FEW YORK: x^ rVames Wafl Paper kc. THE PUBLICATIONS OF "TrrTN, BLAKEMAN, TAYLOR k CO. THE AMERICAN EDUCATIONAL SERIES OF School, and College Text-Books. THE Union Leaders, Spellers, Primer, and Speaker, By PROF. CHAKI.es W. SANDERS. Conforming entirely to Webster'* New lUustrated and Revised Dictionaries. f^umber Three. I Number Four. R, Number Five. IeR, Number Six. OF ENGLISH WORDS. ES, <^c. ban and English Primer. t Reader. ind Reaxier. ^ Reader. rth Reader. \ Reader. I-School Reader. ng Ladies' Reader. lol Speaker. imatics. Ichools, Academieg, and arly half 'rigonometry. separate. Btrj, separate, netry and Conic Sections. fJavigation. Integral Calculus. Itarj Astronomy. 1- in Geometry. for the use of Teachers lONABY. 12. ipringfield, Mass. WEBSTER'S SCHOOL DICTIONAEIES. Richly and Prefurely Illustrated and Embellished with Woodcuts, assisting immeasurably in the d«Smtioa of the words under which they <3Ccur. Webster's Primary^Sehool Dictionarys Webster's High^School DictionaTy. 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BEING A SEQUEL TO THE PROGRESSIVE PRIMARY ARITHMETIC, CONTAININQ MANY ORIGINAL FORMS OF ANALYSIS APPLICABLE TO A GREAT VARIETY OF PRACTICAL QUESTIONS, AND DESIGNED FOR THE MORE ADVANCED CLASSES IN COMMON SCHOOLS AND ACADEMIES. EDITED BY DAIS^IEL W. FISH, A.M. ]S^EW YOKK : IYISOjS", BLAKEMAN, TAYLOK & CO. 47 & 49 Greene Street. PHILADELPHIA: J. B. LIPPINCOTT & CO. CHICAGO: S. C. GRIGGS & CO. 1870. KO B IN S O N'S ^ Tlie most Complete, most Practical, and most Scientific Series of Mathematical Text-Books ever issued in this country. » » » » » Kobinson's Progressive Table Book, - - . - - Rooinson's Progressive Primary Arithmetic, - Robinson's Progressive Intellectual Arithmetic, - Robinson's Rudiments of "Written Arithmetic, Robinson's Progressive Practical Arithmetic, Robinson's Key to Practical Arithmetic, - - - - Robinson's Progressive Higher Arithmetic, - - - Robinson's Key to Higher Arithmetic, - - - - - Robinson's Arithmetical Examples, Robinson's New JEllementary Algebra, Robinson's Key to Elementary Algebra, - - - - - Robinson's University Algebra, ------- Robinson's Key to University Algebra, • - - - - Robinson's New University Algebra, - . - - - Robinson's Key to New University Algebra, - - - - Robinson's New Geometry and Trigonometry, - - - Robinson's Surveying and Navigation, Robinson's Analyt. Geometry and Conic Sections, Robinson's Diflferen. and Int. Calculus, (in prepai?tion,)- Kiddle's New Elementary Astronomy, Robinson's University Astronomy, Robinson's Mathematical Operations, . - - - - Robinson's Key to Geometry and Trigonometry, Conio Sections and Analytical Geometry, . - - - - Entered, according to Act of Congress, in the year 1S58, and again in the year 1S63, by DANIEL W. FISH, A.M., Ib the Clerk's Office of the District Court of the United States for the Northern District of New York. PREFACE. The importance, and the practical benefit to be derived from the studv of Intellectual Arithmetic, not only as a prejjaration for busi- ness' life, but as a means of developing and slrengthenmg the thinking and reasoning powers, and of thorough mental culture, can not" be over-estimated. Not only is it a necessary study tor young pupils, but indispensable to the more advanced student, as a preparation for the prompt and accurate business man. And it is believed that, as a general rule, the most critical, correct, and ready students of mathematics are those who have been most thoroughlv drilled in intellectual arithmetic. This work has been prepared more especially for advanced classes, and is designed for those who have first been well taught in the primary book, and for such as are pursuing the study ot written arithmetic, or algebra, and who have never been thoroughly exer- cised in this branch of study. Only a few of the manv points of difference between this and other similar works, and which, it is believed, renders tins superior to them, will be referred to. It is more complete, comprehensive, and progressive in its char- acter. The arrangement and classification are more strictly sys- tematic, and in accordance with the natural order of mathematical science. The development of principles, and their a j) plications, are shown by a more numerous selection, and greater yarietv of appropriate examples, progressively arranged, commencing with those that are simple and easy, and advancing to those more com- plex and difficult. At intervals, and especially in the closing sections of each chap- ter, examples are given containing such a combination of principles, and forms of analysis, as to require a knowledge of almost every principle previously taught, thus affording the pupil a thorough review, as well as requiring him to classify his knowledge of what he has been over. One of the most important, and, it is thought, one of the most original and useful features of this work, is the full, concise, and uniform system of Analysis it contains, — the result of long expc rience in the school-room. Particular attention is invited to the subjects of Fractions, Per' centage, and Interest ; their treatment is peculiar, and adapted to obviate many of the difficulties, and greatly abbreviate most of the operations in them. (S) 4 PREFACE. The chapter of Miscellaneous Examples will afford a valuable and thorough drill to the advanced student of arithmetic ov alge- bra. They contain a great variety of principles, and while they may be considered difhcult, yet the full analysis given of every principle, and the selection of numbers so adapted to the conditions of the question as to produce results free from large and difficult fractions, will render a mental solution of them comparatively easy. In conclusion, we may be allowed to express the belief, that in this work the thorough teacher Avill find a desideratum long sought in this department of science, — the means of mental dis- cipline and development such as has been furnished by no similar treatise. THE AUTHOR. SUGGESTIONS TO TEACHERS. Pupils of nearly the same degree of advancement should be classed together. Regular exercises should be assigned to the class, and sufficient time allowed them to thoroughly examine their lesson before being called upon to recite. The use of the book at the time of recitation should be strictly prohibited, except, perhaps, in some of the more difficult lessons in the latter part of the work. Each example should be read but once, slowhj and distinctly, the pupils called upon promiscuously, who should arise, stand erect, repeat the example, and then give the analysis. This will secure close attention. Every question should be clearly and tliorougldy analyzed, and the pupil required to adhere strictly to t}\e forms of solution given, unless better ones can be substituted ; and in no case should he be allowed to omit the conclusion, commencing with " Therefore." The class should be encouraged to detect and correct errors in statement or analysis, to criticise and make proper inquiries, all of which should be signaled by the uplifted hand. It is suggested that the class be occasionally exercised upon " Ringing the Changes," as explained in the Appendix, and which niay be applied to a great number and variety of exami)les. It will not only afibrd a valuable diill, but a pleasant and enlivening exercise. INTELLECTUAL ARITHMETIC. CHAPTER I. ADDITION. 1. 1. James had 1 cent, and his father gave him 1 more ; how many had he then ? 2. If a slate pencil cost 2 cents, and a steel pen 1 cent, how many^ cents will both cost ? 3. George spent 2 cents for candy, and had 2 cents left ; how many cents had he a,t first ? 4. A farmer sold a calf for 3 dollars, and a pig; for 2 dollars ; how many dollars did he receive foi.' both? 5. Mary gave 2 cents for some tape, and 5 cents for a thimble ; how many cents did she give for both ? 6. Martin gave John 3 apples, and kept 4 for him- self ; how many apples had he at first ? 7. There are 4 books on one desk, and 2 books on another ; how many books on both desks ? 8. If a lemon cost 3 cents, and an orange 5 cents, how many cents do both cost ? 9. In a certain class there are 5 girls and 4 boys ; how many pupils in the class ? 10. Samuel had 3 marbles, and his brother gave him 3 more ; how manv did he then have ? 11. Bought a barrel of apples for 2 dollars, and a cord of wood for 4 dollars ; how many dollars did both cost ? 1* (5) 6 INTELLECTUAL ARITHMETIC. [S. 3. 1. 1 and 1 are how many ? 2. 1 and 2 are how many ? 3. 2 and 2 are how many ? 4. 2 and 3. are how many^ 5. 2 and 4 are how many ? 6. 2 and Jx^ are how many ? 7. 2 and 6 are how many ? 8. 2 and 7 are how many ? 9. 2 and 8 are how many ? IjP. 2 and 9 are how many ? 11. 3 and 3 are how many ? 12. 3 and 4 are how many ? 13. 3 and 5 are how many ? 14. 3 and 6 are how many ? 15. 3 and 1 are how many ? 16. 3 and 8 are how many ? 17. 3 and 9 are how many ? .| 18. 3 and 1$^ ar(^ how many ? >«8|\ 19. 4 and 2 are how many?.. 20. 4 and 3 are how many ? 21. 4 and 4 are how many ? 22. 4 and 5 are how many ? 23. 4 and 6 are how many ? 24. 4 and 7 are how many ? 25. 4 and 8 are how many ? 26. 4 and 9 are how many ? 27. 4 and 10 are how many ? 28. 5 and 1 are how many ? 29. 5 and 2 are how many ? 30. 5 and 3 are how many ? 31. 5 and 4 are how many ? 32. 5 and 5 are how many ? 33. 5 and 6 are how many ? 34. 5 and 7 are how many ? 35. 5 and 8 are how many ? 86. 5 and 9*' are how many? 1?.J INTELLECTUAL ARITHMETIC. 7 3. 1. A man bought a calf for 7 dollars, and sold it for 3 dollars more than he gave for it ; how much did he sell it for ? 2. Bought a barrel of cider for 2 dollars, and 20 bushels of apples for 8 dollars ; how many dollars did the whole cost ? 3. If a coat cost 10 dollars, and a pair of panta- loons 5 dollars, what will be the cost of both ? 4. A merchant bought 4 boxes of black tea, and 7 boxes of green tea ; how many boxes did he buy of both kinds ? 5. A farmer sold 5 sheep to one man, and 9 to another ; how many did he sell to both ? 6. Ralph walked 4 miles and rode 10 miles ; how many miles did he go ? 7. Philip answered 8 questions in geogi^aphy, and Oliver 5 ; how many questions did both answer ? 8. If a quart of chestnuts cost 10 cents, and a quart of walnuts 4 cents, what will be the cost of one quart of both ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? 9. 6 and 3 10. 6 and 4 11. 6 and 5 12. G and 6 13. 6 and 7 14. 6 and 8 15. 6 and 9 16. 6 and 10 17. T and ^ 18. 7 • anc. 5 19. 7 and 6 20. and 7 21. 7 and 8 22. 7 and 9 23. 7 and 10 24. 8 and 3 8 INTELLECTUAL ARITHMETIC. t"** 25. 8 and 4 are how many? 26. 8 and 5 are how many ? 