9.60 by 2 = $19.20 interest for 90 days. \ of $9.60 = 3.20 interest for 15 days, i of $3.20 = .64 interest for 3 days. $23.04 interest for 108 days. NOTE- -Notice that Aliquot parts are prominent in much of the above work. 198 MODERN BUSINESS ARITHMETIC 719. Solve the following by Bankers' Method ; 1. Find the interest on $342 for 33 days at 6%. 2. Find the interest on $175 for 27 days at 6%. 3. Find the interest on $924 for 54 days at 8%. 4. Find the interest on $3000 for 78 days at 5%. 5. Find the interest on $2150 for 126 days at 9%. 6. Find the interest on $215.60 for 88 days at 10% 7. Find the interest on $321.75 for 37 days at 12% 8. Find the interest on $810 for 76 days at 7%. 9. Find the interest on $1350 for 111 days at 11%. 10. Find the interest on $427.20 for 48 days at CASE II 720. Given, the Interest, Rate, and Time to find the Principal. Use the cancellation method as indicated below . The Interest will, be the dividend and the Time multiplied by the Rate the divisor. FORMULA : Interest -H Rate X Time expressed in years = Principal. EXAMPLE : The interest is $2.80, the time 35 days, and the rate 6%. What is the principal ? 60 300 ds. Int., 8 ($ ), principal 3$ ds., time .00, rate 60 X $8 = $480 == Principal. 721. Solve the following by cancellation method : 1. What principal will produce an interest of $300 in 48 ds., at6%? 2. An interest of $8.26 in 59 ds. at 7% ? 3. An interest of $29.10 in 97 ds. at 9% ? 4. An interest of $8.55 in 114 ds. at 5% ? 5. An interest of $4.62 in 3 mo. 9 ds. at 6% ? INTEREST 199 6. An interest of $58 in 1 yr. 2 mo. 15 ds. at 8% ? 7. An interest of $214.20 in 2 yrs. 6 mo. 18 ds. at 7% ? 8. An interest of $43. 08^ in 1 yr. 5 mo. 7 ds. at 6% ? 9. An interest of $84.50 in 39 ds. at 4% ? 10. An interest of $2133.60 in 320 ds. at 10% ? CASE III 722. Given the Interest, Principal, and Time to find the Rate. Use the cancellation method as indicated below. The Interest will be the dividend, and the Principal multiplied by the Time the divisor. FORMULA : Int. -+- Prin. X Time expressed in yrs. = Rate. EXAMPLE : At what rate will $450 gain $26.25 in 10 mo. ? * 7%, Ans. 723. Solve the following : 1. At what rate per cent, will $540 gain $3.15 in 35 ds. ? 2. Will $1170 gain $54.60 in 7 mo. ? 3. Will $510 gain $61.20 in 1 yr. 6 mo. ? 4. Will $825 gain $9.90 in 1 mo. 24 ds. ? 5. Will $1260 gain $52.92 in 7 mo. 6 days? 6. Will $47.50 gain $4.94 in 1 yr. 3 mo. 18 ds. ? 7. Will $325.50 gain $24.52 in 11 mo. 9 ds. ? 8. Will $1350 gain $36.45 in 216 ds. ? 9. Will $2500 gain $475 in 171 ds. ? 10. Will $8000 gain $810 in 1 yr. 4 mo. 6 ds. ? CASE IV 724. Given, the Interest, Principal, and Rate to find the Titne. Use the cancellation method as indicated in the following solution. The Interest will be the dividend and the Principal multiplied by the Rate the divisor. 200 MODERN BUSINESS ARITHMETIC FORMULA : Int. -*- Prin. X Rate = Time. EXAMPLE: In what time will $720 produce $7.92 interest at *<& ? $00 ds. 66 int., Also : ( ) mo. 2.2 .00 $102 ( ) .00 66 ds., Ans. 2.2 mo., or 2 mo. 6 ds., Ans. 725. Solve the following : 1. In what time wall $320 earn $12.80 interest at 6% ? 2. Will $480 earn $6.16 interest at 6% ? 3. Will $580 earn $5.80 interest at 8% ? 4. Will $780 earn $32.76 interest at 7% ? 5. Will $960 earn $18.80 interest at 5% ? 6. Will $1200 earn $139.50 interest at 9% ? 7. Will $1400 earn $119.70 interest at 6% ? 8. Will $2100 earn $338.10 interest at 7% ? 9. Will $4500 earn $175.50 interest at 4^ % ? 10. Will $18680 earn $700.50 interest at 1% % ? CASE V 726. Given, the Amount, Rate, and Time to find the Principal. Divide the given Amount by the amount cf $1 for the given Time and Rate. FORMULA : Amt. -5- $1 -f- (Rate X Time) == Prin. EXAMPLE : What principal will amount to $430.50 in 5 mo. at 6% ? $1.00 X .06 X 5 /i2 yr. = .02^, Int. on $1 for 5 mo. $1.00 + .02^ = $1.025, Amt. of $1 for 5 mo. $430.50 -*- $1.025 = $420, Prin., Ans. 727. Solve the following : 1. What principal will amount to $250.80 in 9 mo. at 6% ? 2. Will amount to $333.25 in 1 yr. 3 mo. at 6% ? 3. Will amount to $520.53 in 2 yr. 5 mo. at 8% ? 4. Will amount to $675.08 in 33 ds. at 5% ? INTEREST 201 5. Will amount to 4113.90 in 71 ds. at 8% ? 6. Will amount to $1313.27 in 3 mo. 22 ds. at 9% ? 7. Will amount to $2374.50 in 1 yr. 4 mo. 18 ds. at 4% ? 8. Will amount to $5262.60 in 2 yr. 1 mo. 21 ds. at 4 l / 2 % ? 9. Will amount to $7656.25 in 75 ds. at 10% ? 10. Will amount to 12977.50 in 1 yr. 1 mo. 1 da. at Exact Interest 728. Exact Interest is the interest on any sum when the time is computed on the basis of 365 days to the year, or the ex- act year. In leap years 366 days is the basis of exact interest. 729. The interest for whole years is the same as in common interest, therefore the exact method applies only when the time is less than a year expressed in days. 730. In ordinary business transactions this method is seldom used but is strictly legal. 731. The cancellation method of computing exact interest is recommended, but it can also be found by deducting -^ from the common interest, as the 5 days difference in the exact and com- mon years is 3! 3 or 7*5. EXAMPLE : Find the exact interest on $540 for 146 days at 6%. 108 146 ilo. 14 Common Int. Or, 1402 .06 .18 Ext. Int., $12.96, Ans. $12.96 Exact Int. 732. Solve the following : 1. Find the exact interest of $730 for 33 ds. at 6%. 2. Of $1095 for 42 ds. at 7%. 3. Of $292 for 45 ds. at &% . 4. Of $80.30 for 77 ds. at 5%. 5. Of $500 for 90 ds. at 6%. 6. Of $1200 for 110 ds. at 9%. 7. Of $1800 for 132 ds. at 4%. 202 MODERN BUSINESS ARITHMETIC 8. Of $3000 for 219 ds. at 9. Of $4380 for 134 ds. at 10%. 10. Of $549 for 256 days of a leap year at Annual, Semi- Annual, and Quarterly Interest 733. Annual Interest is the simple yearly interest on the principal, and the simple interest on such interest remaining un- paid. 734. Semi- Annual Interest is the simple half-yearly in- terest on the principal, and the simple interest on such interest remaining unpaid. 735. Quarterly Interest is the simple quarterly interest on the principal, and the simple interest 011 such interest remain- ing unpaid. 736. Given, the Principal, Rate, and Time to find the Annual, Semi-Annual, and Quarterly Interest. 1. Find the interest on the principal for the whole time. 2. Find the interest on the interest for* the year, half year, or quarter for the total time that the interest payments are delinquent. 3. The interest due will be the sum of the interest on, the prin- cipal and the interest on the unpaid interest. EXAMPLE : Find the amount due on a note for $1200 dated July 10, 1904 and paid October 25, 1907, at 6%, interest to be paid annually. Yr. Mo. Da. October 25, 1907 = 1907 10 25 July 10, 1905 = 1904 7 10 Dif. in time = 3 3 15 a. Simple int. on $1200 for 3 yr. 3 mo. 15 ds. at 6% a= $237. b. Simple annual int. on $1200 at 6% == $72. Int. on $72 due end of 1st yr. runs 2 yr. 3 mo. 15 ds. Int. on $72 due end of 2d yr. runs 1 yr. 3 mo. 15 ds. Int. on $72 due end of 3d yr. runs 3 mo. 15 ds. Total int. on $72 runs 3 yr. 10 mo. 15 ds. c. Int. on $72 for 3 yr. 10 mo. 15 ds. = $16.74. d. Int. on Prin. $237 + $16.74 = $253.74 total annual int. e. Prin., $1200 + Int., $253.74 = Amt. due, $1453.74, Ans. INTEREST 203 737. Solve the following : 1. Find the total interest, payable annually, on $900 for 4 yrs. 6 mo. at 6% . 2. Annually, on $1500 for 5 yrs. 4 mo. at 6%. 3. Annually, on $1800 for 3 yrs. 7 mo. 12 ds. at 6%. 4. Annually, on $2400 for 5 yrs. 9 mo. 27 ds. at 8%. 5. Semi-annually, on $600 for 2 yrs. at 8%. 6. Semi-annually, on $1050 for 1 yr. 9 mo. at 8%. 7. Semi-annually, on $4500 for 3 yrs. 2 mo. 10 ds. at 6%. 8. Quarterly, on $300 for 1 yr. 5 mo. at 8%. 9. Quarterly, on $2000 for 2 yrs. 1 mo. 15 ds. at 10%. 10. Quarterly, on $4200 for 3 yrs. 3 mo. 3 ds. at 7%. Questions for Review 1. Define Interest. Principal. Rate. Time. Amount. 2. What three methods are used in computing Interest? 3. What i^ Legal Interest? Usury? 4. What is Simple Interest? 5. Explain the Six Per Cent. Method of finding interest. 6. Explain the Bankers' Method of finding interest? 7. Write the formulae for finding the different elements in the problems of Interest. 8. What is Exact Interest? How much less is it than Com- mon Interest ? Why ? 9. What is meant by Annual, Semi- Annual, and Quarterly Interest ? 10. Describe the correct method of finding Annual, Semi- An- nual, and Quarterly Interest? Compound Interest 738. Compound Interest is the interest on the principal and also upon the unpaid interest when due. 739. In computing compound interest the interest for a cer- tain period when due is added to the principal, and this amount is the new principal for the next period. 740. The Period of computation may be yearly, semi-an- nually, or quarterly as agreed upon. Compound interest is not lawful except upon specific contract. 741. Given, the Principal, Rate, and Time to find the Compound Interest. Find the amount of the principal for the first period ; this amount will be the principal for the second period ; continue in like manner for the full tune. The final amount less the first principal will be the compound interest. EXAMPLE : Find the interest of $400 for 3 yr. 4 mo. 24 ds. at 6%, compounded annually. $400.00 = Principal. 24.00 = Int. on $400 for 1 yr. at 6%. 424.00 = Amt. at close of first year. 25.44 = Int. on $424 for 2d year. 449.44 = Amt. at close of 2d year. 26.97 = Int. on 3d principal. 476.41 = Amt. at close of 3d year. 11.43 = Int. for 4 mo. 24 ds. 487.84 = Amt. at close of time. 400.00 = First principal. $87.84 = Compound interest, Ans. 742. Solve the following : 1 . Find the interest compounded annually on $600 for 2 yrs. at 6%. 2. Annually on $1000 for 4 yrs. at 6%. 3. Annually on $1200 for 6 yrs. at 8%. 4. Annually on $2100 for 10 yrs. at 10%. INTEREST 205 5. Semi-annually on $1500 for 2 yrs. 6 mo. at 6%. 6. Semi-annually on $5400 for 4 yrs. 9 mo. at 7%. 7. Semi-annually on $7200 for 8 yrs. 8 mo. 15 ds. at 6%. 8. Quarterly on $900 for 1 yr. 8 mo. 12 ds. at 8%. 9. Quarterly on $1300 for 2 yrs. 2 mo. 3 ds. at 10%. 10. Quarterly on $2000 for 5 yrs. 5 mo. 6 ds. at 6%. 743. The computation of compound interest is greatly abbreviated by using the following table : 744. To use the table, multiply the amount of $1 for the number of periods at the given rate, by the given principal ; the result will be the amount of the principal for the whole periods. Interest for additional time is added as usual. NOTE For semi-annual interest, double the years and take half the annual rate. For quarterly interest, take four times the years and one- fourth the annual rate. COMPOUND INTEREST TABLE Showing the amount of $1 at compound interest at various rates of in- terest for specified periods. Yr 2\ perct. 3 per ct. 3J perct. 4 per ct. 5 per ct. 6 per ct. 1 1.025000 1.030000 1.035000 1.040000 1.050000 1.060000 2 1.050625 1.060900 1.071225 1.081600 1.102500 1.123600 3 1.076891 1.092727 1.108718 1.124864 1.157625 1.191016 4 1.103813 1.125509 1.147523 1.169859 1.215506 1.262477 5 1.131408 1.159274 1.187686 1.216653 1.276282 1.338226 6 1.159693 1.194052 1.229255 1.265319 1.340096 1.418519 7 1.188686 1.229874 1.272279 1.315932 1.407100 1.503630 8 1.218403 1.266770 1.316809 1.368569 1.477455 1.593848 9 1.248863 1.304773 1.362897 1.423312 1.551328 1.689479 10 1.280085 1.343916 1.410599 1.480244 1.628895 1.790848 11 1.312087 1.384234 1.459970 1.539454 1.710339 1.898299 12 1.344889 1.425761 1.511069 1.601032 1.795856 2.012197 13 1.378511 1.469534 1.563956 1.665074 1.885649 2.132928 14 1.412974 1.512590 1.618695 1.731676 1.979932 2.260904 15 1.448298 1.557967 1.675349 1.800944 2.078928 2.396558 16 1.484506 1.604706 1.733986 1.872981 2.182875 2.540352 17 1.521618 1.652848 1.794676 1.947901 2.292018 2.692773 18 1.559659 1.702433 1.857489 2.025817 2.406619 2.854339 19 1.598650 1.753506 1.922501 2.106849 2.526950 3.025600 20 1.638616 1.806111 1.989789 2.191123 2.653298 3.207136 206 MODERN BUSINESS ARITHMETIC Yr 7 per ct. 8 per ct. 9 per ct. lOperct. 11 per ct. 12 per ct. 1 1.070000 1.080000 1.090000 1.100000 1.110000 1.120000 2 1.144900 1.166400 1.188100 1.210000 1.232100 1.254400 3 1.225043 1.259712 1.295029 1.331000 1.367631 1.404908 4 1.310796 1.360489 1.411582 1.464100 1.518070 1.573519 5 1.402552 1.469328 1.538624 1.610510 1.585058 1.762342 6 1.500730 1.586874 1.677100 1.771561 1.870414 1.973822 7 1.605781 1.713824 1.828039 1.948717 2.076160 2.210681 8 1.718186 1.850930 1.992563 2.143589 2.304537 2.475963 9 1.838459 1.999005 2.171893 2.357948 2.558036 2.773028 10 1.967151 2.158925 2.367364 2.593742 2.839420 3.105848 11 2.104852 2.331639 2.580426 2.853117 3.151757 3.478549 12 2.252192 2.518170 2.812665 3.138428 3.498450 3.895975 13 2.409845 2.719624 3.065805 3.452271 3.883279 4.363492 14 2.578534 2.937194 3.341727 3.797498 4.310440 4.887111 15 2.759031 3.172169 3.642482 4.177248 4.784588 5.473565 16 2.952164 3.425943 3.970306 4.594973 5.310893 6.130392 17 3.158815 3.700018 4.327633 5.054470 5.895091 6.866040 18 3.379932 3.996019 4.717120 5.559917 6.543551 7.689964 19 3.616527 4.315701 5.141661 6.115909 7.263342 8.612760 20 3.869684 4.660957 5.604411 6.727500 8.062309 9.646291 PRACTICAL PROBLEMS 1. Find, by using- the table, the compound interest of $1050 for 1 yr. 5 mo. 24 ds. at 10%, interest payable quarterly. 2. Of $1500 for 7 yrs. 3 mo. 15 ds., interest at 6%, payable semi- annually. 3. Of $2700 for 17 yrs. 7 mo. 7 ds., interest at 7%, payable annually. 4. Of $5400 for 24 yrs. 11 mo. 11 ds., at 11%, interest pay- able annually. 5. Of $12000 for 18 yrs. 8 mo. 6 ds., at 10%, interest pay- able semi-annually. Commercial Paper 745. Commercial Paper is the written promise or request to pay money. 746. There are two classes of Commercial Paper, viz : I. PROMISE TO PAY : 1. Promissory Notes. 2. Bonds. 3. Paper Currency. II. REQUESTS TO PAY : 1. Orders. 2. Personal Drafts. 3. Bank Checks. 4. Bank Drafts. 5. Bills of Exchange. 6. Letters of Credit. 747. A Promissory Note is the written promise of one or more individuals to pay a certain sum at a specified time. Promissory Note Payable on Demand. Promissory Note Payable in Gold Coin 208 MODERN BUSINESS ARITHMETIC WL> St/ T-X ^L^~ ^(a^^t^^rt^ /C2-x^^f . ^^^^^C^^U^Z^^A^^r /n^ is /y ' Promissory Firm Note Payable at Bank. Promissory Joint Note Payable at Bank. 748. A Bond is the promissory note of a government, state, or corporation. 749. Paper Currency is the promissory notes of the gov- ernment, or of a national bank, to pay to bearer on demand the sum specified, and is of four kinds, viz : 1 . National Treasury Notes ( Greenbacks ) . 2. National Bank Notes. 3. Government Silver Certificates. 4. Government Gold Certificates. 750. An Order is the informal written request of one per- son upon another to pay a third party a certain sum. 751. A Personal Draft is a formal order and is definite in time, amount, and other conditions. COMMERCIAL PAPER 209 Personal Sight Draft. Personal Time Draft NOTE DRAFTS are sometimes called " Domestic Bills of Exchange" to distinguish from Foreign Bills of Exchange 752. A Bank C/ieci: is an order on a bank to pay a certain sum at sicrht. Bank Check 210 MODERN BUSINESS ARITHMETIC Draft Form of a Bank Check 753. A Bank Draft is the order of one bank on another bank to pay a certain sum either at sight or at a specified time. 'Urtrbnttts ahlimtal wnnk Bank Draft 754. A Bill of Exchange is a bank draft on a bank lo- cated in a foreign country. 755. A L/etter of Credit is a bill of exchange authorizing certain banks to pay to the holder any sum not exceeding a cer- tain amount. ete 4^^ Xf< ^ ~~a5K ^"-<^* ^-" -^ "^^ &Z*7'0_. V^*T*1* _ _ . ,_ y^ ' ^v^ A Bank Draft on a Business House COMMERCIAL PAPER 211 756. A Cashier's Check is the check of the cashier of a bank, and when desired, is given instead of currency. ^~/c, Cashier's Check. Another Form of Cashiers Check. 757. A Certificate of Deposit states that the depositor has a certain amount of cash in the bank which he may draw out upon conforming with the requirements of the certificate. Certificate of Deposit. 212 MODERN BUSINESS ARITHMETIC 758. A Receipt is the written acknowledgment of the pay- ment of a debt or of the delivery of goods. Form of Receipt. 759. An Indorsement is a writing on the back of com- mercial paper for the purpose of : 1. Acknowledging a partial payment. 2. Making the paper transferable. 3. Guaranteeing its payment. 760. Negotiable Paper is commercial paper that can be transferred and usually contains the words ' ' to order, " or "to bearer. ' ' 761. The Pace of the note or draft is the sum for which it is written. 762. The Maker of a note is the one who promises to pay ; the one who signs it. 763. The Drawer of a note is the one who orders another to pay ; the one who signs it. 764. The Payee is the one to whom the money is to be paid. 765. The Drawee of a draft is the one who is ordered to pay. 766. The Indorser is the one who writes his name on the back of the paper. 767. Commercial paper matures upon the day it legally be- comes due. If it becomes due upon Sunday or any other legal holiday, it matures on the next business day following. COMMERCIAL PAPER 213 768. Three Days of Grace were once granted by law, but in most states are not now allowed. 769. To Accept a draft is to write the word "accepted" with date and signature of drawee across the face of it. It then becomes his written promise to pay. 770. An Acceptance is a draft that has been accepted. 771. Sight Drafts are payable on demand, and time drafts are payable at a specified time after sight. 772. To Honor a draft is to pay it or to accept it. 773. Promissory Notes may be payable on demand or at a specified time. They may be individual or joint notes, and may or may not bear interest. 774. The Legal Rate of the state prevails when a note is " icif/i interest " and no rate specified, and all notes bear interest after maturity. 775. To Find the Amount Due on Commercial Paper. Find the interest on the face of the paper for the given time and rate. r Fhe sum of the interest and face of the paper will be the amount due. NOTE To find the time a note WITH INTEREST has to run, compute the time from the date of the note to the date of settlement. If the note is WITHOUT INTEREST, compute the time from maturity to the date of. settlement. EXAMPLE : Find the amount June 25, 1908, of the following note : $720% Chicago, III., January 10, 1907. Nine months after date I promise to pay Henry H. Howe, or order, Seven hundred twenty Dollars, with interest at six per cent. Per annum. D. M. COOK. June 25, 1908 = 1908 yr. 6 mo. 25 ds. Jan. 10, 1907 = 1907 yr. 1 mo. 10 ds. Time note has to run = 1 yr. 5 mo. 15 ds. $.0875 = Int. on $1.00 for 1 yr. 5 mo. 15 ds. 720 63.00 = Int. on $720 for 1 yr. 5 mo. 15 ds. 720.00 = Face of Paper. $783.00 = Amt. due, Ans. 214 MODERN BUSINESS ARITHMETIC 776. Find the amount due at settlement of the following : $810% New York, N. Y., Apr. 20, 1907. One year after date I promise to pay J. E. Olson Eight hun- dred ten Dollars, with interest at seven per cent. G. H. MOORE. Settlement made July 1, 1908. 