27. 8 and 6 are how many ? 28. 8 and 7 are how many ? 29. 8 and 8 are how many ? 30. 8 and 9 are how many ? 31. 8 and 10 are how many ? 32. 9 and 4 are how many? 33. 9 and 5 are how many? 34. 9 and 6 are how many? 35. 9 and 7 are how many ? 36. 9 and 8 are how many? 37. 9 and 9 are how many ? 38. 9 and 10 are how many? 39. 10 and 4 are how many? 40. 10 and 5 are how many ? 41. 10 and 6 are how many? 4. 1. Eli paid 9 shillings for a pair of skates, and 6 shillings for a cap ; how many shillings did he pay for both ? Analysis. Since Mi paid 9 shillings for a pair of skates, and 6 shillings for a cap, he paid for both, the sum of 9 shillings and 6 shillings. The sum of 9 shil- lings and 6 shillings is 15 shillings. Therefore, he paid 35 shillings for both, 2. A farmer sold some oats for 7 dollars, and a ton of hay for 9 dollars ; how many dollars did he receive for both ? 3. Paid 8 cents for some raisins, and 6 cents for some cloves ; how manj^ cents did both cost ? 4. Nancy is 10 years old ; how old will she be 5 years from this time ? 5. A lady paid 7 dollars for a shawl, and 6 dol- lars for a dress \ ^hat was the cost of both ? 5.] INTELLECTUAL ARITHMETIC. ^ 9 6. There are 9 boys in one class, and 7 in anoth- er ; how many in both classes ? 7. Margaret has 8 flower pots in one room, and 5 in another ; how many has she in the two rooms ? 8. If you read 10 pages to-day, and 7 pages to- morrow, how many will you read in both days ? 9. If a firkin of butter is worth 9 dollars, and two cords of wood are worth 8 dollars 5 what are both worth ? 10. Myron has 6 young rabbits and 4 old ones ; how many rabbits has he ? 11. Tiiere are 10 biids sitting on one limb, and 9 on another ; how many birds on both limbs ? 12. A boy, having some peaches given him, put 8 into his hat, and 7 into his pockets ; hovr many peaches were given him ? 13. Edwin found 6 ripe pears under one tree, and 8 under another ; how many pears did he find under both trees ? 14. In one yard are 5 cows, and in another 7 ; how many cows in both yards ? 15. If you work 8 examples in arithmetic to-day, and 8 more to-morrow, how many will you work in both days ? 16. Robert gave 8 nuts to Henry, and kept 9 ; how many nuts had he at first ? 5. 1. 7 and 4 are how many ? 2. 9 and 7 are how many ? 3. 6 anc. 7 are how many ? 4. 5 and 9 are low many ? 5. 8 and 7 are low many? 6. 10 and 6 are how many ? 7. 9 and 6 are how many ? 8. 8 and 8 are how many ? 10 INTELLECTUAL ARITHMETIC. [5. 9. 6 and 8 10. 7 and 9 11. 8 and 10 12. 11 and 5 13. 13 and 7 14. 14 and 6 15. 12 and 4 16. 15 and 8 17. 9 and 12 18. IG and 8 19. 17 and 10 20. 15 and 11 21. 13 and 12 are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? 22. How many are 2 and 2 ? 12 and 2 ? 22 and t2 ? 32 and 2 ? 42 and 2 ? 52 and 2 ? 62 and 2 ?^ 72 and 2 ? 82 and 2 ? 92 and 2 ? 23. How many are 3 and 3 ? 13 and 3 ? 23 and 3 ? 33 and 3 ? 43 and 3 ? 53 and 3 ? 63 and 3 ? 73 and 3? 83 and 3? 93 and 3 ? 24. How many are 4 and 4 ? 14 and 4? 24 and 4? 34 and 4? 44 and 4 ? 54 and 4 ? 64 and 4 ? 74 and 4 ? 84 and 4 ? 94 and 4 ? 25. How many are 5 and 5 ? 15 and 5 ? 25 and 5 ?# 35 and 5 ? " 45 and 5 ? 55 and 5 ? 65 and 5 ? 75 'and 5 ? 85 and 5 ? 95 and 5 ? 26. How many are 6 and 6 ? 16 and 6 ? 26 and 6 ? 36 and 6 ? 46 and 6 ? 56 and 6 ? 66 and 6 ? 76 and 6 ? 86 and 6 ? 96 and 6 ? 27. How many are 7 and 7 ? 17 and 7 ? 27 and 7 ? 37 and 7 ? 47 and 7 ? 57 and 7 ? 67 and 7 ? 77 and 7 ? 87 and 7 ? 97 and 7 ? 28. How many are 8 and 8 ? 18 and 8 ? 28 and 8 ? 38 and 8 ? 48 and 8 ? 58 and 8 ? 68 and 8 ? 78 and 8 ? 88 and 8 ? 98 and 8 ? 29. How many are 9 and 9 ? 19 and 9 ? 29 and 9 ? 39 and 9 ? 49 and 9 ? 59 and 9 ? 69 and 9 ? 6,] INTELLECTUAL ARITHMETIC. 11 80. How many are 8 and 7? 18 and 7 ? 28 and 7 ? 38 and 7 ? 48 and 7 ? 58 and 7 ? 68 and 7.? 78 and 7 ? KS" and 7 ? 98 and 7 ? 31. How many arc 10 and 10 ? 20 and 10 ? 30 and 10? 40 and 10? 50 and 10 ? 60 and 10 ? 70 and 10 ? 80 and 10 ? 90 and 10 ? 32. How many are 4 and 8 ? 14 and 8 ? 24 and 8 ? 34 and 8 ? 44 and 8 ? 54 and 8 ? 64 and 8 ? 74 and 8 ? 84 and 8 ? 94 and 8 ? 33. How many are 6 and 5 ? 16 and 5 ? 26 and 5 ? 36 and 5 ? 46 and 5 ? 56 and 5 ? 66 and 5 ? 76 and 5 ? 86 and 5 ? 96 and 5 ? 34. How many are 11 and 9 ? 21 and 9 ? 31 and 9 ? 41 and 9 ? 51 and 9 ? 61 and 9 ? 71 and 9 ? 81 and 9 ? 91 and 9 ? 35. How many are 9 and 7 ? 19 and 7 ? 29 and 7 ? 39 and 7 ? 49 and 7 ? 59 and 7 ? 69 and 7 ? 79 and 7 ? 89 and 7 ? 99 and 7 ? 36. How many are 4 and 8 ? 14 and 8 ? 24 and 8 ? 34 and 8 ? 44 and 8 ? 54 and 8 ? 64 and 8 ? 74 and 8 ? 84 and 8 ? 94 and 8 ? 37. How many are 3 and 10 ? 13 and 10 ? 23 and 10 ? 33 and 10 ? 43 and 10 ? 53 and 10 ? 63 and 10 ? 73 and 10 ? 83 and 10 ? 93 and 10 ? 6. Addition is the process of uniting several numbers of the same kind into one equivalent number. The result is called the Stun or Amount. The sign of addition is written thus, -|-, and is called j^^i^s. AVhen placed between two numbers or quantities, it shows that they are to be added together. Thus, 5 -{- 3 -{- 2 signifies that 5 and 3 and 2 are to be added together, and is read Jive, plus three, plus two. The sign of equality is written thus, r=. "When placed between two numbers or quantities, it signifies that the latter is equal to the former. 12 INTELLECTUAL ARITHMETIC. [6 1. 6+4+5 are how many? 2. 9 -{- 7 -\- S are how many ? 3. 10 + 6 + 4 are how many? 4. 13 + 8 + 6 are how many ? 5. 12 + 1^ + ^ ^^® l^ow many ? 6. 11 + ^ + '^ ^i'Q l^ow many? 7. 8 -f- 10 + 7 + 6 are how many ? 8. 34 + 25 are how many ? Analysis. ^45 many as the sum of 34: and 25 ; 34 is composed of 3 tens and 4 units, and 25 of 2 tens and 5 units ; 3 tens and 2 tens are 5 tens, or 50, and 4 units and 5 units are 9 units, which added to 50 marges 59. Therefore 34 + 25 «re 59. 9. 46 + 31 are how many ? 10. 35 + 52 are how many ? fr 40 + 30 + 6 are how many? 12. 19 + 12 + 8 are how many ? 13. 60 + 'J'2 + 4 are how many? 14. 48 + 30 + 10 are how many ? 0^5. 13 + 25 + 7 "4 are how many ? 16. 29 + 24 + 30 are how many ? 17. 64 + 40 + 9 are how many ? 18. 29 + 17 + 12 are how many ? 19. 7 + 37 + 26 are how many? 20. 14 + 39 + 4 are how many? 21. 48 + 31 + 9 are how many? 22. 56 + 41 + 10 are liow many? '^'^ 75 + 60 + 20 are how many ? 16 + 19 + 28 are how many ? 43 4- 37 + 15 are how many? 84 + 75 + 20 are how many? 68 + 52 + 45 are liow many? 28. 35 + 77 + 51 arc how many ? 29. 80 + 95 + 12 are how many? 80. 42 + 38 + 17 + 9 are how many ? 24. 25. 26. 27. 7.] INTELLECTUAL ARITHMETIC. 13 7. 1. A man gave 12 dollars for some corn, 8 dollars for a ton of hay, and 6 dollars for a barrel of flour ; how much did he pay for all ? Analysis. He pc.z^. the sum of 12 dollars, 8 dollars, and G dollars ; 12 and 8 are 20, and 6 are 26 dollars. Therefore, ^-c. 2. Emily paid 12 shillings for a dress, 10 shillings for a pair of shoes, and 6 shillings for a pair of gloves ; what was the cost of the whole ? 3. A drover had 15 horses in one pasture, 13 in another, and 9 in another ; how many horses had he ? 4. James has 10 cents, Henry has 7, and John has 5 ; how many cents have the three boys ? 5. Bought a pound of candles for 14 cents, a pound of coffee for 12 cents, and a bar of soap for 9 cents ; w*hat was the cost of the whole ? 6. In a shop are 7 men, 9 boys, and 6 .girls at work ; how many persons at work in the shop ? 7. A lady sold 10 pounds of butter at one time, 12 pounds at another, and 8 pounds at another ; how many pounds did she sell in all ? 8. William bought an arithmetic for 15 cents, a quire of paper for 12 cents, and a bottle of ink for 6 cents ; what was the cost of the whole ? 9. Peter, Dexter, and Irwin gave some money to a beggar ; Peter gave him 10 cents, Dexter 11 cents, and Irwin 13 cents ; how many cents did they all give him ? 10. In a certain school there are 18 girls and 24 boys ; how many pupils in the school ? 11. A man bought a sleigh for 20 dollars, paid 10 dollars for repairing it, and 6 dollars for paint- ing it ; what did it cost liim ? 12. Morgan earned 25 cents one day, and 32 the next ; how much did he earn in both days ? 14 INTELLECTUAL ARITHMETIC. [7. 13. A farmer sold a cow for 22 dollars, a ton of hay for 11 dollars, and a calf for 7 dollars ; what did he receive for all ? 14. A traveler walked 3C miles one day, 26 miles the next, and 21 miles the next; how many miles did he travel in the three days ? 15. One day Sarah wrote 18 lines, Maria 16, and Carrie 15 ; how many lines did they all write ? 16. A man gave 60 dollars for a horse, 23 dollars for a saddle, and 9 dollars for a bridle ; what was the cost of the whole ? 17. Rollin received 36 new cents on his birthday, 34 on Christmas day, and 27 on New Year's day ; how many cents did he receive ? 18. A man bought a piece of land for 56 dollars, and paid 25 dollars for fencing it ; for how much must he sell it to gain 15 dollars ? 19. Amasa, going into the orchard, found 12 ripe apples under one tree, 15 under another, 11 under another, and 9 under another ; how many apples did he find under the four trees ? 20. A grocer bought some hams for 20 dollars, some oats for 19 dollars, some fowls for 16 dollars, and five barrels of apples for 10 dollars ; what did he pay for all ? 21. A miller shipped by railroad 28 barrels of flour at one time, 37 at another, and 40 at another ; how many barrels did he ship ? 22. If Lucian gave 45 cents for a penknife, 15 cents for some paper, 12 cents for a folder, and 7 cents for some wafers, what did the whole cost him ? 23. A drover bought 26 sheep of one man, 30 of another, 37 of another, and 40 of another ; how many sheep did he purcliase ? 24. Bought a horse for 75 dollars, and sold him so as to gain 25 dollars ; how much did I receive for him ? 7.] INTELLECTUAL ARITHMETIC. 15 25. A lady went shopping, and bought a silk dress for 22 dollars, a muff for 16 dollars, a shawl for 14 doHars, and had 7 dollars left ; how much money had she at first ? 26. Peleg bought a knife for 85 cents ; he gave the knife and 12 cents for a sled, which he sold so as to gain 10 cents on the cost; how much did he receive for the sled ? 27. In a certain orchard are 31 apple trees, 27 peach trees, and 19 pear trees ; how many trees in the orchard ? 28. A farmer raised 54 bushels of wheat, 6Q bush- els of oats, and 40 bushels of corn ; how many bush- els of grain did he raise ? 29. If it be 62 feet from the ground to the belfry of a church, and 76 feet from the belfry to the top of the steeple, how high is the top of the steeple from the ground ? 30. In March are 31 days, in April 30, in May 31 ; how many days in those three months ? 