2. $1080% Eos Angeles, Cat., Oct. 26, 1905. Six months after date I promise to pay Henry Brayton, or order, Ten hundred eighty Dollars, with interest. BYRON R. MARSH. Settlement made May 5, 1908. Legal rate, $420% San Francisco, Cal., Apr. 14, 1907. One day after date I promise to pay E. P. Heald, or order, Four hundred twenty Dollars. JOHN H. DOE. Settlement made July 1, 1908. 4. $2000% Milwaukee, Wis., Nov. so, 1906. Three months after date I promise to pay Geo. W. Peck, or order, Tivo thousand Dollars, without interest. W. C ROBERTS. Settlement made December 31, 1907. Legal rate, 1%. 5. $642.60 Detroit Mich , September i, Sixty days after date we promise to pay A r land & Co- Six hundred forty-two 6 %oo Dollars, with interest at eight per cent, per annum. F. O. GARDINER & CO. Settlement made at maturity. COMMERCIAL PAPER 215 _6. __ $500% Cincinnati, Ohio., Feb. 4, 1905. One year after date I promise to pay P. R. Spencer, or order, Five hundred Dollars, with interest at six per cent, per annum, to be paid semi-annually , and if not so paid to draw interest until settlement. H. A. REID. Settlement made October 25, 1907. $3000% Santa Rosa, Cal.,Jan. 1 Two years after date I promise to pay the SAVINGS BANK OF SANTA ROSA Three thousand Dollars, with interest at eight per cent, per an- num, payable quarterly, and if not so paid to bear interest until settlement. R. G. BRACKETT. Settlement made at Maturity. 8. _ ' _ $2400% Cedar Rapids, Iowa, June 10, 1006. Two years after date I promise to pay A. N. Palmer, or order, Twenty- four hundred Dollars, with interest at six per cent. , com- pounded semi-annually. E. Z. MARK. Settlement made at maturity. 9. _ ____ $1000% Stockton, Cal.,June 17, 1907. On demand after date, at three o'clock p. m., of that day, for value received I promise to pay the order of the Stockton National Bank, of Stockton, Cal. One thousavd Dollars, with interest from date at the rate of seven per cent, per annum until paid, interest to be paid quarterly, and if not so paid, to be added to the principal and bear the same rate of interest until paid: both principal and interest payable in Gold Coin of the United States. G. L. GILMORE. Settlement made December 5, 1908. 216 MODERN BUSINESS ARITHMETIC 10. /tf^^ W S What is due on the above note at maturity, the interest for the first quarter having been paid? Questions for Review 1. Define Commercial Paper and classify its subdivisions. 2. What is a Promissory Note? Write one. 3. How does a Bond differ from a Promissory Note.- 4. Describe and classify the different kinds of Paper Cur- rency. 5. Describe the following : Order. Personal Draft. Bank Check. Bank Draft. Bill of Exchange. Letter of Credit. 6. How does a Cashier's Check differ from a Certificate of Deposit ? 7. What are Indorsements, and for what purposes are they made? 8. Define : Negotiable Paper. Maker. Drawer. Payee. Drawee. 9. What is meant by "Accepting a Draft," and what is an accepted draft called ? 10. What is meant by * ' Honoring a Draft " ? By Legal Rate ? Partial Payments 777. Partial Payments are payments in part on a note, bond, or other obligation to pay. 778. The Acknowledgment of a partial payment is usu- ally made by a writing on the back of the note and is called an Indorsement. Acknowledgments of payments may also be written on a separate sheet of paper. 779. There are two methods in regular use in computing in- terest when partial payments have been made, viz : The "United States Method," and the " Merchants Method." 780. The United States Method is taken from the de- cision of the Supreme Court of the United States and prevails when appeal is made to the courts. 781. The Merchants' Method is in more common use as it is briefer and the interest more readily computed. United States Method 782. In computing interest by the United States method, the following points must be observed : 1. In computing time, find the time by compound subtraction from the date interest begins to the time of the first payment. 2. If the payment equals or exceeds the interest due, subtract the payment from the amount of the note and treat this difference as a new principal. 3 . // the interest due is greater than the payment, continue the interest on the former principal until such time as the sum of the payments exceeds the interest due, then subtract the sum of the pay- ments from the amount, and treat the result thus obtained as a new principal. 4. Find the amount of the last principal to the date of settle- ment. 218 MODERN BUSINESS ARITHMETIC EXAMPLE : Find the amount due July 1, 1908 : Indorsed as follows : SOLUTION : Face of note, first principal $600.00 Int. to Oct. 16, 1907, 3 mo. 15 ds. 10.50 Amount 610.50 Payment 40.50 Second principal $570.00 Int. on 2d prin. to Jan. 10, 1908, 2 mo. 24 ds. 7. 93 Amount 577.98 Payment 77.9.S Third principal $500.00 Int. on 3d prin. to Apr. 1, 1908, 2 mo. 21 ds. $6.75 Int. on 3d prin. to June 1, 1908, 2 mo. 5.00 Amount. Sum of payments $5.00 + $26.75 Fourth principal $480.00 Int. to July 1, 1908, 1 mo. 2.40 Amount due $482.40 PARTIAL PAYMENTS 219 783. Find the amount due at settlement of the following, the indorsements of each note will be found on page 220 : 1. 2. Settlement made at maturity. f:*V^X* ^6^to^ ^T^ " ^ /#* ja&tfdafa&}!%l _ W## /s%fot>td*^^~ ^?^<^^^^* What was due at maturity? 3. What was due January 1, 1608? 220 MODERN BUSINESS ARITHMETIC , j b 1 ) ^ *> 3 5 H \ 5 ^ ^ sj| 1 ^ ^ i ^ ^ x" ^ v \ ^ T^ ^ i ^ a PARTIAL PAYMENTS 221 4. What was due July 2, 1907? 5. What was due Feburary 29, 1908? Merchants' Method i. What was due March 10, 1908? 222 MODERN BUSINESS ARITHMETIC sS: - t 1 \/A * (5 NS V t V \ V 4 i 1 \3 V ^ 1 1 sk ^^ \ [ I \ ^ $ 1 PARTIAL PAYMENTS 223 784. The Merchants' Method of computing interest when partial payments have been made is the one used by most banks when the time to run is less than a year. 1. Find the amount of the note or debt from its date to the time of settlement. 2. Find the amount of each payment from its date to the time of settlement. 3. From the amount of the note or debt take the sum of the amounts of the payments, the difference will be the amount due. 2. What was due July 1, 1908 on a note for $600 bearing 6% dated July 1, 1907, and having the following indorsements: Sept. 16, 1907, $100.00 Nov. 13, 1907, 75.00 Jan. 10, 1908, 125.00 April 19, 1908, $200.00 3. What was due on a twelve months' note for $900 dated May 10, 1906, bearing 8% interest, and having the following in- dorsements : July 1, 1906, $240.00 Sept. 10, 1906, 324.00 Jan. 1, 1907, 180.00 Mar. 10, 1907, 120.00 4. A note for $1200 dated Sept. 1, 1907, payable in six months with interest at 7 % had the following endorsements : October 25, 1907, $150.00 Nov. 30, 1907, 300.00 Jan. 2, 1908, 450.00 Feb. 12, 1908, 210.00 What was due at maturity, interest on payments computed for the exact number of days and 360 days to the year ? 5. Payments were made on an interest bearing debt of $3300 due in one year from June 1, 1906 with interest at 9% as follows : Sept. 12, 1906, $300.00 Jan. 2, 1907, 1000.00 March 25, 1907, 1000.00 May 5, 1907, 1000.00 What was due at maturity ? 224 MODERN BUSINESS ARITHMETIC HOME WORK No. 22 785. Solve the following by Merchants' Method : 1. Find the amount due December 31, 1907, on a note for $600 drawing 7% interest, dated Feb. 15, 1907, and indorsed as follows: March 25, 1907, $150; June 1, 1907, $75; Oct. 10, 1907, $100. 2. Find the amount due at maturity of a note for $720 dated Jan. 25, 1908, payable in 9 months, with interest at 7%, and in- dorsed as follows : March 2, 1908, $225; May 5, 1908, $175; June 29, 1908, $220; Aug. 1, 1908, $75. 3. A debt of $2100 due April 5, 1907, was paid off as fol- lows: $180 on May 10, 1907; $240 on July 1, 1907; $645 on Aug. 5, 1907 ; $375 on Oct. 1, 1907. What was due December 31, 1907, interest at 6% ? 4. What is the amount due on a note for $855 dated July 5, 1908, due in one year, and bearing interest at 8%, and indorsed as follows: Nov. 10, 1908, $210 ; Jan. 2, 1909, $150; March 25, 1909, '$120; May 15,1909, $120; May 15, 1909, $100? 5. A bought a farm and gave his note for $4500 dated Sept. 7, 1907, with interest at 7^%, payable one year after date. If the following endorsements were made, what was due at matur- ity : Oct. 17, 1907, $500; Nov. 27, 1907, $500: Feb. 29, 1908, $500; April 11, 1908, $500; June 15, 1908, $500? DISCOUNT 786. Discount is an allowance made for the payment of a debt before it becomes due. 787. The Present Worth of a debt is such a sum as placed on interest for the term of discount at the given rate will amount to the debt. 788. The True Discount is the difference between the present worth and the face of the debt. 789. A Bank is an institution organized for the purpose of receiving money on deposit, making loans, discounting commer- cial paper, selling and cashing bills of exchange, making collec- tions, and in the case of national banks, issuing a paper cur- rency. 790. Bank Discount is a deduction made by a bank in buying commercial paper. 791. Days of Grace in states allowing the same are always considered when computing bank discount. NOTE In this work no days of grace are used except when especially mentioned. 792. The Term of Discount is the time from the day of discount to maturity. 793. The Collection is a sum charged by a bank for mak- ing collections on commercial paper. It is always charged on the face of the paper. 794. The Pace of the debt is the total amount due at the end of the Term of Discount. 795. The Proceeds of a collection is the amount collected less the discount, collection, protest, or other charges. 796. A Protest is a formal statement in writing made by a Notary Public giving legal notice to an indorser or maker that a note or draft has not been paid when due. 226 MODERN BUSINESS ARITHMETIC 797. Given, the Pace of the Debt, the Time, and the Rate to find the true discoimt. FORMULA : Face -*- $1.00 + (Rate X Time) = Pres. Worth. Face Pres. Worth = True Discount. EXAMPLE: What is the true discount on a bill of $284.90 due in 90 days, money worth 7% ? $284.90 -* $1.0175 = $280, Pres. Worth. $284.90 $280 = $4.90, True Discount. 798. Given, the Face of the Debt, the Time, and the Rate to find the bank discount. FORMULA : Face X Rate X Time = Bank Discount. EXAMPLE : What is the discount on a note for $600 due in 1 year, with interest at 6%, discounted at bank for 7 mo. 21 ds. at 10% ? $600 X .06 = $36, Int. $600 + $36 $636, Face of Debt. Int. on $636 for 7 mo. 21 ds. at 10% = $40.81, Bank Dis. PRACTICAL PROBLEMS 799. Solve the following : 1. What is the present worth of a debt of $245.04 due in 3 mo. 18 ds., money worth 7% ? 2. What is the true discount of a bill of mdse. amounting to $684.90 due in 2 mo. 6 ds. discounted at 8% ? 3. What is the bank discount of a note for $475 without in- terest, due in 4 mo. 24 ds., discounted at 6% ? 4. What are the net proceeds of a note for $1150 due in 1 yr. 3 mo. 18 ds., without interest, discounted at bank at 7% ? 5. What is the difference between the true and the bank dis- count of a note for $1007.60 due in 11 mo. 27 ds., money worth 5%? 6. A merchant bought a bill of goods for $1350 on 90 days time, or a cash discount of 2%. Which was preferable and how much, if money at true discount is worth 7% ? DISCOUNT 227 7. An invoice of structural steel for $22500 was billed on 6 months time, or a discount of 3% for cash in 30 days. Which would be preferable and how much, to let the bill run, or borrow money at the bank at 8 % , and pay cash ? 8. On Nov. 10. 1907, I sold at bank the following note at S% discount : $3000% Oakland, Cat., July 1, 1907. One year after date I promise to pay W. E. Gibson, or order, Three thousand Dollars with interest at six per cent, per annum. L. W. WATSON. Find net proceeds. 9. I have an account for $890.12 that must be settled. If I borrow the money at the bank, for how much must my note be drawn if it is to run 5 mo. 15 ds. discounted at 8% ? 10. Find the proceeds of the following note discounted at bank December 24, 1906, at 9% for time yet to run, paying collection $5400% Sacramento, CaL, Apiil 1, 1906. Two years after date I promise to pay Edw'd Howe, or order, Fifty -four hundred Dollars with interest at six per cent, per annum. S. J. ROBERTSON. Banking and Exchange 800. A Bank is an institution chartered by law to receive deposits, loan money, discount commercial paper, sell and cash bills of exchange, make collections, and in the case of national banks, to issue bank bills, or national bank currency. 801. There are two classes of banks, viz: National Banks and State Banks. 802. A National Bank is one that is chartered under the laws of the United States and has certain privileges not granted to state banks. 803. A State Bank is one that is chartered under the laws of the state in which it is located. 804. A Savings Bank is a bank which makes a specialty of receiving deposits, large or small, on which it pays interest. Banks of savings only, do not do regular commercial business, but loan their money only on the best real and chattel security. NOTE The methods of CREDITING INTEREST on deposits in savings banks are so various that it is needless to discuss the subject in this work except in a general way. 805. Interest on Savings is credited monthly, quarterly, or semi-annually according to the custom of the bank. 806. Interest on Withdrawals is charged for the re- mainder of the term on the amount withdrawn. EXAMPLE: A deposits $600, Jan. 1, 1908, in a savings bank which pays 4% interest on all deposits. Feb. 1, 1908, he draws out $150, and on March 1, 1908, $150. Find amount in bank at end of the first quarterly period. SOLUTION : January 1, A's deposit $600.00 January 1, 3 month's interest to April 1 6.00 Total amount of deposit and interest $606.00 February 1, 1st withdrawal $150.00 February 1, interest to April 1 1.00 March 1, 2d withdrawal 150.00 March 1, interest to April 1 .50 Total withdrawals and interest 301.50 Balance in bank $304.50 NOTE The foregoing method is only one of several but is considered one of the latest and best in computing interest on savings accounts. BANKING AND EXCHANGE 229 807. To find the amount due on a savings account, subtract the sum of the amounts of the withdrawals at the end of the term from the sum of the amounts of the deposits to the same time. 808. Overdrafts are allowed by some banks to special patrons who are charged a higher rate of interest than on ordi- nary loans. 809. Most banks charge ten or twelve per cent, on over- drafts, the charge being made on the average amount checked out. EXAMPLE : A's overdraft was $3000 on July 1st, and for 5 days thereafter. On the 7th he deposited $1000. On the 12th checks came in against him for $2400. On the 21st $4500 more was checked out. On the 27th he put in $2900. Charging 12%, what will be the interest on his overdrafts for July ? $3000 for 6 days = $18000 for 1 day 2000 for 5 days = 10000 for 1 day 4400 for 9 days = 39600 for 1 day 8900 for 6 days = 53400 for 1 day 6000 for 5 days = 30000 for 1 day Total overdraft, $151000 for 1 day so 300 $151000 Or, 1 day $151000 . ^ _ tf . n 77 , , .&% ---30 $50.33, Int. Int., $50.33 810. To find the interest on overdrafts , divide 1% of the total amount of the daily overdrafts by 30 if for 12% , by 36 if for 10% , by 40 if for 9% , and by 45 if for 8% , etc. 811. The Profits of a bank are distributed to three differ- ent accounts : 1. To the Surplus Fund. 2. To the Dividend Account. 3. To the Undivided Profits. 812. National Banks, before declaring their regular semi- annual dividends, are required to place 10% of their profits in the Reserve Fund until it equals 20% of their capital stock. 230 MODERN BUSINESS ARITHMETIC EXAMPLE : If the net profits of a National Bank whose capi- tal stock is $100000 are $5280, they may be divided as follows : 10% of $5280 $528, carried to Surplus Fund. 4% on Cap. Stock = 4000, carried to Dividend Account. Remainder = 750, carried to Undivided Profits. $5278, Total Profits. 813. Exchange is the process of making payments at a distance without actually sending the money. 814. Exchange is one of the functions of a bank in receiving the money to be paid and by issuing a Draft or Bill of Exchange on its correspondent in the distant city. 815. Collection and Exchange are the charges made by a bank for making collections on Commercial Paper, and for is- suing. Drafts and Bills of Exchange. 816. Domestic Exchange is the exchange between cities of the same county. 817. Foreign Exchange is the exchange between cities of different countries. 818. The Charges on domestic exchange are usually com- puted at a certain rate per cent, on the face of the draft, and that on foreign exchange depends upon the market quotations which may be either above or below the intrinsic value. NOTE The intrinsic value of the is $4.8665 ; of the franc, $.193 ; of the mark, $.2385. French quotations at 5.20 means that 5i francs equal $1 in United States money. German quotations at 95 means that 4 marks equal $.95 in United States money. PRACTICAL PROBLEMS 819. Solve the following : 1. Find the exchange on a draft on New York for $1244 at 2. A bank charged }i% on a draft for $760. What was the cost of the draft ? 3. The exchange on a draft on Boston was $9.15. - If the rate was /^ % , what was the cost of the draft ? BANKING AND EXCHANGE 231 4. I paid my banker $256.64 for a draft on San Francisco. If the rate of exchange was l /i % , what was the face of the draft? 5. What will a ,600 draft on London cost if the quotation is 4.87 and %% exchange is added? 6. Find the cost of a draft on Paris for 1573.20 francs if the market quotation is 5.17/4. 7. I bought a draft on Berlin for 840 marks, when the mar- ket quotation was 96. What did it cost me ? 8. A national bank has a capital of $100000. If its net prof- its are $7325.40, and it declares a dividend of 5%, what, amounts should be placed in the Surplus Fund, in the Dividend Account, and in the Undivided Profits Account ? 9. A bank with a Capital Stock of $150000, a Surplus Fund of $12500, an uncollected Subscription Account of $30000, and whose net profits at the close of the year are $18345.20, declares the highest whole rate per cent, dividend possible on paid up stock after placing 10% of the profits in the Surplus Fund. What are the total Surplus Fund, the Rate of Dividend, and the Undivided Profits ? 10. What will be A's balance at the end of a year in a savings bank that allows 4% interest on all balances and deposits, and which charges interest on all withdrawals for the remainder of each quarter? July 1, 1907, deposited $800; August 16, de- posited $400 ; September 1, withdrew $200; November 1, de- posited $500; December 24, deposited $1000. February 5, 1908, withdrew $450; April 1, deposited $300; April 18, withdrew $100 ; May 10, withdrew $150 ; June 1, deposited $120. 