31. If a farm contain 83 acres of cleared land and 25 acres of wood land, how many acres are in the whole farm ? 32. The distance from Boston to Worcester is 44 miles, from Worcester to Warren 29 miles, and from Warren to Springfield 25 miles ; how many miles from Boston to Springfield ? 33. Batavia is 37 miles west from Rochester, and 81 miles east from Buffalo by railroad ; what is the distance from Rochester to Buffalo ? 34. A tailor bought three pieces of cloth, the first containing 29 yards, the second 26 yards, and the third 25 yards ; how many yards did tlie three pieces contain ? 35. A mechanic sold a carriage for 15 dollars, and a sleigh for 48 dollars ; what did he receive for both ? Id INTELLECTUAL ARITHMETIC. [8* 36. A soldier was 33 years of age when he en- gaged in the battle of New Orleans ; what was his age 44 years after ? 37. A farmer received 29 dollars for some pork, 18 dollars for some hay, 15 dollars for some oats, and 12 dollars for four cords of wood ; how many dollars did he receive for the whole ? 38. Thomas hoed 13 rows of corn, Lyman 16 rows, Cyrus 14 rows, and Warren 10 rows; how many rows did they all hoe ? 39. A gentleman gave 30 dollars for a coat, 7 dollars for a vest, 11 dollars for a pair of pantaloons, and 5 dollars for a hat ; what was the cost of all ? 40. Paid 60 dollars for a carriage, which, with 25 dollars, I gave for a horse ; paid 12 dollars for his keeping, and then sold him for 20 dollars more than he cost me ; for how much did I sell him ? 41. A man deposited 40 dollars in a bank, which was 15 dollars less than his neighbor deposited at the same time ; how much did both deposit ? CHAPTER II. SUBTKACTION. 8. 1. James, having 5 cents, gave 2 cents for a pencil ; how many cents had he left ? Analysis. S'mce James had 5 cents^ and gave 2 cents for a pencil^ he had left the difference between 5 cents and 2 cents. The difference hetioeen 5 cents and 2 cents^ is 3 cents. Therefore^ he had 3 cents left. 2. Mary had 3 peaches, and ate 1 of them ; how many had she left ? 3. Ella had 6 pinks, and gave her sister 2 ; how many had she left ? 8.j INTELLECTUAL ARITHMETIC . 17 4. On a rose bush were 7 roses, and Eliza picked 3 of them ; how many were left ? 5. A man bought 10 sheep and sold 5 of them ; how many had he left ? 6. A bad boy robbed a bird's nest of 7 eggs, and broke 4 of them ; how many remained unbroken ? 7. If there are 8 pigs in a pen, and five of them get out, how many remain ? 8. If a merchant have 12 barrels of flour, and be sell 7 of them, how many barrels will he have left ? 9. Margaret is 11 years old, and Julia 4 years younger ; what is Julia's age ? 10. Steplien had 9 marbles, and lost 3 of them ; how many had he left ? 11. A man, earning 10 dollars a week, spends 6 dollars for i^rovisions; how many dollars has he left? 12. Giles borrowed 12 dollars, and paid 7 dollars of it; how much of it remained unpaid ? are how many? are how many ? are how many ? are how many? are how many ? are how many? are how many? are how many? are how many ? are how many ? are how many ? are how many? are how many ? are how many ? are how many ? 13. 5 less 3 14. 9 less 2 15. 7 less 4 16. 11 less 3 17. 8 '.ess 2 18. 6 less 4 19. 10 less 6 20. 7 ^.ess 5 21. 14 less 8 22. 12 less 7 23. 9 less 8 24. 15 less 9 25. 20 less 6 26. 23 less 10 27. 18 2 less 4 18 INTELLECTUAL ARITHMETIC. [9. 28. 11 from 14 leaves bow many ? 29. 9 from 12 leaves Low many ? 30. 7 from 16 leaves how many? 31. 12 from 20 leaves how many ? 32. 10 from IT leaves how many? 33. 8 from 18 leaves how many? 34. 6 from 15 leaves how many? 35. 11 from 21 leaves how many ? 36. Take 5 from 12, and how many remain ? 37. Take 10 from 19, and how many remain ? 38. Take 7 from 11, and how many remain? 39. Take 9 from 13, and how many remain? 40. Take 12 from 23, and how many remain? 41. What is the difference between 14 and 6 ? 42. What is the difference between 20 and 8? 43. What is the difference between 19 and 15 ? 44. What is the difference between 11 and 22 ? 45. What is the difference between 17 and 6? 46. What is the difference between 25 and 9 ? O. Subtraction is the process of finding the difference between two numbers ; the result is called the Difference or Remainder. The sign of subtraction is written thus, — , and is read minus. Placed between two numbers, or quan- tities, it shows that the one after it is to be taken from the one before it. 9 — 5 shows that 5 is to be subtracted from S, and is read nine minus fi.ve. 1. How many are 10 — 6 ? 2. How many are 9 — 4 ? 3. How many are 12 — 7 ? 4. How many are 15 — 9 ? 5. How many are 20 — 8 ? 6. How many are 18 — 5 ? 7. How many are 17 — 3 ? 8. How many are 21 — 9 ? 10.] INTELLECTUAL ARITHMETIC. 19 9. How many are 16 — 7 ? 10. How many are 19 — 9 ? 11. How many are 21 — 12? 12. How many are 17 — 10 ? 13. How many are 18 — 9 ? 14. How many are 20 — 11 ? 15. How many are 25 — 10 ? 16. How many are 32 — 12 ? 17. How many are 46 — 10? 18. How many are 57 — 34 ? Analysis. 57 is equal to 5 tens and 7 units, and 34 is equal to 3 tens and 4 units ; 3 tens from 5 tens leave 2 tens, or 20, and 4 units from 7 units leave 3 units, which added to 20 make 23. Therefore, 57 — 34 = 23. 19. 39 — 27 are how many ? 20. 43 — 32 are how many ? 21. 29 — 17 are how many ? 22. 54 — 21 are how many ? 23. 67 — 45 are how many ? 24. 75 — 25 are how many ? 25. 89 — 74 are liow vnany ? 26. 39 — 19 are how many ? 27. 41 — 30 are how many ? 28. 96 — 81 are how many? 10. 1. If you have 12 turkeys, and sell 9 of them, liow many will you have left ? 2. A grocer had 10 boxes of lemons, and sold 6 boxes ; how many boxes had he left ? 3. There are 20 men and 8 boys at work in a bookbindery ; how many more men than boys are xhere ? 4. From a cistern holding 36 barrels of water, 12 barrels leaked out ; how many barrels remained ? 20 INTELLECTUAL ARITHMETIC. [ 5. A mail, having 25 dollars due him, received a ton of hay worth 11 dollars, and the remainder in. money ; how much money did he receive ? 6. There are 46 .trees in an orchard ; 35 of them are apple trees and the remainder peach trees ; how many are peach trees ? 7. From a piece of broadcloth containing 27 yards, 15 yards were cut ; how many yards remahied ? 8. A jeweler bought a watch for 60 dollars, and sold it again for 75 dollars : how much did he gain ? 9. The whole number of pupils registered in a certain school is 87, and but Qo are in attendance ; how many are absent ? 10. Charles has 48 cents, and buys a slate for 16 cents ; liow many cents has lie left ? 11. There are 36 wild ducks in a flock, and a huntsman fires at them and kills 13 ; how many are left? 12. A farmer sold a cow for 22 dollars that cost him 30 dollars ; how much did he lose by the bar- gain ? 13. A grocer bought a quantity of sugar for 39 dollars, and sold it for 50 dollars ; how much did he gain ? 14. In a school are 27 boys and 35 girls ; how many more girls than boys ? 15. The distance from Cincinnati to Miamisburg by railroad is 49 miles, and to Dayton 60 miles ; wliat is the distance from Miamisburg to Dayton ? 16. In a warm day the thermometer indicated 85 degrees ; how many degrees was that above the freezing point, which is 32 degrees ? 17. A man died at the age of 77 years, having been married 49 years ; what was his age when he married ? II.] INTELLECTUAL ARITHMETIC. 21 II. 1. 4 and 7 and 9, less 8, are how many ? 2. 9 and 12 and 6, less 7, are how many ? 3. 14 and 10 and 12, less 24, are how many ? 4. 20 and 16 and 5, less 14, are liow many ? 6. 44 and 20 and 10, less 50, are how many ? 6. 27 and 15 and 12, less 30, are how many ? 7. How many are 9 + 12 + 15 — 25 ? 8. How many are 26 + 15 + 7 — 18 ? ■ 9. How many are 40 + 10 + 8 — 20 ? 10. How much less than 64, is 25 + 20 ? 11. How much less than 5Q, is 28 -f 16 ? 12. How much less than 100, is 46 + 34 ? 13. How many are 16 + 12 + 9 -}- 5 — 32 + 8? 14. How many are 33 + 28 -f 9 — 30 ^h 15 ? 15. How many are 84 + 26 + 15 — 70 + 25 ? 16. A man, having 30 dollars, paid 15 dollars for a coat, 5 dollars for a vest, and 4 dollars for a hat ; how much had he left ? Analysis. He had left the diffei-ence between SO dollars and the sum of \b -\- 6 -\- 4 dollars; 15 dollars and 5 dollars are 20 dollars, and 4 dollars are 24 dollars, and 30 dollars less 24 dollars are 6 dollars. Therefore, 8^c, 17. Ellen had 15 pinks, and she gave 6 to Mary and 4 to Jane ; how manv had she left ? 18. A woman, having 25 pounds of butter, sold 15 pounds at one time, and 10 pounds at another ; how many pounds had she left ? 19. Amasa has 45 cents in three boxes ; in the first are 15 cents, in the second 19 cents ; how many cents are in the third box ? 20. A boy found 8 apples under one tree, 10 under another, and 6 under another ; he ate 3, gave away 7, and carried the remainder home; how many did he tak^ home ? L 22 INTELLECTUAL ARITHMETIC. [II. 21. Martin, having 27 marbles, gave 12 to Albert, and lost 5 ; how many had he left V 22. Reuben had 16 cents ; Charles gave him 10, Elisha gave him 9, and Henry gave him enough to make his number 42 ; how many cents did Henry give him ? 23. A merchant bought a hogshead of sugar for 50 dollars ; he paid 6 dollars for freight and customs, and sold the whole for T5 dollars ; how much did he gain ? 24. A man bought a watch for 40 dollars, a chain for 15 dollars, and a key for 3 dollars, and he sold the whole for 50 dollars ; how much did he lose by the bargain ? 25. fSarah bought a comb for 12 cents, some rib- bon for 16 cents, a thimble for 10 cents, and some thread for 6 cents ; how much had she left of fifty cents, after paying for these articles ? 26. A drover bought 9 sheep of one man, 12 of another, and 15 of another ; he afterwards sold 8 and butchered 5 ; how many had he left ? 27. From a piece of calico containing 26 yards Jane bought a dress of 9 yards, and Josephine an- other of 10 yards ; how many yards were left in the piece ? 28. Richard, receiving 45 dollars for labor, paid 20 dollars for a cow, 7 dollars for a barrel of flour, and 9 dollars for three cords of wood; how many dollars had he left ? 29. Four men bought a horse for 80 dollars ; the first gave 25 dollars, the second 20 dollars, and the third 18 dollars ; how much did the fourth give ? 30. A boy had 12 marbles ; another boy gave him 10 more, another 9, and another enough more to make his number 40 ; how many did the last boy give him ? 11.] • INTELLECTUAL ARITHMETIC. 23 31. A man traveled 22 miles one day, and 26 miles the second day, and on the third day he trav- eled 30 miles on his return ; how many miles was he from the place from which he first started ? 