232 MODERN BUSINESS ARITHMETIC HOME WORK-NO. 23 1. Bought a draft on New York for $2320, paying exchange at % % . What did the draft cost me ? 2. A Chicago merchant bought a draft on San Francisco, paying exchange $3.78 at $%. What was the face of the draft ? 3. A draft on Chicago cost me $430.11. If the exchange was $1.71, what was the rate charged? 4. I paid $8502.30 for a draft on St. Louis. If the rate of exchange was }4 % , what was the face of the draft ? 5. What will a draft on Liverpool, England, for ^720 cost when the exchange is the intrinsic value plus > % ? 6. What should a draft on Berlin for 2500 marks cost if the rate of exchange is 95 ? 7. A traveler bought a draft on Berlin for 6228 marks, pay- ing $1200 for the same. What was the market quotation ? 8. The net profits of a National Bank are $14255.60. If the capital stock is $150000, and the subscription $50000, what should be the undivided profits after allowing for surplus fund and declaring a dividend of 10% ? 9. Jan. 1, 1907, A deposits $1200 ; Jan. 21, $400; Feb. 10, $200; March 15, $150. If he withdraws $500 Feb. 1, and $600 Mar. 1, what will be his balance Apr. 1, in a savings bank that pays 4% interest ? 10. What would be the balance of the above Apr. 1, 1907, if simple interest was allowed on the exact amount in the bank for the number of days it remained unchanged ? Equation of Payments 820. Equation of Payments is the process of finding the time when several sums due at different times may be paid without loss to payer or payee. 821. The quantities considered are : 1 . The Items Charged. 2. The Focal Date. 3. The Terms of Credit. 4. The Products for a unit of time. 5. The Average term of credit. 6. The Equated Date. 822. The Items Charged are the several amounts to be paid. 823. The Focal Date is a fixed date from which time is reckoned. The earliest or latest date is most convenient, al- though an} 7 date may be used for the focal date. 824. The Terms of Credit are the intervals of time from the focal date to the date each item is due. 825. The Products are found by multiplying each item by its term of credit. 826. The Average Term of Credit is found by dividing the sum of the products by the sum of the items. 827. The Equated Date is the date when all the bills may be paid in equity to both debtor and creditor. It is found by computing the average term of credit from the focal date. 828. An Account is a written statement of charges and credits together with the date and time of credit allowed each item . 829. To Average an Account is to find the time when an account may be settled in equity to both debtor and creditor. 830. Equation of payments and averaging accounts are used only by wholesalers, jobbers, manufacturers, and large concerns 234 MODERN BUSINESS ARITHMETIC where the amounts are large and interest on overdue balances is demanded. CASE I 831. To find the Average Term of Credit and the Equated Date. 1. Multiply each item by its term of Credit ', and divide the sum of the products by the sum of the items. The quotient is the aver- age term of credit. 2. Compute the average term of credit from the focal date to find the equated date. EXAMPLE: I bought goods Jan. 1, 1907, as follows: $400 on 2 mo., $600 on 3 mo., and $800 on 4 mo. What is the aver- age term of credit and the equated date ? The use of $400 for 2 mo. = $800 for 1 mo. 600 for 3 mo. = 1800 for 1 mo. 800 for 4 mo. = 3200 for 1 mo. Total Items, $1800 $5800, Total Products. $5800*H- $1800 = 3% mo., Average term of Credit. 3% mo. after Jan. 1, 1907 = Apr. 8, 1907, Equated Date. 832. Solve the following : 1. The interest on $50 for 8 mo. equals the interest on $1 for how many months ? On how many dollars for 2 mo. ? Analyze carefully. 2. The interest on $200 for 6 mo., and on $400 for 4 mo. equals the interest on $1 for how many months ? On how many dollars for 7 mo. ? 3. If I borrow $300 for 4 mo., for how many months shall I lend $200 to equalize the interest ? 4. If John borrows from James $800 for 7 mo., what sum should John lend James for 4 mo. to equalize the obligation ? 5. Find the average term of credit of $500 due in 4 mo., $750 due in 3 mo., and $1000 due in 2^2 mo. 6. I owe $140 due in 2 mo., $240 due in 3 mo., $240 due in 1 mo. When can I pay them all in equity with a single check? EQUATION OF PAYMENTS 235 7. On a debt of $2800 due in 6 mo. from Feb. 1, the follow- ing payments were made : May 1, $500 ; July 1, $600; Sept. 1, $1200. When is the balance due? 8. Find the average term of credit and the equated date of payment from July 1, 1908, of $450 due in 30 ds., $300 due in 60 ds., and $750 due in 90 ds. 9. Sold A. J. Rutherford goods as follows: June 1, 1908, $250 on 2 mo. credit; July 15, $300 on 3 mo. credit; Aug. 10, $400 on 4 mo. credit; September 12, $600 on 2 mo. credit. What is the average term of credit and the equated date ? 10. I bought merchandise as follows: Sept. 15, 1907, $100 on 30 ds. ; Oct. 10, 1907, $275 on 2 mo. ; Nov. 15, 1907, $750 on 90 ds. ; Dec. 20, 1907, $240 on 60 ds. ; and Jan. 15, 1908, $300 on 30 ds. What was due on this account March 1, 1908, if no payments had been made? Money worth 8%. CASE II 833. To find the Equated Date and the Cash Balance of an Account Current, or of an Account Sales. PRODUCT METHOD 1. Find the date each item is due, both debits and credits. 2. Multiply each item by the number of days from the focal date to the date it is due. 3 . Divide the difference of the sums of the products by the bal- ance of the items, the result is the average term of cr-edit. 4. If the balances of items and products are both debits or both credits, the equated date is found by reckoning forward from the focal date ; if one is a debit and the other a credit, the equated date is found by reckoning backward from the focal date. EXAMPLE : Find the equated date of paying the balance of the following account. Dr. B. L. Trowbridge Cr. 1908 1908 Jan. 10 Mdse. net 80000 Feb. 15 Draft 30 ds. 400 IK) Feb. 2 Mdse. 2 mo. 50000 Mar. 5 Note 60 ds. (int.) 600 00 Mar. 12 Mdse. 3 mo. 120000 Apr. 10 Note 90 ds. May 4 Mdse. 4 mo. 80000 (no int.) 900 00 236 MODERN BUSINESS ARITHMETIC Jan. 10 $800 X Mar. 16 $400 X 66 = 26400 Apr. 2 500 X 83 = 41500 Mar. 5 600 X 55 = 33000 June 12 1200 X 154 == 184800 July 9 900 X 181 == 162900 Sept. 4 800 X 238 = 190400 $1900 222300 $3300 1900 $1400 416700 222300 ) 194400 ( 139. ds. May Balance, $1400, due 139 days from January 10, 1908. 28, 1908, equated date. 834. The Interest Method may be used in finding the equated date and cash balance as follows : 1. Find the time of each item from the focal date, as in the pro- duct method, and compute the interest at i% per month on each item. 2. Divide the balance of the total debit and the total credit in- terests by the interest on the balance of items for one month at i%. The result will be the average term of credit. NOTE When a time draft or a note without interest is an item of an account, the time of such credit ends with the maturity of the draft or note. If the note draws interest, no time of credit is allowed on that item. PRACTICAL PROBLEMS 835, Find the equated date of the following 1. Dr. A. C. Jones Cr. 1907 1907 June 1 Mdse. 900 00 Aug. 1 Cash 500 00 July 1 Mdse. 400 00 Sept. 1 Cash 700 00 Sept. 1 Mdse. 1200 00 Nov. 1 Cash 1000 00 Oct. 1 Mdse. 1600 00 2. Dr. $. A. Mills Cr. 1908 Jan. Jan. Mar. Mar. 10 30 5 25 Mdse. 60 ds. Mdse. 60 ds. Mdse. 60 ds. Mdse. 60 ds. 800 600 400 700 00 00 00 00 1908 Feb. Feb. Apr. 1 29 1 Cash Cash Cash 500 500 500 00 00 00 3. Dr. EQUATION OF PAYMENTS W. W. Willis 237 Cr. 1907 1907 Aug. 1 Mdse. net 240 00 Sept. 15 Cash 300 00 Sept. 1, Mdse. 60 ds. 180 00 Oct. 15 Cash 20000 Oct. ; 1 Mdse. 30 ds. 450 00 4. Dr. B. F. Strong Cr. 1908 1908 Mar. 15 Mdse. 3 mo. 800 00 May 10 Cash 400 oo Apr. 3 Mdse. 4 mo. 900 00 July 1 Note (with int.) 500 00 May 10 Mdse. 6 mo. 1200 00 Aug. 15 Cash 600 00 5. Dr. M. I. Pronini Cr. 1907 1907 Aug. 5 Mdse. 90 ds. 650 00 Oct. 1 Cash 500 00 Sept. 10 Mdse. 30 ds. 437 50 Nov. 1 Cash 400 0(7 Nov. 1 Mdse. 60 ds. 277 50 Dec. 15 Note 60 ds. Dec. 1 Mdse. 30 ds. 320 00 (no int.) 600 00 HOME WORK-NO. 24 1. Find the equated date and cash balance Dec. 3, 1908, of the following, allowing interest at 8% : Dr. Robison & Shirley Cr. 1908 1908 Jan. 5 Mdse. 4 mo. 1500 00 Feb. 5 Mdse. 4 mo. 600 00 Jan. 15 Mdse. 3 mo. 1200 00 Mar. 1 Cash 1500 00 Apr. 1 Mdse. 60 ds. 2800 00 Mar. 24 Draft 30 ds. 3000 00 Apr. 30 Mdse. 30 ds. 2000 00 Apr. 15 Cash 1000 00 2. Average the following, and find the amount due Nov. 7, 1908, interest at 6% : Dr. Hawes & Gil more Cr. 1908 1908 I Apr. 1 Cash advanced 250 00 Mar. 10' Mdse. 4 mo. 500 00 Apr. May 15 10 Freight charges Freight charges 42 25 25 75 Apr. May i; Mdse. 90 ds. 15 Mdse. 60 ds. 400 600 (M) (M) 238 MODERN BUSINESS ARITHMETIC 3. Find the amount due Aug. 23, 1908, bank discount al- lowed on balance at 7 % . Dr. . W. Scarlett & Son Cr. 1908 1908 June 1 Mdse. 30 ds. 150 00 June 15 Cash 200 00 11 10 Mdse. net 312 50 July 1 Draft 30 ds. 300 00 21 Mdse. 60 ds. 475 50 " 15 Cash 250 00 July 1 Mdse. 60 ds. 321 75 Aug. 1 Note 60 ds. on int. 500 00 15 Mdse. 30 ds. 46225 4. Average the following Account Sales ; find when the net proceeds will be due, and find the amount required to liquidate the account on June 30, 1908, money being worth 8%. TAI,BOT J. POWERS COMPANY Produce and Commission San Francisco, Cal., June 21, 1908 E. C. ATKINSON & COMPANY, Sacramento, Cal. We render you an Account Sales of your consignment of: 2412 doz. Eggs Received May 1, 1908. 1908 SAI/ES : May 3 720 doz. Eggs .20 18 540 " " .22 June 12 360 " " - .23 20 792 " " .21 CHARGES: May 1 Freight 41 20 it 1 Cartage 14 30 21 Storage and Insurance 13 50 Commission, 10^ on sales ## ## Net Proceeds *** ** NOTE- -The date of the commission is found by averaging the sales. EQUATION OF PAYMENTS 239 5. Average the following Account Sales, find when the net proceeds will be due, and find the amount required to liquidate the account on June 10, 1908, money being worth 8% : Hollman, Kinnard & Company COMMISSION MERCHANTS Chicago, 111., April 21, 1908. C. WESTON CLARK, Los Angeles, Cal. Dear Sir : We render you an Account Sales of your consignment of: 600 boxes of Oranges Shipped via S. P. and C. B. & Q. R'y. Received March 2, '08. 1908 SALES: Mar. 3 4 5 12 15 20 80 bxs. Wash. Navels 90 's 45 " " " 126' s 36 " " " ISO's 120 " Merced Sweets 176' s 204 " do. (on 60 days) 200' s 204 " Tangerines (on 30 days) 2 2 2 2 2 1 25 50 50 40 75 CHARGES : Mar. t ( 2 20 18 12 Freight Storage and Insurance Guaranty Cash advanced Commission, 8/6 124 33 31 500 75 50 65 Statements and Balance Sheets 836. A Statement is an itemized schedule of the resources and liabilities of any firm or corporation. Statement 837. By Resources is meant all available properties or values . STATEMENTS AND BALANCE SHEETS 241 838. By Liabilities is meant the debts or obligations to pay. 839. A Trial Balance is a schedule showing the debit and the credit footings of the ledger accounts of a business. Trial Balance NOTE It will be .noticed in the above that equals the sum of the liabilities. the sum of the resources 242 MODERN BUSINESS ARITHMETIC 840. A Balance Sheet consists of a Trial Balance together with a detailed statement showing the Loss or Gain, the Inven- tories, and the Present Worth of a business. \ is S I \ ^ <\ N Q \3 ^ * > ^ S * * S ! \ \ ^ *) i <* Ns ^ ^ \ STATEMENTS AND BALANCE SHEETS 243 841. The Present Worth of a business is the difference between the sums of its Resources and Liabilities. 842. The Net Investment or Working Caital is the amount invested. 843. An Inventory is a list of goods or chattels on hand. The word inventory is also applied to a class of unpaid items ; as, unpaid rent, interest payable, etc., called liability inventories. 844. Capital Stock is the total sum which a concern may invest as its working capital. 845. Subscriptions are the amounts promised by the sub- scribers to make up the working capital. 846. Treasury Stock is the unsubscribed capital stock of a company. It is the difference between the entire capital stock and the total subscriptions. 847. To find the Present Worth, the Loss or Gain, or any Resource or Liability required. 1. From the sum of the Resources subtract the sum of the Lia- bilities, the result is the Present Worth. 2. The difference between the Net Investment and the Present Worth is the Loss or Gain. 3. The difference between the Resources and the Liabilities, in- cluding the Present Worth, will be the missing Resource or Liabil- ity. 4. To find the Gain or Loss on merchandise, or any other prop- erty account, take the difference between the total debits and the sum of the inventory and the total credits of the account. PRACTICAL PROBLEMS 848. Solve the following : 1. Separate A's resources from his liabilities, and find his present worth from the following: Cash on hand, $1974.74; Merchandise, $3777 ; Bills Receivable, $750 ; Bills Payable, $1155 ; Furniture and Fixture inventory, $225. A owes I. J. King on account $250. M. N. Long owes A on account $90. 244 MODERN BUSINESS ARITHMETIC 2. If A 's merchandise purchases amounted to $5659.50, his sales, $2427.50, and his unsold stock, $3777, what was the gain on his merchandise ? 3. Briggs's net investment was $19000. His resources at the close of the year were as follows: Merchandise, $1840.20; Cash, $4250 ; Bills Receivable, $520 ; Real Estate, $12000 ; Store Fixtures, $580.25; Accounts Receivable, $3849.75. His liabilities were: Bills Payable, $275.25; Accounts Payable, $1942.60. Find his present worth and net gain. 4. Anderson's statement of losses and gains is as follows : MERCHANDISE: Sales, $4967.20. Inventory, $1825.60. Pur- chases, $5435.40. STOCKS: Cost, $884. Sales, $928. None on hand. REAL ESTATE : Cost, $12000. Income, $450. In- ventory, $12200. FURNITURE AND FIXTURES : Cost, $320 ; In- ventory, $280. EXPENSE : General, $320. INTEREST : Paid, $122.40. Received, $245. 80. What was his net loss or net gain? 5. E. Wyckoff & Co.'s statement at the close of the year is as follows : Cash on hand, $84500 ; Merchandise inventory, $7246.50; Bills Receivable, $1200; Bills Payable, $320 ; Mort- gages Payable, $1000 ; Interest Receivable, $15.80 ; Interest Pay- able, $35.40; Accounts due the firm, $2765.75; Accounts due others, $875 ; due E. Wyokoff, private account, $750 ; Rent un- paid, $200; Insurance, prepaid $27.50. Find the firm's present worth. HOME WORK-NO. 25 1. The following are the assets and liabilities of Heitman & Hadrich at the close of the year : Cash overdraft, $1250 ; Cash in safe, $245.50; Merchandise inventory, subject to 10% dis- count, $7324 ; Notes Receivable, subject to 4% discount, $796.25 ; Notes Payable, $600 ; Doubtful Accounts Receivable, subject to 40% discount, $480; Real Estate, $12450; Mortgage on same, $5000; Books, Stationery, etc., $184.50; Fuel and Feed on hand, $97.50 ; Teams and Wagons, $685 ; Accounts Receivable, $9450 ; STATEMENTS AND BALANCE SHEETS 245 Accounts Payable, $4155.65. What is the present worth of each if Heitman's share is double that of Hadrich? 2. Find the loss or gain of the L,. Kelch Company from the following: Merchandise inventory, Jan. 1, 1907, $5840; Mer- chandise purchases, $22764.25, less rebates and returns, $324.10; present Merchandise inventory, Jan. 1, 1908, $8354.25; total sales, $25498.69, less rebates and returns, 171.40; Furniture and Fixtures bought, $276.80; Furniture and Fixtures inventory, $260; Clerks' Salaries, $1225; Advertising, $400. 3. F. B. Bill & Co.'s trial balance is as follows : Cash deb- its, $21465.40; Cash credits, $19326.10; Merchandise debits, $34596.50; Merchandise credits, $28976.15; Accounts Receivable, debits, $16350; Accounts Receivable, credits, $14366.25 ; Ac- counts Payable, debits, $ 2854.10; Accounts Payable, credits, $5820 ; Interest and Discount, debit balance, $426.30; Store, lot, and building, $3000 ; Mortgage on same, $1000 ; Insurance paid, $46.80; Expenses paid, $1640. If 10% discount is allowed on net balances due the firm, and the merchandise on hand amounts to $11438.90, what is the net loss or gain, and what is the firm's present worth ? 4. A is employed by a firm to sell sewing machines at a weekly salary of $25. He is given $32 in cash, and $312.40 in merchandise to start with. His sales for the week amounted to $288.60, and he buys and receives merchandise valued at $128. 75. If he returns $244.45 worth of merchandise to the firm, did the firm gain or lose on his week's work, and how much ? 5. I engaged with the Wiley B. Allen Piano Company to sell pianos at a monthly salary of $175 and expenses. They gave me pianos valued at $5240, cost price, and $100 expense money to start with. My report at the end of the first month was as follows : Piano sales for cash, $2160 ; piano sales on account, $1860 ; second-hand pianos taken in trade valued at $490 ; addi- tional new pianos received from the firm, $1200 ; rent paid in cash, $50 ; stenographer's service, $15 ; hauling, freight, and express, $27.25 ; pianos in stock unsold, valued at $3450. Did the firm gain or lose, and how much ? PARTNERSHIP 849. Partnership is the association of individuals for the purpose of transacting business. 850. The Firm Name is the title by which any firm, com- pany, house, or concern is known. 851. The Capital is the money, property, or other assets .invested. 852. Net Capital, or present worth, is the excess of the assets over the liabilities. 853. Net Insolvency is the excess of the liabilities over the assets. 854. Partners are the individuals composing the firm or company. 855. Partners are oifonr kinds, viz : 1. Actual and known partners. 2. Limited partners. 3. Siknt partners. 4. Nominal partners. 856. Actual Partners are those who contribute to the capital stock and whose names are made known to the public generally. 857. l/imited Partners are those whose liabilities are re- stricted to the value of the shares which they hold. 858. Silent Partners are those whose names do not ap- pear in the firm title but who share in the profits of the concern. 859. Nominal Partners are those whose names appear in the firm title, but who do not share in the profits of the business. 