32. George sold two dozen eggs for 20 cents, one bushel of apples for 37 cents, and received a pair of skates worth 75 cents ; how much did he still owe for his skates ? 33. A man owed his grocer 18 dollars, his tailor 20 dollars, iShd a merchant 25 dollars ; he paid the grocer 10 dollars, the tailor 12 dollars, and the merchant 15 dollars ; how much did he still owe them all ? 34. Bought a horse for 90 dollars, a cutter for 40 dollars, and a harness for 20 dollars, and then sold the whole for 50 dollars more than the horse cost me ; did I gain or lose by the bargain, and how much ? 35. A lady bought a new bonnet for 7 dollars, a dress for 12 dollars, a pair of shoes for 2 dollars, and a parasol for 3 dollars ; she gave the merchant 3 ten dollar bills ; how many dollars must be re- turned ? 36. A tailor bought a piece of cloth containing 31 yards, from which he sold 13 yards to one man, and 11 yards to another ; how many yards were left of the piece ? 37. A farmer had 45 sheep in one lot, 37 in an- other, and 30 in another ; from the first he sold 20, from the second 15, and from the third 12 ; how many had he at first, and how many had he left? 38. A person, sitting down to play, counted his money, and found that he had 1 twenty dollar bill, 5 ten dollar bills, and 3 five dollar bills ; when he got up from play, he had 7 ten dollar bills and 6 five dol- lar bills ; did he gain or lose, and how much ? 24 INTELLECTUAL ARITHMETIC. [13. 13. 2 times 2 times 2 times 2 times 2 times 2 times CHAPTER III. MULTIPLICATION. 1 are how many ? 2 t 2 are how many ? 2 are how many ? 4 are how many ? 5 are liow many ? 6 are how many ? 2 t 2 t 2 t 2t 3 times 1 3 times 2 3 times 3 3 times 4 3 times 5 3 ■ times 6 4 times 1 4 times 2 4 times 3 4 times 4 4 times 5 4 times 6 are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? 3 3 o O 3 3 3 are how many ?j 4 t: are how many ? j 4 t are how many ?, 4 t are how many ?j4 t are how many ? ; 4 are how many ? 1 4 mes 7 are how many ? mes 8 are how many ? mes 9 are how many ? mes 10 are how many ? mes 11 are how many r mes 12 are how many ? mes 7 are how many ? mes 8 are how many ? mes 9 are how many ? mes 10 are how many ? mes 11 are hovy many ? mes 12 are how many ? mes 7 are how many ? mes 8 are how many ? mes 9 are how many ? mes 10 are how many ? mes 11 are how many ? mes 12 are how many ? 1. How many are 2 times 6 ? 2 times 8 ? 2 times 7 ? 2 times 11 ? 2 times 9 ? 2 times 12 ? 2. How many are 3 times 5 ? 3 times 10 ? 3 times 9 ? 3 times 7 ? 3 times 6 ? 3 times 12 ? 3. How many are 4 times 4 ? 4 times 7 ? 4 times 9 ? 4 times 6 ? 4 times 10 ? 4 times 8 ? 4. At 9 dollars a ton, what will 3 tons of hay cost ? Analysis. Si7ice one ton costs 9 dollars^ 3 to7is^ icJiich are 3 times 1 ton^ lolll cost 3 times 9 dollars ; 3 times 9 dollars are 27 dollm^s. Therefore^ at 9 dollars a ion^ S ^o;r5 ^ Aa?/ «^?^7^ co5^ 27 dollars. 13.] INTELLECTUAL ARITHMETIC. 25 5. At 8 cents a quart, what will 4 quarts of blue- berries cost ? 6. If you answer 11 questions at each recitation, how many questions would you answer at 3 recita- tions ? at 4 ? 7. What will 4 pairs of shoes cost at 12 shillings a pair ? 8. If a ream of paper cost 3 dollars, what will 2 reams cost ? 3 reams ? 4 reams ? 9. Eight New York shillings make a dollar ; how many shillings in 3 dollars ? in 4 dollars ? in 5 dollars ? 10. At 12 cents a yard, what will 3 yards of calico cost ? 4 yards ? AS. 5 times times times times times times 5 5 5 5 6 5 5 5 5 6 times 1 6 times 2 6 times 3 6 times 4 6 times 5 6 times 6 7 times 1 7 times 2 7 times 3 7 times 4 7 times 5 7 times 6 1 are how many ? 2 are how many ? 3 are how many ? ^ 4 are how many ? 5 5 are how many ? 1 5 6 are how many ? [ 5 are how many ?'6 are how many ? 6 are how many ? 6 are how many ? 6 are how many ?'6 ar~ ^ "^ '^ re now iiiciiiy : 'u L'e how many ? 1 6 are how many ? are how many ? are how many ? are how many ? are how many ? are how many ? times 7 are how many ? times 8 are how many ? times 9 are how many ? times 10 are how many ? times 11 are how many? times 12 are how many ? times 7 are how many? times 8 are how many ? times 9 are how many ? times 10 are how many? times 11 arc how many ? times 12 are how many ? times 7 are how many ? times 8 are how many ? times 9 are how many ? times 10 are how many ? times 11 are how many ? times 12 are how many ? 26 INTELLECTUAL ARITHMETIC. [14. 1. How many are 5 times 6t 5 times 8 ? 5 times 4 ? 5 times 3 ? 5 times 7 ? 5 times 12 ? 5 times 9 ? 5 times 11? 2. How many are 6 times 3 ? 6 times 10 ? 6 times 6 ? 6 times 9 ? 6 times 7 ? 6 times 11 ? 6 times 8 ? 6 times 12 ? 3. How many are 7 times 2 ? 7 times 7 ? 7 times 4 ? 7 times 9 ? 7 times 12 ? 7 times 10 ? 7 times 8 ? 7 times 11 ? 7 times 6 ? 4. If you recite 8 perfect lessons in 1 week, how many would you recite in 5 weeks ? in 6 weeks ? in 7 weeks ? 5. What will 6 pounds of sugar cost at 10 cents a pound ? at 9 cents ? 6. If you write 5 lines a day, how many lines will you write in 4 days ? in 7 days ? 7. What cost 5 yards of ribbon, at 8 cents a yard ? at 9 cents ? 8. AVliat cost 7 barrels of apples at 2 dollars a barrel ? 9. At 12 dollars a ton, what will 6 tons of hay cost ? 7 tons ? 5 tons ? 10. If a boat sail 9 miles an hour, how far will she sail in 4 hours ? in 6 hours ? in 7 hours ? 11. What cost 7 barrels of flour, at 11 dollars a barrel ? 12. There are 7 days in 1 week ; how many days in 5 weeks ? in 6 weeks ? in 9 weeks ? 1 J& JO. ■ 8 times 1 are how many ? 1 8 times 7 are how many ? 8 times 2 are how many ? 8 times 8 are how many ? 8 times 3 are how many ? 8 times 4 arc how many ? 8 times 5 arc how many ? o iiuitis c> circ iiuw many : o innes ii are now many ; 8 times 6 are how many ? ^ 8 times 12 are how many ? 8 times 9 are how many ? 8 times 10 are how many ? 8 times 11 are how many ? 14.] INTELLECTUAL ARITHMETIC. 27 9 times 1 are how many ? 9 times 7 are how many ? 9 times 2 are how many ? 9 times 8 are how many ? 9 times 9 are how many ? 9 times 10 are how many ? 9 times 11 are how many ? 9 times 12 are how many ? 9 times 3 are how many t 9 times 4 are how many ? 9 times 5 are how many ? 9 times 6 are how many ? 10 times 1 are how many ? 10 times 7 are how many ? 10 times 2 are how many ? 10 times 8 are how many ? 10 times 3 are how many ? 10 times 4 are liow many ? 10 times 5 are how many ? 10 times 6 are how many ? 10 times 9 are liow many ? 10 times 10 are how many ? 10 times 11 are how many ? 10 times 12 are how many ? 1. How many are 8 times 6 ? 8 times 4 ? 8 times 9 ? 8 times 5 ? 8 times 10 ? 8 times 7 ? 8 times 11 ? 8 times 8 ? 8 times 12 ? 2. How many are 9 times 3 ? 9 times 7 ? 9 times 4 ? 9 times 6 ? 9 times 8 ? 9 times 12 ? 9 times 9 ? 9 times 5 ? 9 times 11 ? 9 times 10 ? 3. How many are 10 times 10 ? 10 times 8 ? 10 times 4 ? 10 times 7 ? 10 times 11 ? 4. What will 8 barrels of flour cost, at 9 dollars a barrel ? 5. What will 9 chairs cost, at 10 shillings apiece ? 6. If 5 boys can sit on one bench, how many can sit on 7 benches ? on 8 benches ? 7. If Harvey can earn 10 dollars, in one month, how many dollars can he earn in 8 months ? in 9 months ? in 7 months ? 8. If 8 men can do a piece of work in 7 days, how many days will it take one man to do it ? 9. If two barrels of flour last 8 persons 3 months, how lon^' will they last one person ? 10. How many dollars will buy 10 tons of hay, at 12 dollars a ton ? 28 INTELLECTUAL ARITHMETIC. [1*5. 11. A farmer divided his farm into 9 fields, con- taining 11 acres each ; how many acres in his farm ? 12. If a man travel 6 miles an hour, how far will he travel in 7 hours ? in 8 hours ? in 9 hours ? in 6 hours ? 13. When eggs are 11 cents a dozen, what will be the cost of 7 dozen ? of 9 dozen ? of 10 dozen ? 1*5. • 11 times 1 are how many ? 11 times 2 are how many ? 11 times 3 are how many ? 11 times 4 are how many ? 11 times 5 are how many ? 11 times 6 are how many ? 11 times 7 are how many ? 11 times 8 are how many ? 11 times 9 are how many ? 11 times 10 are how many ? 11 times 11 are how many ? 11 times 12 are how many ? 12 times 1 are how many ? 12 times 7 are how many ? 12 times 2 are how many ? 12 times 8 are how many ? 12 times 3 are how many ? j 12 times 9 are how many ? 12 times 4 are how many ? , 12 times 10 are how many ? 12 times 5 are how many ? 1 12 times 11 are how many ? 12 times 6 are how many ? \ 12 times 12 are how many ? 1. How many are 11 times 6 ? 11 times 10 ? 11 times 7 ? 11 times 12 ? 11 times 8 ? 11 times 11 ? 11 times 5 ? 2. How many are 12 times 10 ? 12 times 9 ? 12 times 7 ? 12 times 8 ? 12 times 6 ? 12 times 11 ? 12 times 5 ? 12 times 12 ? 3. What will be the cost of 11 bunches of grapes, at 10 cents a bunch ? 4. What will be the cost of 12 barrels of pork, at 11 dollars a barrel ? 5. What will 11 yards of cloth cost, at 6 dollars a yard ? 4 1«5,] INTELLECTUAL ARITHMETIC. 29 6. In an orchard are 12 rows of trees, and 11 trees in each row ; how many trees in the orchard ? 7. What will 11 turkeys cost at 6 dimes apiece ? at 7 dimes ? 8. At 12 dollars a hundred, what will 7 hundred oak posts cost ? 9 hundred ? 11 hundred ? 9. At 9 dollars a week, what will 5 weeks' board cost ? 8 weeks' ? 11 weeks' ? 12 weeks' ? 10. If the fare for one person from Albany to Bos- ton is ^5 dollars, what will be the fare for 6 persons ? for 9 persons ? for 12 persons ? 11. At 12 dollars a month, how many dollars can a man earn in 4 months ? in 6 months ? in 9 months ? in 12 months ? 12. If it take 9 yards of calico for one dress, how many yards will be required to make 4 dresses ? 7 dresses ? 13. If a farmer put his oats into 7 bins, each containing 12 bushels, how many bushels has he ? 14. If I put 8 dolkxrs in the savings bank every month, how many dollars will I deposit in 7 months ? in 8 months ? in 12 months ? 15. What will 11 dozen of eggs cost, at 9 cents a dozen ? at 10 cents ? at 11 cents ? 16. If a quantity of provision will last 9 men 12 days, how long will the same provision last one man ? 17. When flour is 7 dollars a barrel, what must be paid for 7 barrels ? for 8 barrels ? for 9 barrels ? for 11 barrels ? 18. If 12 bushels of apples be picked from each of 11 trees, how many bushels will be picked from R @» Multiplication is the process of finding a number which shall contain one of two given numbers as many times as there are units in the other ; the result is called the Product. 30 INTELLECTUAL ARITHMETIC. [16. The sign of multiplication is written thus, X, and, placed between two numbers or quantities, shows that they are to be multiplied together. 