860. The Net Gain or Net Loss is the difference between the total gain and the total loss. PARTNERSHIP 247 861. Pour Cases are possible in finding the loss or gain of the several partners, viz : CASE I. When the investments of each partner are equal and the periods of investment are the same, the losses or gains should be divided equally. EXAMPLE : A and B each invest $2500 for 2 years and gain $4000. The shares of the gain should be equal, or $2000 each. CASE II. When the investments are equal and the periods of investment are different, the losses or gains should be divided in proportion to the periods of investment. EXAMPLE : A invests $2500 for three years, and B invests $2500 for 1 year, and their gain is $4000. A should receive $3000 and B $1000. CASE III. When the investments are unequal and the periods of investment are the same, the profits or losses shouid be divid- ed in proportion to the investments. EXAMPLE: A invests $1500 for 2 years, and B invests $2500 for 2 years, and the gain is $2000. A's share of the gain should be f of $2000, or $750, and B's share should be of $2000, or $1250. CASE IV. When both investments and periods of investment are different, the losses or gains should be divided in proportion to the products of the periods and the investments. EXAMPLE : A invests $1500 for 2 years, and B invests $2500 for 4 years, and their gain is $2600. A's $1500 for 2 years = $3000 for 1 year. B's $2500 for 4 years =_ 10000 for 1 year. A's and B's = $13000 for 1 year. A's share is T \ of $2600, or $600. B's share is \\ of $2600, or $2000. NOTE Salaries of partners may be allowed, and interest given and received on deficiency or surplus of stated capital furnished, and the profits or losses shared according to special agreement. PRACTICAL, PROBLEMS 862. Solve the following : 1. A invests $5000 ; B, $4000 ; C, $2000. If their gain is $2200, what is the share of each ? 2. Jan. 1, 1907, A puts in $1500 ; Mar. 1, B puts in $2000; June 1, C puts in $2500. At the end of the year the total gain is $1665. What is the share of each ? 248 MODERN BUSINESS ARITHMETIC 3. Brown, Green, and Black each invest $2000 in a property that rents for $1200 per year. If Brown sells out to Green at the end of six months, what should be the share of each in the year's income? 4. A, B, C, and D invest in a manufacturing plant. At the close of the year, A's share of the gain was $3240 ; B's, $2700 ; C's, $2430, and D's, $1890. What was the investment of each, if. the total capital was $38000 ? 5. Adams, Brown, and Cook formed a partnership Jan. 1, 1908, and invested and withdrew as follows: Jan. 1, 1908, Adams invested $800 ; Brown invested $600, and Cook invested $400. April 1, Adams invested $1000; July 1, $400, and Oct. 1, withdrew $500. May 1, Brown invested $1200; Sept. 1, $600, and Nov. 1, withdrew $1000. June 1, Cook invested $400; Aug. 1, $400; Oct. 1, $400; Dec. 1, $400. If their total gain is $2395, what should be the share of each partner ? HOME WORK (Final) 1. Kelch, Mize, and Holmes were associated in business for 3 years. Kelch invested $8000; Mize, $10000, and Holmes, $12000. They agreed to organize on a basis of $10000 each, and to pay 6% interest on deficiencies, and accept 6% interest on surplus. At the beginning of the second year, Kelch puts in $3000 ; Mize, $2000', and Holmes, $5000. At the beginning of the third year Kelch puts in $2000 ; Mize, $1000, and Holmes draws out $10'000. If the total gain of the firm is $4980, what is the present worth of each partner at the end of 3 years ? 2. Wheeler, Wyckoff, and Willis are partners. Wheeler in- vested $2000 in cash and $4500 in merchandise. Wyckoff in- vested a note for $6000 due in one year with interest at 8 % , and cash, $1000. Willis invested merchandise valued at $5000 and furnished the store building for which he was to receive $75 per month rent. Wheeler's salary as manager was $1500, Wyckoff s $1200, and Willis's $1000 per year. After all expenses were paid they agreed to share the gains or bear the losses equally. Find the present worth of each partner at the end of the year if the total gain was $10030. PARTNERSHIP 249 3. Snow invests as follows: Cash, $1200; Merchandise, $2200: Bills Receivable, $840; Bank Stock, $1000; Interest Receivable, $260, and is to receive $600 per year salary. Frost invests : Cash, $500 ; Store and Fixtures, $3000, subject to a mortgage of $1000 at 6% interest; Merchandise, $1800; Notes Receivable, $1300; Accounts Receivable valued at $1250, sub- ject to a 20% discount for bad debts ; and is to receive a salary of $800. They agree that the one investing the least amount of capital shall pay the other 6% on one-half his surplus. Find the present worth of each at the end of the year, if the total gain of the business is $3800 and they divide the net gain equally. 4. R. L,. and L. S. Goodyear are partners under the firm name of Goodyear Bros., and are dealers in rubber materials of all kinds. R. L,. invests $12000, cash, and L. S. invests the en- tire contents of his store, valued at $10000. They agree that each partner shall receive 7% per annum on his investment, and that all withdrawals in excess of $100 per month salary shall be charged to private account of the partner withdrawing the same. At the end of the year, their statement is as follows : Merchandise sales, $78450 ; Merchandise purchases, including original stock, $87300 ; Merchandise on hand, $15550 ; Sundries losses, $320 ; Expenses, not including salaries, $750. R. L,. Goodyear has $580, and L,. S. Goodyear has $340 charged to his account. Find the net gain, which is divided equally, and pres- ent worth of each partner at the end of the year. 5. Heald and Ingram form a co-partnership. Heald invests store and lot, $22000, subject to a mortgage of $7000 bearing 6% interest; accounts against H. E. Cox for $2400, J. H. Jan- son for $1525.75, and H. L. Gunn for $834.40; Cash $1840. He also owes W. E. Gibson on account, $524.50, and an unpaid note in favor of First National Bank for $6000 bearing 7 % int- erest, on which there is accrued interest, $75.65, which liabili- ties the firm assumes. Ingram invests Merchandise, $8425.60; Notes Receivable, $3271.90, on which there is $148.20 accrued interest; accounts against O. B. Parkinson for $380.40, Edw'd Howe for $1135.50, J. R. Humphreys for $576.75, and L. W. Zinn $650 ; and cash sufficient to equalize their investments. 250 MODERN BUSINESS ARITHMETIC Before opening the store for business, L,. A. Jordon offers to buy a one-third interest in the firm by giving to each of the partners his note for a sufficient sum to equalize their investments, which offer is accepted. At the end of the year the sales of Merchan- dise amounted to $135420, the purchases were $142375.50, and the inventory of goods on hand was $23245.60. After paying running expenses $1245, interest on mortgage and on note held by the First National Bank, what was each partner's present worth at the end of the year ? ANSWERS Article 49 3. $1806 Article 163 1. 2. 3. 4. 5. 6. $5155.11 231851 mi. $41135.60 751045 ft. 7373736# $543811.50 4. 5. 6. 7. 8. $2668 $435 $315 13 boxes $1408 A's $704 B's $352 C's 706 acres 1. 2. 3. 4. 5. 6. 217i yds. 672-j^ acres 226J yds. 16J and 11| 9. 205000 7. $130} Article 50 10. $208 8. $3785^jj- 1. 2. 3. $161416.75 $92774.50 ' $148198.84 1. Article 129 72 9. 10. $1009| $277HB's $3845| C's $8962| total . 5. $5480316.50 2. 3. 1056 12 11. 12. $3 4 1785 13. tfggJL. Article 64 5. -L 1 O*-J 13ft. 14. $151646A 1. $5881.30 5892 15. $725iJ 2. $9580.95 6. $227.50 3. $1028.50 7. $126 Article 174 4. 5. $6494 $2800.50 8. 9. 5 9 11 140 ft. 3696 gal. 1. 2. $2100 $2800 $9600 Article 95 10. 57 gal. 37 59 67 3. 4. $1500 Vs of estate 1. $5330 5. $420 Jones 2. 3. $155.66 $93.75 Article 131 $1260 Brown $3150 Green 4. $7198.75 1. 11 tons 6. $600 5. $8 1.25 lost 2. 64 brls. 7. $3600 6. $29103.75 3. 13 crates 8. $240 Muir 7. $382.44 4. $2.80 $320 Nunn 8. $4500 ' 5. 144 bu. $360 Hakes 9. $61766 6. 160 bu. 9. 46% doz. 10. $264.60 7. 7 chests 10. $16080 8. 49 yrs. 98 yrs. $6432 shoes Article 107 9. 10. 50 yds. $3920 groceries $2880 tea 1. 580 100 yds. $2260 hay 2. $115 200 yds. 252 MODERN BUSINESS ARITHMETIC Article 198 3. $67.50 Article 251 1. 196 acres 4. 10i ds. 50 j 1. 3p.m. 2. 789. 15 chains 3. 339.05 acres 4. $922.92} 5. 606. 66i acres d as. 6. 6 weeks 7. 2| ds. 8. 2976 mi. 9f\ 2. 4 a. m. 3. 6 p. m. 4. 4:48 p. m. 5. 9 a. m. 6. $70.43| 7. 107 bu. y men 10. 16200 Ibs. Article 252 8. 135 Ibs. 9. 309 bu. Article 248 1. 55 10. 330.925 mi. 1. 32 marbles 2dtO 2. 5i 5 T past 1 3. 27 1\ past 5 Article 222 1. $290.94 5M 3. $100 4. $4.95 4. 49 iV past 3 5. 21 T 9 T past 4 2. $535.75 3. $3220.39 5. $39.60 6. 81 Article 253 4. $1595.35 7. 15 yrs. 1. 72 in. 5. 1951.20 8. 14 and 21 2. 54 in. 9. I 3. 80 ft. Article 224 10. 360 ft. 4! 32 ft! 1. $183.80 5. 120 ft. 2. $724 Article 249 3. $750 4. $4468.75 5. 1 10 bu. barley 220 bu. wheat 440 bu. corn. r. $60 A's $150 B's 2. $210 A's $280 B's Article 254 1. 16 yrs. 2. 16 yrs. 36 yrs. 3. 42 yrs. 70 yrs. $350 C's 4. 5 yrs. 15 yrs. Article 232 3. $135 Jones $144 Brown 5. 18 yrs. 36 yrs. 1. $51.98 2. $412.65 $126 Smith 4. $294 White Article 255 3. $49.28 $336 Green 1. 25^ A 4. $705.30 $140 Black 10^ B 5. $582.25 5. $140 3 mo. 2. 40 mi. 6. $614.80 7. $1144.50 $900 3. 300 yds. 4. $135 8. $1006.21 9. $983.25 Article 250 5. $5.09| A $2.90f B 10. $537.86 1. Ifds. Article 247 2. 2| ds. 3. 37i ds. Article 381 1. $132 4. 7i ds. 1. 1027s. 2. $27 5. 21 ds. 2. 13958 far. ANSWERS 253 3. 3 Id. 6. $864 5. 14 bbls. 4 gal. 3 4. 45164 far. 7. $3220 qt. 1 pt. 3 gi. 5. /3S 19s. 8d. If. 8. $55.38 6. 33| bbls. 6. lOOd. 9. 16800# 7. 240 bottles 7. 696 far. 336 bu. barley 8. 144 bottles 8. /3 10s. 5d. 3 f. 300 bu. flaxseed 9. $33 9. $245.88 280 bu. wheat 10. 90^ 10. ^1172 10s. 525 bu. oats 10. $945 Article 388 Article 382 Article 385 1. f 3 7904 1. 32.4 francs 2. IH26385 2. 4200 centimes 1. 357 drams. 3. mll09315 3. $409.74 2. 9355 gr. 4. O5f5lOf34ml6 4. 5. 11000 fr. 5043.05 fr. 3. 4. 58 56 92 gr.5 43 Ibs. 57 3292 5. Cong. 15 07 f5l5 f36 6. 42.8 marks 5. 280 capsules 6. 1408 bottles 7. 7500 pf . 6. 3 Ibs. 37 36 7. Cong. 23 O2 8. $62.13 7. $43.75 8. $1.05 9. 11000 marks 8. $184.80 9. $44 10. 386 marks 9. 4800 doses 10. 4032 bottles 10. $52.68 Article 383 Article 386 Article 389 '1. 1340 pwt. 1 8-A- 1h<; 1. 189 qts. 2. 3. 4. 5. 19570 gr. 98374 gr. 12 oz. 37 Ibs. _L . 2. 3. 4. 