5 X 4 =r 20, shows that 5 multi- plied by 4 is equal to 20. The sign is commonly called tiiiies, 5 X 4 is read 5 times 4. 1. 5x3 are how many ? 2. 7x4 are how many ? 3. 10 X T are how many ? 4. 3x8 are how many ? 5. 7x9 are how many ? 6. 12 X 6 are how many ? 7. 9x8 are how many ? 8. 8 X 11 are how many ? 9. 6x9 are how many ? 10. 5x 7 are how many ? 11. 11 xlO are how many ? 12. 8x 4 are how many? 13. 11x11 are how many ? 14. 12x12 are how many? 15. What is the product of 7 X 6 ? of 9 X 5 ? of 7 X 7 ? of 11 X 6 ? 16. What is the product of 4x3x2? of 5x 2 X 3? of 3 X 3 x9? 17. What will be the cost of 3 cows, at 23 dollars apiece ? Analysis. Since 1 cow cost 23 dollars, 3 coivsj ivJach are 3 times 1 cow, will cost 3 times 23 dollars. 23 is equal to 2 tens and 3 units ; 3 times 3 units are 9 units, and 3 times 2 tens are 6 tens, or 60 ; QO and ^ areQ%. Therefore^ if 1 cow cost 23 dollars, 3 cows will cost 69 dollars, 18. At 31 cents a bushel, what will be the cost of 6 bushels of oats ? 19. What will be the cost of 7 bushels of apples, at 25 cents a bushel ? 20. If a man travel 26 miles in one day, how far can he travel in 10 days ? 21. Mary bought 6 yards of muslin at 18 cents a yard ; what was the cost of the whole ? 22. Ephraim is 17 years old, and his father is 4 times as old ; how old is his father ? 16.] INTELLECTUAL ARITHMETIC. 31 23. At 50 dollars a share, what will 7 shares of bank stock cost ? 24. What will 9 pounds of tea cost, at 56 cents a pound ? 25. At 44 cents a day, what will 10 days' labor amount to ? 26. At 3 dollars a yard, what wdll be the cost of a piece of cloth containing 36 yards ? 27. What will be the cost of 12 pounds of coffee, at 15 cents a pound ? 28. If the cars run 24 miles an hour, how far will they run in 7 hours ? 29. In an orchard are 16 peach trees, and 6 times as many apple trees ; how many apple trees in the orchard ? 30. What will be the cost of 45 lemons, at 5 cents apiece ? 31. If 11 men can do a piece of work in 13 days, in what time will one man do the same work ? 32. If a man labor 12 months for 17 dollars a month, how much will his wages amount to ? 33. At 3 dollars a barrel, what will be the cost oi 28 barrels of potatoes ? 34. If in an orchard are 12 rows of trees, and 32 trees in each row, how many trees in the or- chard ? 35. If a man can dig 28 bushels of potatoes in one day, how many bushels can he dig in 3 days ? in 4 days ? in 5 days ? 36. At 80 dollars apiece, what will be the cost of 3 horses ? of 4 horses ? of 6 horses ? 37. At 43 dollars an acre, what will 10 acres of land cost ? 12 acres ? 38. If 8 horses eat 3 bushels of oats in one day, how many bushels will they eat in 7 days ? in 9 days ? g2 INTELLECTUAL AEITHMETIC. [17. 17. 1. What will be the cost of 6 tons of coal, at 5 dollars a ton, and of 4 cords of wood at 3 dol- lars a cord ? Analysts. They luill cost the sum of the products of 6X5 dollars, and o/ 4 X 3 dollars ; 6 times 5 dollars are 30 dollars, and 4 times 3 dollars are 1 2 dollars ; 30 dollars ojid 12 dollars are 42 dollars. Titer ef or e, ^c. 2. A farmer sold 12 sheep at 4 dollars a head, and 9 lambs at 2 dollars each ; how many dollars did he receive for all ? 3. What will be the cost of 5 pounds of coffee at 15 cents a pound, and 14 pounds of rice at 6 cents a pound ? 4. If two persons start from the same point, and travel in opposite directions, one at the rate of 6 miles an hour, and the other 4 miles an hour, how far apart will they be in 7 hours ? in 9 hours ? in 12 hours ? 5. If they travel in the same direction, how far apart will they be in 5 hours ? in 7 hours ? in 24 hours ? 6. If I hire a man and his son to labor, the father at 14 shillings a day, and the son at 8 shillings, how much will be due them both in 6 days ? in 9 days ? 7. Asa has 16 marbles, and Omar 3 times as many ; how many have both ? 8. A drover bought 28 sheep at 3 dollars a head, and 5 cows at 26 dollars apiece ; what was the cost of the whole ? 9. Justin bought 9 oranges at 4 cents apiece, 7 lemons at 3 cents apiece, and 10 lead pencils at 2 cents apiece ; how much was the cost of the whole ? 10. Charles is twice as old as Byron, and Byron is 14 years old ; what is the sum of their ages ? 11. In a 8chool-room 16 pujoils can sit on each 18.] INTELLECTUAL ARITHMETIC 83 of 5 seats, 8 on each of 3 seats, and 20 on the re- mainder of the seats ; how many pupils can be seat- ed in the room ? 12. A farmer has 30 sheep in each of 3 pastures, 35 in each of 2 pastures, and 40 in another pas- ture ; how many sheep has he in all ? 13. If one boy earns 12 cents a day, another 15 cents a day, and another 20 cents a day, how much can the 3 boys earn in 5 days ? 14. A man bought 9 yards of cloth for a suit of clothes, at 5 dollars a yard ; he paid 7 dollars for making the coat, 2 dollars for making the pantaloons, and 1 dollar for making the vest ; what did his suit coet him ? 18. 1. A farmer bought a horse for 85 dollars, for which he gave 7 tons of hay at 9 dollars a ton, and the remainder in money ; how much money did he pay ? Analysis. He paid in money, the difference between 85 dollars and the product of 7 times 9 dollars ; 7 times 9 dollars are 63 dollars, and 85 dollars less 63 dollars are 22 dollars. Tfierefore, SfC. 2. John worked 5 days for 15 cents a day, and Norman worked 4 days for 20 cents a day ; how much more did Norman earn than John ? 3. A drover bought 35 sheep at 2 dollars a head, and sold them for 90 dollars ; how much did he gain ? 4. A mechanic earned 32 dollars a month for five months, and his apprentice 12 dollars a month for the same time ; how much more did the one earn than the other ? 5. If a man earn 90 cents a day, and pay 40 cents a day for his board, how much will he save in 6 days ? 84 INTELLECTUAL ARITHMETIC. [18. 6. A farmer sold a grocer 7 pounds of butter at 20 cents a pound, and received in payment 12 pounds of fish at 6 cents a pound ; how much was still due the farmer ? 7 c !P-OW much difference does Mr. Jones receive, by exchanging 5 cows at 18 dollars a head, for 1 head of yovmg cattle, at 9 dollars each ? 8. A merchant poured into a cask 14 quarts of camphene 3 different times, and from the same cask filled 2 cans, holding 8 quarts each, and 3 jugs, hold- ing 6 quarts each ; how many quarts remained in the cask ? 9. Nellie picked 6 quarts of blackberries, and Laura picked 4 times as many, wanting 5 quarts ; how many quarts did Laura pick ? 10. What is the difference in the cost of 30 yards of cloth at 4 dimes a yard, and 25 yards at 3 dimes a yard ? 11. A lady bought 6 yards of satin, at 2 dollars a yard, 2 shawls at 9 dollars each, and some lace for 3 dollars ; she paid 4 ten dollar bills ; how much ought she to receive back ? 12. A drover bought 50 sheep for 125 dollars ; he sold 30 at 4 dollars a head, and the remainder at 3 dollars a head ; how many dollars did he gain by the bargain ? 13. Three boys talking of their money, one said he had 35 cents, another said he had twice as many, and the third said he had as many as both the others, wanting 10 cents ; how many cents had the last ? 14. Two men bought a horse for 75 dollars ; they paid 2 dollars a week for keeping liim, and at the end of 12 weeks sold him for 90 dollars ; how much did they lose by their bargain ? 15. A man, owing 100 dollars, gave a sleigh worth 40 dollars, 12 cords of wood, at 3 dollars a cord, .] INTELLECTUAL ARITHMETIC. i35 and the remainder in money ; Iioav miicli money did he pay ? 16. I bought a book-case for 28 dollars, a table for 14 dollars, and 6 chairs at 2 dollars each ; I paid for the table ; how much did I still owe ? 17. If a blacksmith earn 11 shillings a day, and a joiner 11 shilHngs a day, what will the difierence in their earnings amount to in 12 days ? 18. Perry paid 3 cents for a lemon, Elisha twice as much for a pineapple, and for a melon Albert paid 6 tunes as much, lacking 15 cents, as was paid for both the lemon and the pineapple ; what would be the cost of 3 melons at the same rate ? 19. At a public meeting are 35 gentlemen, and 8 times as many ladies lacking 30 ; how many ladies are there, and how many ladies and gentlemen ? 20. Peter has 4 times 5 peaches, and Marcus has 3 times 6 ; how many will they both have left after Peter gives away 7, and Marcus 5 ? 21. How many are 4 times 20, plus 3 times 10 ? 22. How many are 7 times 15, plus 9 times 12 ? 23. How many are 12 times 11, minus 10 times 7 ? 24. How many are 10 times 11, less 15, plus 6 times 5 ? 25. How much less is 7 times 14, than 3 times 40 ? 26. How much less is 10 times 10, than 6 times 20 plus 25 ? 27. How much more is 8 times 16, than 7 times 13 minus 11 ? 28. How many are 9 times 12, plus 22 -f- 10 — 30 ? 29. How many are 15 X 12, -f- 20 X 5 ? 30. How manv are 40 X 4, + 27 X 3 ? 31. How many are 16 X 9, — 13 X 6 ? 32. How many are 10 + 12, X 6, — 40 ? 38. How many are 14 X 8, + 18, + 12, --^ 7 ? 36 INTELLECTUAL ARITHMETIC. [19. CHAPTER lY. DIVISION. 19. 1. When wheat is 2 dollars a bushel, how many bushels can be bought for 12 dollars ? Analysis. Since 2 dollars ivill buy 1 bushel^ 12 <:?o/- Zars ■^^^7/ t>wy «5 many bushels as 2 dollars, the price of 1 bushel, is contained times in 12 dollars j '2 dollars is contained in 12 dollars G times. Therefore, at 2 dollars a bushel, G bushels of 'tcheat can be bought for 12 dollars, 2. How many peaches at 2 cents apiece, can be bought for 18 cents ? 3. If you can buy one lead pencil for 3 cents, how many can you buy for 24 cents ? 4. For 16 dollars, how many cords of wood can be bought at 4 dollars a cord ? 5. At 3 cents apiece, how many oranges can be bought for 21 cents ? 6. In how many days can a man earn 20 dollars, if he earn 2 dollars a day ? 7. Edward has 15 peaches, which he wishes to di- vide equally among his 3 brothers ; how many must lie give to each ? 8. How many times 2 in 8 ? in 6 ? in 10 ? in 14 ? in 16 ? in 20 ? in 24 ? 9. How many times 3 in 6 ? in 12 ? in 18 ? in 21 ? in 9 ? in 27 ? in 33 ? in 24 ? in 36 ? 10. How many times 4 in 12 ? in 8 ? in 16 ? in 20 ? in 36 ? in 24 ? in 40 ? in 32 ? in 48 ? 11. How many tons of coal, at 4 dollars a ton, can be bought for 48 dollars ? 12. If one penholder can be bought for 4 cents, how many can be bought for 20 cents ? for 32 cents ? for 40 cents ? so.] INTELLECTUAL ARITHMETIC. 87 13. Paid 36 dollars for 3 gold cliaiiis ; what was the cost of each ? 14. How many barrels of apples, at 3 dollars a barrel, can be bought for 36 dollars ? 15. If you give 41 cents to 4 beggars, how many do you give to each ? 16. If a man Avalk 3 miles an hour, how many hours will it take him to walk 30 miles ? 17. Bought 4 barrels of flour for 28 dollars ; what was the cost of one barrel ? 18. If I pay 27 cents for 3 pounds of sugar, how much do I pay a pound ? 19. 15 are how many times 3 ? 5 ? 20. 36 are how many times 3 ? 6 ? 4 ? 21. 42 are how many times 6 ? 7 ? 3 ? 22. 24 are how many times 2 ? 6 ? 4 ? 8 ? 23. 16 are how many times 4 ? 2 ? 8 ? 24. 40 are how many times 8 ? 5 ? 4 ? 25. 72 are how many times 8 ? 6 ? 12 ? 26. 56 are how many times 7 ? 8 ? 4 ? 27. 48 are how many times 4 ? 6 ? 8 ? 12 ? 28. 32 are how many times 8 ? 2 ? 4 ? 29. 30 are how many times 5 ? 6 ? 3 ? SO. 1. How many spools of thread, at 5 cents a spool, can be bought for 40 cents ? for 50 cents ? 2. When lard is 7 cents a pound, how many pounds can be bought for 56 cents ? for 63 cents ? 3. If a farmer divide 84 bushels of potatoes equally among 7 laborers, how many bushels will each receive ? 4. If an orchard contain 64 trees, and 8 trees in a row, how many rows are there ? 5. If a man travel 72 miles in 6 hours, how far does he travel in one hour ? 38 INTELLECTUAL ARITHMETIC. [!^0. 6. Levi paid 7 cents for liis ball ; how many balls at the same price could he buy for 28 cents ? for 56 cents ? for 6S cents ? for 84 cents ? • 7. How many bins will be required to hold 72 bushels of wheat, if each bin contain 8 bushels ? 8. At 5 dollars a week, how long will it take a man to earn 45 dollars ? 50 dollars ? 9. At 8 cents a pound, how many pounds of su2:ar can be bouorht for 96 cents ? 10. If a man spend 6 cents a day for cigars, how many days will 60 cents last him ? 11. A man bought some sheep for 48 dollars, at 4 dollars apiece ; how many sheep did he buy ? 12. If one man can do a job of work in 60 days, in what time can 5 men do tlie same Avork ? 13. 45 are how many times 5 ? 9 ? 3 ? 14. 36 are how many times 4 ? 6 ? 9 ? 12 ? 15. 80 are how many times 10 ? 8 ? 4 ? 5 ? 16. 96 are how many times 8 ? 6 ? 12 ? 4 ? 17. 44 are how many times 11 ? 4 ? 2 ? 18. 24 are how many times 2 ? 8 ? 4 ? 6 ? 12 ? 19. 60 are how many times 6 ? 5 ? 10 ? 12 ? 20. 63 are how many times 9 ? 3 ? 7 ? 21. 84 are how many times 7? 12? 4? 6? 22. 90 are how many times 9 ? 6 ? 10 ? 23. 108 are how many times 12 ? 9 ? 6 ? 24. 100 are how many times 10 ? 20 ? 5 ? 25. 99 are how many times 9 ? 11 ? 3 ? 26. 81 are how many times 9 ? 27. 6Q are how many times 11 ? 6 ? 3 ? 28. 75 are how many times 15 ? 5 ? 25 ? 29. 88 are how many times 4 ? 11 ? 8 ? 30. 120 are how many times 12 ? 10 ? 8 ? 31. 140 are how many times 7 ? 10 ? 20 ? 32. 200 are how many times 20 ? 40 ? 50 ? SH.] MTELLECTUAL ARITHMETIC. , 39 SI, 1. If 6 men receive 72 dollars for building a barn, how many dollars will each man receive 't Note. If the pupil is sufficiently acquainted with FractionSf the iollowing Analysis is often prelerred.* ANALYSIS. If G 7nen receive *72 dollars, 1 man, loMch is J o/Q onen, vnll receive J of 72 dollars ; ^ of 72 dol- lars is 12 dollars. Therefore if G ^nen receive 72 dol- lars for building a barn, each man will receive 12 dollars, 2. If 81 cents be paid for 9 dozen of eggs, what will be the cost of 1 dozen ? 3. A mechanic sold a wagon for 77 dollars, and took his pay in hay, at 11 dollars a ton ; how many tons did he receive ? 4. How long will it take 12 men to perform a piece of work that 1 man can do in 48 days ? 5. Paid 108 dollars for 9 thousand feet of lum- ber ; what was the cost of a thousand feet ? 6. How many barrels of flour can be bought for 5G dollars, at 7 dollars a barrel ? at 8 dollars ? 7. How many cows, at 12 dollars a head, can be bought for 60 dollars? for 96 dollars? for 120 dollars? 8. When steak is 10 cents a pound, howluany pounds can be bought for 50 cents ? for 80 cents ? for 100 cents ? 9. At 11 cents a pound, how many poimds of sugar can be bought for 88 cents ? for 99 cents ? * When it is necessary to express a qunntity less than a unit, we ma/ regard the unit as diviaed into some number of equal parts, aud ubo one of these parts as a new unit of less value than the unit divided. Thus, if a yard be divided into two equal parts, each of the parts is culled one half ; -when into tliree equal parts, each of the parts is called one tJurd ; "VVi.en into four equal parts, each of the parts is called one fourth ; when into^i'^ equal parts, each of the parts is called one-fifth ; two of the parts, tuvjfths, &c. ; when into sic equal parts, each of the parts is called one such j tivo ox the parts, tivo sixths, three of the parts, tliree sixths, (tc. 40 INTELLECTUAL ARITHMETIC. [31. 10. A man planted an orchard of 132 trees, and put 11 trees in a row ; how many rows in the orchard ? 11. A farmer sold a horse for 120 dollars ; how many cows at 12 dollars each would pay for the horse ? How many young cattle at 8 dollars each ? How many sheep at 5 dollars each ? 12. If 25 sheep cost 75 dollars, what will 1 sheep cost ? 13. If a boy read 7 pages a day, how long will it take him to read 56 pages ? to read 84 pages ? 98 pages ? 14. At 15 cents a pound, how many pounds of coftee can be bought for 45 cents ? for 60 cents ? for 90 cents ? 15. If 1 man can do a piece of work in 72 days, m what time can 6 men do it ? 8 men ? 9 men ? 12 men ? 16. If a certain quantity of provision will last 1 man 36 days, how many days will it last 4 men ? 9 men ? 12 men ? 17. A man earns 66 dollars in 11 weeks ; how much does he earn in 1 week ? how much in 1 day ? 18. ^ If a painter receive 100 dollars for painting 5 carriages, how much does he receive apiece ? 19. How many lots containing 12 acres each can be sold from a farm of 120 acres ? how many lots of 20 acres each ? 20. If a steamboat run 11 miles an hour, how long will she be in running 44 miles ? 88 miles ? 110 miles ? 21. How many men, at 8 dollars a month, can be hired one month for 96 dollars ? how ma^iy at 12 dollars ? how many at 16 dollars ? 22. If I travel 120 miles in 6 days, how many iniles do I travel in 1 day ? 22.] INTELLECTUAL ARITHMETIC. 41 22. 1. If 3 pounds of coffee cost 2T cents, wlmt "will 6 pounds cost '? Analysis. Jf S pounds of coffee cost 27 cents, 1 pound, u-Jiich is 1 third of 3 pounds, ivill cost 1 ^/^/rc? o/' 27 cents, cr 9 cen^s. Jf \ pound cost 9 cents, 6 pounds, which are 6 ^me5 1 pound, will cost G ^mes 9 ce?i^5, or 54 ce?i('s. Therefore, if 3 pounds of coffee cost 27 ce?i^5, G pounds will cost 54 ce7Z^5. Or thus : Q pounds ivill cost G tiines 1 third of 21 cents; 1 jf/i/rc? ci/'27 ce?i^s is 9 ce/^^5, a;zc^ G times 9 cew^s are 54 cents. Therefore, ^c. Or pounds, ivMch are 2 ii?ne5 3 r>ound?, will c^st 2 times 27 cewi^?, b dollars, are simple numbers. A Compound Number contains two or more names or denominations ; thus, 5 dollars 25 cents, 16 bushels 3 pecks, 3 days 10 hours, are compound numbers. Reduction is the process of changing numbers from one denomination to another, without altering their value ; thus, changing pounds to ounces, ounces to pounds, dollars to cents, &c., is reduction. 1. How many mills in 2 cents? in 8 cents? 2. How many cents in 1 dime ? in 3 dimes ? 3. How many dimes in 8 dollars? in 4 dollars? 4. How many dollars in 2 eagles? in 5 eagles? 5. How many cents in 4 dimes and 7 cents? 6. How many dimes in 3 dollars and 6 dimes? 7. If Jamas earned 12 dollars, and his father 3 eagles, how many dollars did they both earn ? 8. A man has 4 eagles, 4 five dollar bills, and 4 dimes ; how many dollars and cents has he ? 9. How many dimes are equal to 40 cents? to 70 cents ? 10. What is the diiference in the cost of 8 yards of cloth at 2 dimes a yard, and 6 yards at 30 cents a yard ? 26, 27.] intellectual arithmetic. 49 26. Table of English Money. 4 farthings (far.) make 1 penny, d. 12 pence (( 1 shilling, s. 20 shillings u 1 pound, £, Note. A sovereign (sov.) is equal in value to one pound. 1. How many farthings in 1 penny ? in 3 pence ? in 6 pence ? in 9 pence ? 2. How many pence in 1 shilling ? in 4 shillings ? in 5 shillings ? in 9 shillings ? in 10 shillings ? 3. How many pence in 8 farthings ? in 24 far- things ? in 48 farthings ? 4. How many shillings in 24 pence ? in 84 pence ? in 108 pence ? 5. How many pounds in 40 shillings ? in 120 shil- lings ? 6. At 5 shillings a yard, how many pounds will 20 yards of carpeting cost ? 7. At 7 shillings a pair, how many pairs of shoes can be bought for 2 sovereigns ? ST. Table of Troy Weight. 24 grains (gr.) make 1 pennyweight, pwt. 20 pennyweights " 1 ounce, oz. 12 ounces " 1 pound, lb. 1. How many grains in 2 pennyweights ? in 4 ? 2. How many pennyweights in 3 ounces ? in 5 ? 3. How many pennyweights in 96 grains ? in 124 grains ? 4. In 120 pennyweights how many ounces ? in 200 pennyweights ? 5. What will a gold chain, weighing 15 penny- weights cost, at 8 dimes a pennyweight ? how many dollars and cents ? 4 60 intellectual arithmetic. [28. 38, Table of Avoirdupois Weight- 16 drams (dr.) make 1 ounce, oz. 16 ounces " 1 pound, lb. 100 pounds " 1 hundred weight, cwt. 20 hundred weight " 1 ton. T. 1. How many drams in 3 ounces ? in 4 ounces ? in 6 ounces ? 2. How many ounces in 32 drams ? in 48 drams ? in 64 drams ? 8. How many ounces in 3 pounds ? in 5 lbs. ? in 7 lbs. ? 4. How many ounces in 2 lbs. 6 oz. ? in 4 lbs. 10 oz. ? 5. In 3 cwt. and 5 lbs., how many pounds ? 6. In 5 pounds, how many ounces ? 7. How many pounds in 3 cwt. ? in 6 cwt. ? in 9 cwt. ? 8. In 16 tons, how many cwt. ? in 25 tons ? 9. In 1 ton and 5 cwt., how many cwt. ? how many pounds ? 10. How many dollars will 3 cwt. of flour cost, if 25 pounds cost 5 dimes ? 11. What will 1 ton and 5 cwt. of hay cost, if 5 cwt. cost 3 dollars ? 12. What will 2 cwt. 10 lbs. of beef cost at 6 cents a pound ? 13. If 8 ounces of tea cost 4 dimes, what will 2 pounds cost ? 14. What will be the cost of 4 cwt. of sugar, at 7 cents a pound ? 15. Which will cost the more, 5 cwt. of fish at 6 cents a pound, or 3 tons of \my at 50 cents a cwt. ? 16. What will 1 ton of hay cost at 1 cent a pound ? 29.] intellectual arithmetic. 61 29. Table of Long Measure. 12 inches (in.) mak( 3 1 foot, ft. 3 feet 1 yard, yd. 5^- yards, or IG^- feet, " 1 rod, rd. 40 rods " 1 furlong, fur. 8 furlongs, or 320 rods, " 1 mile, mi. 3 miles " 1 leao'ue, lea. O 7 69i miles " 1 degree, deg. or ^. 860 deo-rees " 1 circle of the earth. 1. Ho^v many inches in 3 ft. ? in 5 ft. ? in 10 ft. ? in 12 ft.? 2. How many feet in 4 yards ? in 6 yards ? in 9 yards ? 3. How many yards in 15 feet ? in 24 feet ? 4. How many yards in 2 rods ? in 4 rods ? 5. How many furlongs in 5 miles ? in 7 miles and 4 furlongs ? 6. How many furlongs in 80 rods ? in 120 rods ? in 160 rods ? 7. In 2 miles 4 fur. 20 rods, how many rods ? 8. How many leagues in 9 miles ? in 18 miles ? in 36 miles ? 