3lT -lus. 12H Ibs. 12 Ibs. 51 36 92 10 Ibs. 105 43 1 rv ~ 2. 3. 4. 5. 1111 pts. 1102 pts. 2bu. 900 bu. 1 pk. 7 6. 7. 8. 9. 10. 6 Ib. 1 oz. 5 pwt. 19 gr. $14 40 spoons $85 $1189.02 5. 6. 7. 8. 10 gr. 21 Ibs. 6 oz. 16 pwt. 26 gr. Feathers 1240 gr. Gold 42^ gr. Lost $106.25 6. 7. 8. 9. 10. qt. 1 pt. $11.52 $3 18 bu. $5.72 $4.65 9. $85.83 Article 384 10. $5.17 $6.20 Article 390 1. 2. 9212 oz. 5648 Ibs. Article 387 1. 2. 1795 in. 67082.4 in. 3. 1.6 cwt. 1. 47 pts. 3. 942636 in. 4. 18 T. 7 cwt. 28 2. 3745 gi. 4. 1 mi. 1 fur. 2 yd. Ibs. 2 oz. 3. 8964 gi. 1 ft. 5. 13 T. 4. 9 bbls. 5. 4 mi. 38 ch. 241. 254 MODERN BUSINESS ARITHMETIC 6. $11200 Article 394 Article 410 7. 10725 ft. 8. 2610 mi. 1. 4545 ds. 1. 1 hr. 6 min. 17 9. $382.80 2. 72740 min. sec. 10. 306662.4 times 3. 67 ds. 12 hrs. 2. 51min.32if sec. 4. 15 ds. 12 hr. 59 3. 8 hr. 58 min. 14 Article 391 5. min. 42 sec. 41760 min. 4. sec. a. m. 5 hrs. 9 min. 1. 7128 sq. in. 6. 86400 sec. 56i sec. p. m. 2. 59553 sq. yd. 7. 161 ds. 5. 10 hrs. 12 min. 3. 104684 sq. ft. 8. 129600 times 25 sec a. m. 4. 11 sq. yd. 29 sq . 9. 2 yrs. 6 mo. 18 6. 121 30' 15" in. ds. 7. East 5. 45.21875 acres 10. 6 mo. 10 ds. 23 11' 15" 6. $1642.67 8. East, Cincinnati 7. $240 8. $177.78 Article 395 9. 8 hr. 36 min. 56 sec., or 15 hr. 9. $6050 1. 26670" 23 min. 4 sec. 10. $452.60 2. 165054" 10. Gain 10 hr. 58 3. 358 5' min. 37 sec. Article 392 4. 127 11' 4" Also one whole day in calendar caused by 1. 2560 acres 5. 6. 10028. 2 mi. 2665180 sec. crossing the Interna- tional Date Line. 2. 10 acres 3. 257500 sq. 1. 7. 2903| mi. A r\Q Article 413 4. 1 sq. ch. 11 sq. rd. 467 sq. 1. 5. 360 sq. ch. 8. 9. 10. 40 24897.6 mi 66 7' 30" 1. 2. 3. 5s. 7d. 2 far. 7s. 4d. 2 far. 3 yd. 7-J in. 6. 64| acres , 7. 40 acres Article 396 4. 1 fur. 38 rds. 2 yds. 7.2 in. 8. $2800 9. $10000 1. $43.20 5. 6 oz. 10 pwt. 12 gr. 10. $156.25 2. $36 6. 7 cwt. 30 Ib. 12 3. $6.375 oz. Article 393 4. 40 yrs. A 7. 240 acres 1. 29508 cu. in. 60 yrs. B 8. 14 gi. fU.-4 r\ ** 2. 697 cu.'ft. 3. 1536 cu. ft. 5. 20 yrs. C 36 yrs. James 9. 10. $1.2o 1234.5 sq. links 4. 30 cu. ft. 5. 497664 cu. in. 6. 48 yrs. Henry 960 sheets Article 415 6. $76.80 7. $27 1. iV gal. 7. 9 cords 8. $1.92 2. A yd. 8. $39.27 9. 10000 sheets 3. Tib bu. 9. 123354 bricks 10. 5000 booklets 4. yj* mi. 10. $84270 16 pp. each 5. .0225 ton ANSWERS 255 6. .0075 ds. 3. 174 gal. 2 qt. 3. 32206.30^ sq, .ft. 7. leu mark 4. 5752 bu. 2 pk. 4. 50.93 acres. 8. J6.016J 5. $75.26 5. 12880.56 sq. ft. 9. A 10. 12 yrs. 27 yrs. Article 428 Article 468 Article 417 1. 35 A 90 sq. rds. 1. 624 sq. ft. 1. rd. 9 sq. yds. 6 sq. ft. 57 sq. 2. 3. 263.9 sq. in. 3.1416sq. ft, 2. .8775 cwt. in. 4. 706.86 sq. in 3. .671875 bu. 2. 5 11s. Id. 1 5. $14137.20 4. .3125 sq. yd. far. 5. 6. H i hhd. 3. 7 gal. 2 qt. 1 pt. if gi. Article 480 7. vo^B 4. 243 bxs. 1. 48 cu. ft. 8. .0325 cwt. 5. 150 farms 2. 35937 cu. in. 9. .05009375 3. 1331 cu. in. 10. .6375 Article 457 4. 5. 216 gal. 384 bu. Article 420 1. 116} sq. rds. 1. 20 cwt. 2 Ib. 14 2. 850 sq. ft. Article 482 .2. oz. 11 da. 23 min. 5 sec. 3. 4. 5. 31 sq yd. 316 sq. yd. 1100 sq. yd. 1. 2. 100 cu. ft. 16200 cu. ft. $5103 3. 4. 27 yd. 1 ft. 3 hhd. 1 bbl. 23 Article 459 3. 4. $4640 150 cu. in. 5. gal. 1 pt. 1 gi. 29 Ib. 35 53 11 1. 2. 102 sq. ft. 400 sq. ft. 5. 11309.76 cu. in. gr. 3. 80 sq. ft. Article 484 Article 423 4. 5. 2}| acres $14832.28 1. 75 cu. ft. 1. 10 rd. 3yd. 2ft. 2. 20800 cu. ft. 2 in. Article 461 3. 2261. 952 cu. ft. 2. 3. 3 pk. 2 qt. | pt. 25 cd. 5 cd. ft. 1. 336 sq. ft. 4. 5. 9629-B cu. ft. 93i board ft. 12 cu. ft. 2. 147 sq. ft. 4. 5. 31 gal. 3 gi. 135 A 4 sq. ch. 3. 4. 5. 125 A 682 sq. ft. 378 sq. ft. 1. Article 485 33.5104 cu in Article 427 2. 523.6 cu. ft. Article 463 3. 65.45 cu. in. 1. 1 mi. 3 rd. 1 yd. 4. 268,083,200,000 1 ft. 8 in. 1. 7854 sq. ft. cu. mi. 2. 44 bu. 5 qt. 2. 314.16sq. yd. 5. 202. 1096 cu. in. 256 MODERN BUSINESS ARITHMETIC Article 486 Article 504 1. 16 tons 1. 186.01 bu. 2. 108 sq. rd. 2. 3456 bu. 3. 16 Ibs. 3. 3 ft. 2 in. 4. 6f hrs. 4. 10 ft. 3 in. 5. 259i Ibs. 5. $1440 Article 489 6. 628 T 4 T gal. 7. 68.39 bbls. 1. $24.60 8. 270 gal. 2. $30.49 9. 50.49 bbls. 3. $80.75 10. 20 ft. 4. $92.11 5. $74.08 Article 513 6. $68.04 1 R Q 7. $139.01 X U O 9 3fi 8. $28.33 . OU 1 1 9. $40 O. 9 4. Q 10. $363.33 or $356.53 by cut- T-. t/ 5. 245 6 10 ting strips 7: It Article 494 8. 21J 1. $51 10 TTT 2. $40.50 *v go 3. 8280 bricks 4. $131.71 Article 521 5. $269.64 1. 30 6. $86.40 2. 30 7. $57.82 3. 84 8. $112.48 4. 76 9. $466.22 5. 8 10. $836.14 6. 119 Ibs. Article 499 7. 5f bu. 8. 4 ds. 1. 4-I-, cords 9. 2 men 2. 7* cords 10. 20 men 3. 134 ft. 4. 560 ft. Article 525 5. 25i feet 6. $408.24 1. $4.50 7. $121.50 2. 96 horses 8. $219.28 3. 96 sheep 9. $198 4. $47.50 10. 26280 shingles 5. 8 mo. 6. 220 rods 7. 1600 books 8. 21504 bricks 9. 10 men 10. 8 men Article 543 1. $21 108 Ibs. 2. 180 bu. 280 tons 3. 117 hrs. $259 4. $129J- 5. $2700 6. $4140 7. $800 8. $2250 9. $625 10. $18000 Article 545 1. 50% 25% 2. 24% 20% 3. 400% 300% 4. 80% 90% 5. 6. 7. 8. $1584 32% 9. 20% 10. 75% Article 547 1. 576 429 2. $2520 $1372 3. 192 ft. 4. $1101.82 5. $7500 6. $355 7. $1500 8. $50000 9. 42 gal. 10. 700 head ANSWERS 257 Article 549 1. 80 96 2. $200 $360 3. 546 sheep 4. 75 marbles 5. $800 6. $13500 7. 700 acres 8. $570 9. $35 10. 11000 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Article 559 $100 15^ per bu. $250 $240.63 $208.25 $54 $1875 $2385 $39.90 $1745.05 Article 561 1. 25% 2. 25% 3. 18% 4. 43 J% 5. 30% 6. 1U% 7. 25% 8. 47H% 9. 20% 10. 100% Article 563 1. $50 2. $700 3. $3240 4. $1960 5. $4900 6. $20 5. $2225 7. $1927.50 6. $24 8. $270 7. $437.50 9. $2000 8. $580 10. $100000 9. 18|% 10. 16% Article 565 Article 600 1. $25 2. $336 3. $1333i 4. $106.66f 5. $1480 6. $560 7 ftfi 1. $36 2. $106.50 3. $57.50 4. $1347.84 5. $152.77 6. $425.36 / . fl5U 8. $32 lost 9. $2835 10. 60% 7. $3229.20 8. $876.02 9. $422.60 10. $1872 Article 576 Article 602 1. $375 1. 2% 2. $735 2. 6% 3. $900 3. 2i% 4. $2700 4. 124% 5. $540 5. 2f% 6. $1120 6. 3% 7. $576 7. 5% $480 8. 4% $432 9. 4i% $384 10. 6% $212 $288 8. $1157.62 Article 604 9. $495.72, 8 ds. $523.26, 20 ds. 1. $7000 $550.80, 40 ds. 2. $4940 10. 50, 20, and 10, 3. $223.10 better by l\ % 4. $1420 5. $1450 Article 579 6. $2569.75 $3208.40 1. $350 7. $601.60 2. $735 8. $692.23 3. $840 9. 48225 Ibs. 4. $1337.50 10. $2850 258 MODERN BUSINESS ARITHMETIC Article 606 4. 6J% 6. $1750 5. 120 shares 7. $1485240 1. $540 2. $17240 6. $7515 7. 6's at 120, 8. $209.50 .0115+ 3. $922.40 $180 9. $859.04 4. $20.70 8. $195 increase 10. $10000 5. $12560 6. $1973.79 7. $32. 85 gain 8. 1550 Ibs. 9. 204347# Island 235600# Ala. $82.75 surplus 9. $4 decrease $8.75 surplus 10. $17820 Mich. 6 $35640 Ohio 5' Article 696 's 1. $58.10 s 2. $173.84 3. $152.10 10. $5200 $4750 Article 651 4. 540.76 5. $2160 Article 634 1. $160200 6. $3082 ffaf* S\ f\ 2. $325000 7. $246 1 . $600 2. $20.50 3. $1024 4. $392 5. $4500 $75 6. $345 7. $8352 3. $36800 4. $189 5. $45.80 6. $209.75 7. $562400 8. $385952.85 9. $126.40 8. 27 yrs. 9. $2000 10. '65 yrs. Article 713 1. $.1725 8. $308 2. $37.60 9. $560 10. $5500 $495 Article 669 3. $243.38 4. $187.68 1. $460 5. $448.25 Article 636 2. $974.50 6. $782.25 3. $128 7. $2660.97 2-| -t /T/ 4. $604.45 8. $825.84 . 11% 31 rrt 5. $2394.33 9. $574.56 . i% 6. $17374.85 10. $1125.25 4. 4-|% 51 /7^ 7. 20% 8% 6. 8}% 7. 7% $3750 8. $4151.66 9. $1116 10. $2160 Article 719 1. $1.88 8. 15J% 9. 12% $1210.68 $4320 2. $.79 3. $11.09 10. 7% Article 686 4. $32.50 .ji/irr ^7O 5. $67.73 Article 638 1. $15 6. $5.27 2. $37.50 7. $3.97 1. 320 shares 3. $31.50 8. $11.97 2. $29835 4. $1928 9. $45.79 3. $8883.75 5. $4500 10. $2.56 ANSWERS 259 Article 721 4. $672 10. $764.19 1. $37500 2. $720 3. $1200 4. $540 5. $280 5. $4050 6. $1277.50 7. $2250 8. $4800 9. $7500 Article 776' 1. $878.04 2. $1270.89 6. $600 10. $12000 3. $455.77 7. $1200 4. $2124.83 8. $500 Article 732 5. $651.17 9. $19500 10. $24003 1. $3.96 2. $8.82 6. $587.26 7. $3513.60 8. $2701.22 Article 723 3. $2.88 4. $8.47 9. $1107.17 10. $1006.72 1. 6% 5. $7.40 2. 8% 3. 8% 6. $32.55 7. $26.04 Article 783 4. 8% 8. $81 1. $711.55 5. 1% 9. $160.80 2. $1376.08 6. 8% 10. $28.80 3. $303.27 7. 8% 4. $568.87 8. 4^% Article 737 5. $363.85 9 4% ^ ^r // 10. 7|% 1. $268.92 Article 784 2. $543 Article 725 3. $422.03 4. $1335.36 1. $701.80 2. $122.44 1. 8 mo. 5. $101.76 3. $67.48 2. 77 ds. 6. $164.56 4. $117 3. 45 ds. 7. $931.35 5. $216.10 4. 7 mo. 6 ds. 8. $35.28 5. 4 mo. 21 ds. 9. $465 Article 799 6. 1 yr. 3 mo. 15 10. $1058.83 ds. 1. $240 7. lyr. 5 mo. 3 ds. Article 742 2. $9.90 8. 2 yr. 3 mo. 18 ds. 1. $74.16 3. $11.40 4. $1045.35 9. 312 ds. 2. $262.48 5. $2.36 10. 6 mo. 3. $704.25 6. Cash discount 4. $1256.86 $3.78 Article 727 5. $238.91 6. $2088.44 7. Let bill run $52.50 1. $240 7. $4850.45 8. $3016.76 2. $310 8. $129.76 9. $924 3. $436.20 9. $311.64 10. $5342 MODERN BUSINESS ARITHMETIC Article 819 6. In 2 mo. 4. $1814.80 gain 1. $3.11 7. 7 mo. 24 ds. after 5. $8909.65 2. 3. 4. 5. $760.95 $7329.15 $256 $2929.31 8. 9. Feb. 1, or on Sept. 25th. 66 ds. Sept. 5 88 ds. Oct. 28, 1 QH& Article 862 1. $1000 A 6. 7. $304 $201.60 10. ItJUo $1677.58 $800 B $400 C 8. $732.54 Article 835 2. $12000 A $5000 $10000 B $1592.86 1. July 7, '07 $9000 C 9. $14334.52 13% 2. June 18, '08 $7000 D $910.68 3. Oct. 18, '07 3. $200 Brown 10. $2288.75 4. Oct. 30, '08 $600 Green 1. Article 832 400 mo. $200 5. July 19, '07 Article 848 $400 Black 4. $540 A $600 B 2. 2800 mo. $400 1. $5411.74 $525 C 3. 6 mo. 2. $545 5. $975 A 4. $1400 3. $21812.35 $860 B 5. 3 mo. $2812.35 $5600 236567