9. How many inches in 3 yds. 1 ft. 10 in. ? 10. In 108 inches how many yards ? in 144 inches ? 11. If a man travel 5 miles an hour, how long will it take him to travel 20 leagues ? 12. If a ship sail 20 leagues a day, how long will it take her to sail from New York to Liverpool, it being 3000 miles ? 13. In 100 inches how many yards, feet, and inches ? 14. At 8 dimes a foot, how many dollars will 3 yds. 1 ft. of iron railing cost ? 15. In 2 rods 5 feet, how many inches ? 52 INTELLECTUAL ARITHMETIC. [SO, 31, SO. Table of Cloth Measure. 2| inches (in.) make 1 nail, na. "^ ii3.ils " 1 quarter of a yard, qr. 4 quarters " 1 yard, yd. 1. How many nails in 3 qrs. ? in 5 qrs. ? 2. How many nails in 2 yds. 2 qrs. ? 3. How many quarters in 5 yds. ? in 6 yds. 3 qrs. ? 4. How many yards in 16 qrs. ? in 56 qrs. ? 5. How many qrs. in 36 nails ? in 64 na. ? 6. How many qrs. in 5 yds. ? in 6 yds. ? in 7 yds. ? 7. In 4 yards, how many nails ? 8. In 6 yards, how many qrs. ? 9. In 123 nails, how many yards ? 9 square feet 30:^ square yards 40 square rods 4 roods 640 acres US. Table of Land or Square iviiiASURE. 144 square inches (sq.in.) make 1 square foot, sq. ft. 1 square yard, sq.yd. 1 square rod, P. 1 rood, R. 1 acre, A. 1 square mile, Sq. M. 1. How many square feet in 5 square yards ? in 10 square yards ? in 20 square yards ? 2. How many square yards in 36 sq. ft. ? in 72 sq. ft. ? in 108 sq. ft. ? 3. How many square rods in 3 roods ? in 5 roods ? in 7 roods ? 4. How many acres in 20 roods ? in 80 roods ? 5. At 4 dollars a square rod, what would 2 roods 10 rods of land cost ? 33. 33.] INTELLECTUAL ARITHMETIC. 53 3S. Table of Cubic Measure. 1728 cubic inches (cu. in.) make 1 cubic foot, cu. ft. 27 " feet " 1 cubic yard, cu. yd. 24| " feet " 1 perch of stone, Pch. 16 " feet " 1 cord foot, c. ft. 8 cord feet, or ) u -\ ^ ? An -ic^cy ^^ V \ \ 1 cord 01 wood, C. 128 cubic feet ) ' 1. How many cubic feet in 2 cubic yards ? in 3 cubic yards ? 2. How many cubic feet in 2 perch of stone ? in 4 perch ? in 6 perch ? 3. How many cord feet in 3 cords of wood ? in 7 cords ? in 9 cords ? 4. How many cord feet in 120 cubic feet of wood ? in 200 cubic feet ? 5. How many cords in 24 cord feet ? in b^ cord feet? ^3. Table of Liquid Measure. 4 gills (gi.) make 1 pint, pt. 2 pints " 1 quart, qt. 4 quarts " 1 gallon, gal. 31|- gallons " • 1 barrel, bar. 2 barrels, or 63 gallons " 1 hogshead, hhd. 1. How many gills in 4 pints ? in 6 pints ? in 10 pints ? 2. How many pints in 3 quarts ? in 8 quarts ? in 1 gallon ? in 3 gallons ? 3. How many gills in 4 quarts ? in 6 quarts ? in 8 quarts ? 4. How many quarts in 3 gallons? how many pints ? how many gills in 3 quarts ? in 1 gallon and 2 quarts ? 54 INTELLECTUAL ARITHMETIC. [34, 5. How many gills in 2 gallons 2 qts. ? 6. How many quart cups could be filled from a 10 gallon keg of wine ? how many pint bottles ? 7. In 48 gills, how many pints ? quarts ? 8. How many gallons in 64 gills ? in 96 gills ? 9. How many quarts in 56 pints ? gallons ? 10. In 10 gallons, how many quarts ? pints ? gills ? 11. What will be the cost of 6 gallons of burning fluid, at 15 cents a quart ? 12. If a pint of molasses cost 7 cents, what will a gallon cost ? 13. If one gallon of oil cost 90 cents, what will 3 gallons and 2 quarts cost ? 14. If you should draw 10 gallons and 3 quarts from a hogshead of molasses, how much would re- main ? Table of Dry Measure. 2 pints (pt.) make 1 quart, qt. 8 quarts " 1 peck, pk. 4 pecks " 1 Wshel bu. 1. How many pints in 1 peck ? in 2 pks. 4 qts. ? 2. How many quarts in 1 bu. 2 pks. ? §. In 2 bu. 1 pk. 6 qts. how many quarts ? 4. In 64 quarts how many pecks ? bushels ? 5. In 80 pints how many pecks ? 6. At 3 cents a pint,^ what will be the cost of one peck of chestnuts ? 7. If one bushel of hickory nuts cost 160 cents, what will be the cost of 6 quarts ? 8. Bought 2 pecks of cranberries for 96 cents, and sold them for 5 cents a pint; how much was the gain ? 35.] INTELLECTUAL ARITHMETIC. m 35. Table of Time. 60 seconds (sec.) make 60 minutes 24 hours 7 days 12 calendar months 365 days 366 days 100 years u ii a a ii. u u 1 minute. m. 1 hour, hr. 1 day, ' d. 1 week, w. 1 year, yr. 1 common year, yro 1 leap year, yr. 1 century, C. The divisions of the year, the names of the months, and the number in each, are shown in the following table : — Wnrf Of (1st ( 2d month, January has 31 days Y > lliLt-'i . a February ' ' 28* " (3d a March < ' 31 '^ Spring. {4th a April * ' 30 " (5th a May * •' 31 " (6th ii Juno * =' 30 " Summer. ^Tth ii July '.i 31 a (8th ii August u 31 a ( 9th ii September ''' 30 " Autumn. \ 10th ii October u 31 a ( 11th u ^SJ^ovember ^' 30 " Winter. 12th u December u 31 u The following lines will help to remember the number of days in each month : — Tliirty 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. * In leep-year, 29. B6 INTELLECTUAL ARITHMETIC. [S6, 1. How many seconds in 2 minutes ? in 5 minutes ? 2. How many seconds in 10 minutes ? in 20 minutes ? 3. How many seconds in 1 hour ? in 2 hours ? 4. How many minutes in 3 hours ? in 5 hours ? 5. How many liours in 2 days ? in 3 days ? 6. In 2 days and 12 hours how many hours ? 7. In 6 weeks how many days ? in 9 weeks ? 8. How many weeks in 49 days ? in 84 days ? 9. How many weeks and days in 75 days V in 90 days ? 10. How many hours in 3 days 10 hours ? 11. In 36 months how many years ? in 84 months ? 12. How many days from January 1st to March 10 th, inclusive ? 13. How many days from April 10th to the 15th of June ? !6. Miscellaneous Table.. 12 units mak e 1 dozen. 12 dozen " 1 gross. 12 gross " 1 great gross. 20 units " 1 score. 24 sheets of paper " 1 quire. 20 quires " 1 ream. 5Q pounds " 1 bushel of corn. 60 pounds " 1 bushel of wheat. 196 pounds " 1 barrel of flour. 200 pounds " J 1 barrel of beef, pork, ( or fish. 1. TVhat cost 1 ream of paper, at 20 cents a quire ? 2. What cost 3 dozen lemons, at 3 cents apiece ? 3. What cost 2 gross of pens, at 5 cents a dozen ? 4. At 7 dollars a hundred pounds, what will 2 barrels of pork cost ? 37.] INTELLECTUAL ARITHMETIC. 57 CHAPTER YI. FKACTIONS. S7o 1. TVhat is understood by one half, one third, one fourth, one fifth, &c. ? Ans. When a number or thing, as a unit or an apple, is divided into two equal parts, each of the parts is called one half; when into three equal parts, each of the parts is called one third ; two of the parts are called two thirds^ 4f . 22. Divide | of i of 14 by | of 31 23. -| are how many times 6 ? 24. -^j are how many times 4 ? 25. ^1 are how many times 15 ? 26. 1^ are how many times 6^ ? 27. 12 are how many times | ? 28. 16 are how many times |- ? 29. 25 are how many times ^ ? 30. 14 are how many times -f^ ? 31. 14f are how many times | ? 32i 6 1 are how many times |- ? 33. 21^ are how many times 5 ? 34. 32-| are how many times 7 ? 35. 17 1 are how many times 8 ? 36. 15 are how many times 7-J ? 37. ISf are how many times 2^ ? 38. 221 are how many times 3| ? 39. 4:^Q are how many times 6| ? 40. 7f are how many times 4^ ? 41. 8| are how many times 3| ? 96 INTELLECTUAL ARITHMETIC. [61. Gt. 1. What is 1 of 3 ? AvALTSTS. That number lohich^ taken 4 times, will make 3. Since 1 fourtJi of 1 is ^,1 fourth of 3 is 3 ti?nes I of 1, or ^ of 1. Therefore | o/3 is | ofl, or^. 2. What is -1 of 3 ? of 4 ? of 6 ? of T ? 3. What is -J of 7 ? of 3 ? of 9 ? of 15 ? 4. What is 1 of 2 ? of 4 ? of 5 ? of 11 ? 5. What is J of 3 ? of 5 ? of 7 ? of 13 ? 6. What is I of 2 ? of 3 ? of 5 ? of 7 ? 7. What is i of 3 ? of 5 ? of 9 ? of 14 ? 8. What is -} of 4 ? of 6 ? of 12 ? of 18 ? 9. What is l of 5 ? of 3 ? of 20 ? of 30 ? 10. What is -jV of 7 ? of 9 ? of 16 ? of 47 ? 11. AVhat is j\ of 4 ? of 7 ? of 11 ? of 63 ? 12. What is -^\j of 2 ? of 7 ? of 11 ? of 34 ? of 75 ? 13. What is 2V of 13 ? of 9 ? of 17 ? of 50 ? of 91 ? 14. If 5 bushels of wheat cost $9, what will 1 bushel cost ? An-alysts. If 5 bushels cost $9, 1 bushel, which is 1 of 5 bushels, will cost i 0/ |9 ; i 0/ $9 is $14. There- fore, if 5 bushels cost $9, 1 bushel will cost Si J. 15. If 6 turkeys are worth $5, what are they worth apiece ? 16. If you divide 6 oranges equally among 7 boys, what part of an orange will each receive ? 17. If a man travel 29 miles in 9 hours, how far does he travel in 1 hour ? 18. If 1 man can build a barn in 20 days, in what time can 3 men build it ? 19. If a horse eat 5 bushels of oats in 8 days, what part of a bushel does he eat in 1 day ? 20. What will 1 hat cost, if 4 hats cost $17 ? 6S.] INTELLECTUAL ARITHMETIC. 97 63. 1. What are | of 3 ? AxALYsis. i of S are 3 times ^ o/ 3 ; | o/ 3 is | of 1, and 3 times | are | or 2|. Therefore^ i of ^ ere 2i. * 2. What are I of 5 ? of 4 ? of 7 ? 3. What are f of 4 ? of 6 ? of 8 ? 4. What are | of 2 ? of 3 ? of 9 ? > 6. What are | of 3 ? of 5 ? of 10 ? of 12 ? 6. What are -^^ of 4 ? of 7 ? of 15 ? of 18 ? 7. What are | of 2 ? of 3 ? of 14 ? of 20 ? 8. What are | of 5 ? of 8 ? of 19 ? of 28 ? 9. What are i\ of 7 ? of 13 ? of 21 ? of 30 ? 10. What are f of 2 ? of 6 ? of 15 ? of 24 ? 11. What are -^V of 7 ? of 36 ? of 50 ? of 63 ? 12. AVhat are -^^ of 35 ? of 60 ? of 77 ? of 91 ? 13. What are o^ of 10 ? of 15 ? of 120 ? of 150 1 14. If 4 cords of wood cost $14, what will 5 cord3 cost ? Analysis. If 4 cords of loood cost $14, 5 co?'cZi? will cost 5 ^rmes ;i o/|14. \ o/$14 zs $3^, and 5 ^jmea $3 A are $17A. Therefore 5 corc^s 24 ; 7 is contained in 24 3| times. Therefore^ |- o/" 35 is f o/'3| times 7. 18. "I of 54 is |- of how many times 5 ? 19. f of 24 is -^-^ of how many times 12 ? 20. I of 75 is -^ of how many times 8 ? of 56 is |- of how many times 20 ? 91 4 "V 22. I of 108 is -\ of how many times 9 ? ft 108 INTELLECTUAL ARITHMETIC. [70. 23. -^j of 121 are | of how many times 7 ? 24. 1^ of 33 are -J of how many times 6 ? 25. II of 34 are f of how many times 14 ? 26. |- of 30 are |-| of how many times 20 ? 27. I of ^ of 63 are ^ of | of how many times 11 ? 28. I of I of 50 are J of J of how many times 8 ? 70. 1. ^- of 56 are |- of 3 times what number ? * Analysis. 4 0/ 56 are | 0/ 3 times i of 9 times | of 4 times ^ of B6 ; 4 of 5Q is 8, and 4 ^zmes 8 z5 32 ; ^0/32 is 4, and 9 times 4 is 36 ; j o/36 es 12. ^^a^e- /ore, 4 // may wse the form of analysis used in section 2^5 onjnige 41. 2. If 9 pounds of sugar cost 75 cents, what will 12 pounds cost ? 8. If G men can cut 45 cords of wood in 3 days, how many cords can 8 men cut in the same time V 4. If 31 yards of cloth cost $10i , how much will 7 yards cost ? 5. If 4| pounds of butter cost QQ cents, what will 2 1 pounds cost ? 6. If a mechanic earn 13|- shillings in 1^- days, how much can he earn in a week ? 7. If %1\ will buy 3|- cords of wood, how many cords can be bouglit for $10 J- ? 8. If -J barrel of flour cost ^^, what will | of a barrel cost ? Analysis. What part of ^ is ^"^ i = ^, and § = |- ; the ratio of ^ to ^ is the same as of 3 ^o 4, = |-. Then^ since 4 barrel of four cost $4^, § 0/ a barrel will cost ^ of $4^ ; lof ^ =z %6- — $6. Therefore, ^-c. 9. If a man can run 6 miles in f of an hour, how far can he run in 3^ hours ? 10. How many yards of carpeting |- of a yard wide are equal to 12 yards -| of a yard wide ? 11. If a staff 3 feet long cast a shadow 5 feet in length, what would be the length of the shadow cast by a pole 13 feet long ? 12. If the sawing of |- of a cord of wood cost 6^ shillings, what would the sawing of 3|- cords cost ? " 75.] INTELLECTUAL ARITHMETIC. 117 13. John earns 9 cents as often as James earns 15 cents ; when John has earned 63 cents, how much has James earned ? 11. Two persons start from different points and travel towards each otlier ; the lirst one travels T miles while the otlier travels 5 miles, and when they meet the first one has traveled 70 miles ; how far apart were they when they started ? 15. If 4 men can build a wall 60 feet Ions: in 6 dsijs, in what time can 3 men build a wall yO feet in length ? Analysis. In J of ^ of Q days, ickich are 12 days. Or thus : if it ivill take 4 men 6 days to build a wall 60 feet long, it will take 1 man 4 times 6 days, or 24 days, and 3 men can do it in ^ of 24, or 8 days ; to build a icall 1 foot long ivill require ^'^ of 8, or -^^ days, and to build a ivall 'dO feet long ivill require 90 times as many days, or DO times -^fj, equal to 12 days. Tlierefore, S^c. 16. If 5 men can do a piece of work in 10 days, how many men will do a piece of work 4 times as larore in 20 davs ? 17. If a man perform a journey in 8 days, by traveling 9 hours a day, how many days will he re- quire to perform the same journey, if he travel 12 hours a day ? 18. If 5 horses eat 11 tons of hav in 1 month, how many tons will 6 horses eat in 2|- months ? 19. How many days will it take 5 men to earn $11| , if 3 men earn 8J in ^ of a day ? 20. If 1 horse eat 1^ bushels of oats in 3 davs, in how many days will 4 horses eat 49 bushels ? 21. If a barrel of flour will supply a family of 4 persons 5 weeks, how much will supply a family of 3 persons 2^ weeks ? 22. If 3 furnaces consume 124 tons of coal in 7 days, how long will VJ^ tons last 5 furnaces ? 118 INTELLECTUAL ARITHMETIC. [76. 76. CHAPTER YIII. PERCENTAOE. The terms^ percentage and per cejit.,s\gmfy hy the hun- dred^ or hundredths, that is, a certain number of parts of each one hundred parts, of whatever denomination. Thus, by 5 per cent, is meant o cents of every 100 cents, $5 of every $100, 5 bushels of every 100 bushels, &c. Therefore, 5 per cent, equals 5 hundredths, (y^^,) or ^V- ^ P^i" cent., 8 hundredths, (-fnuO o^' i^h ^^ ^^^^ given number or quantity. 1. A man, having $40, lost 3 per cent, of it ; lioW many dollars did he lose ? Analysts. Si.jice he lost 3 per cent,, or yf^, on $1, on $40 he lost 40 times y^^, or \l% of $1, equal to $1^. Therefore, S^^c. s 5 per cent, of |25 ? of ISO ? of $45 ? s 7 per cent, of |15 ? of 140 ? of $200 ? s 6 per cent, of $18 ? of $37 ? of $54 ? s 3 per cent, of 50 bushels of corn ? s 10 per cent, of 160 tons of plaster ? s 25 per cent, of 96 gallons of wine ? s 12 per cent, of 331 pounds of sugar ? s 15 per cent, of 110 barrels of flour ? s 8 per ceht. of 28 yards of cloth ? s f per cent, of $45 ? 2. What 3. What 4. What 6. What 6. What 7. What 8. What 0. What 10. What 11. What Analysts. Si7ice 1 per cent of $45 is yV^, % of I per cent, is f of j%% or -fjj^, equal to $f^. 77ierefore, Sfc. 12. What 13. What 14. What 15. What 16. What s I per cent, of $28 ? of $44 ? of $36 ? s i per cent, of $63 ? of $120 ? s I per cent, of 30 barrels of cider ? s 3|- per cent of 70 sheep ? of 35 cows ? s 2| per cent, of 34 hundred weight ? 77.] INTELLECTUAL ARITHMETIC. 119 17. A man bought 75 barrels of apples, and on opening tliem, found 8 per cent, of them spoiled ; how many barrels did he lose ? 18. If I have 1200 deposited in the bank, and draw out 15 per cent, of it, how much remains ? 19. A farmer, having 176 sheep, sold 75 per cent, of them, and kept the remainder ; how many did he keep? 20. A young man, having |104, lost 12^ per cent, of it in gambling; how many dollars did he lose, and what per cent, of the whole had he left ? 77. 1. What fraction of a number is 8 per cent, of it ? Analysis. Since 1 per cent, is y^^, 8 per cent, is 8 times y^g-, or yf ^, = ^%. Therefore 8 per cent, equals /^ of any number or thing. 2. What fraction of a number is 6 per cent. ? 7 per cent. ? 10 per cent. ? 12^ per cent. ? 3. What fraction of a number is Q\ per cent. ? 16f per cent. ? 20 per cent. ? 37|- per cent. ? 40 per cent. ? 4. If you have $120, and lose SSJ per cent, of it, what part of it will you lose ? 5. James, having 250 marbles, lost 40 per cent, of them at play ; what part of the whole had he left, and how many did he lose ? 6. What per cent, of a barrel of flour is |^ of it ? Analysis. Since the whole of any number or thing is equal to 100 per cent., f of one barrel of flour is equal to f (t/* 100 per cent., or 40 per cent. Therefore, S^c. 7. If a man save f of his income, what per cent, does he spend ? 8. If a merchant invest f of his money in dry goods, what per cent, does he invest ? 120 INTELLECTUAL ARITHMETIC. [78. 78. 1. A farmer, having 20 sheep, lost 5 of them by disease ; what per cent, did he lose ? Analysis. Since 20 sheep are 100 per cent., or all that he had, 5 sheep are -^q-, or ^, of all he had; and ^ of 100 per cent, is 25 per cent. Therefore, ^c. 2. What per cent, of 21 is 7 ? 3. What per cent, of 50 is 5 ? 10 ? 20 ? 25 ? 4. What per cent, of 140 is $5 ? $8 ? $25 ? 130 ? 5. What per cent, of 18 pounds is 3 pounds ? 12 pounds ? 6. What per cent, of 42 miles is 6 miles ? 7 miles ? 7. What per cent, of 12i- is 2} ? Q>\ ? 8. What per cent, of 30''is 12"? 15 ? 20 ? 9. What per cent, of 18 is 9 ? 12 ? 15 ? 10. 11 is what per cent, of 9 ? of 15 ? of 21 ? 11. 2| is what per cent, of 7^- ? of 12^- ? of 10 ? 12. l^is what per cent, of 3l"? of 16|"? of 20 ? 13. -1/ is what per cent, of 8 ? of 12 ? of 20 ? 14. If from a hogshead of molasses a grocer draw 42 gallons, what per cent, of the whole will remain ? 15. From a box of tea containing 60 pounds, 15 pounds were sold at one time, and 25 pounds at another ; what per cent, of the whole remained un- sold ? 16. In a heap of potatoes containing 150 bushels, 3 bushels of every 5 are bad ; what per cent, are bad, and how many bushels are good ? 17. A gambler, liaving |250, lost $80 at play ; what per cent, of his money did he lose, and what per cent, had he left ? 18. James, having 62^- cents, gave 37|^ for a book ; what per cent, of his money had lie left ? 19. A grocer, having a barrel of sugar containing 200 pounds, sold \ of it at one time, and ^ of tlie remainder at another time ; what per cent, remained unsold ? 79.] INTELLECTUAL ARITHMETIC. 121 79. 1. A person collects ^240, and receives 5 per cent, commission on what he collects ; what com- pensation does he receive ? Analysis. Since the cojnmission is 5 per cent., or y§^, equal to ^-V? ^f ^^^^ *^^"^ collected, he receives ^'g- of $240, which is $12. Therefore, Sfc. 2. What will be the expense of collecting a note of 8800, at 10 per cent, commission ? 3. What mnst be paid for collecting a tax of $300, allowing 12| per cent, commission ? 4. An agent sells 81200 worth of merchandise, at 25 per cent, commission ; how much will he receive for his services ? 5. An auctioneer sold goods to the amount of $500 ; what will his commission amount to, at 2^ per cent. ? 6. Paid an attorney 8^ per cent, to collect a debt of $640 ; how much did he receive for his services ? 7. If a man fail in business, and can pay but 40 per cent, of his debts, how much will a creditor receive on a debt of 8175 ? 8. Bought 81000 worth of books, receiving a com- mission of 3| per cent. ; how much did I receive for my services ? 9. If a broker sell 8600 worth of New York Cen- tral Railroad stock, and charge f per cent, for sell- ing, how much will he receive ? 10. At 4. of 1 per cent., what will be the expense of negotiating a bill of exchange of 8625 ? 11. A broker in Chicago exchanged 81200 on the Chemical Bank of New York, at | per cent. ; what amount of brokerage did he receive ? 12. A real estate agent sells a house and lot for 82000, and charges 1^ per cent, commission for sell- ing ; how much does he receive ? 122 INTELLECTUAL ARITHMETIC. [80, 8I>. 1. A merchant sends his agent 1780 to ex- pend for merchandise, after deducting his commis- sion of 4 per cent. ; what sum will he expend ? Analysis. The money to he exjjended is \%^ of itself and the commission y^ij, or ^y, of this sum; hence the whole amount se7it to the agent is |^^-, or §|. Since $780 is 5.|, _i_. is 2^g. of $780, or $30, his commission ; and f-| is 25 times 30, or $750, the sum to be expended. 2. I gave a broker $810 to invest in bank stock, after deducting his commission of 1^ per cent. ; what was his commission, and how much did he invest ? 3. A distiller sent Mr. B. 81550, with which to buy corn, after deducting his commission of 3^ per cent. ; how much did he expend, and how much did his commission amount to ? 4. How many bushels of wheat, at $1 a bushel, can an agent buy for $1230, and retain 2 J- per cent, commission for his trouble ? 5. A farmer employed a man to thresh his wheat, agreeing to give him 12 per cent, of all he threshed ; how many bushels must he thresh that the farmer may retain QQ bushels? Analysis. Since the thresher received -^^^, or -^-^ of all he threshed^ the farmer received the difference between \%%^ or §^ and ^\, which is |f. The?! 66 bushels is §^ of the whole number of bushels threshed; since 66 bushels is ^f, ^\ ^5 ^V of 66, or 3 bushels, and f | is 25 times 3 bushels, or 75 bushels. Therefore, Sfc. 6. What amount must be collected on a rate bill, that the collector may retain his fee of 5 per cent., and pay over $228 ? 7. What amount of accounts must an individual collect in order to pay over $1100, and retain 8J per cent, for collecting ? §3, J INTELLECTUAL ARITHMETIC. 123 §1. 1. 'Wh^t must be paid for insuring a house and furniture for $1000, at 1^ per cent, premium ? * Analysis. Since the premium is 1^ per cent., or ^-S^, equal to ^V ^f ^^^^ ccmount insured, the prejnium on $1000 will he -gi^ of $1000, or $12^. Therefore, &>c. 2. What will be the premium for insuring 200 barrels of flour, valued at $1200, at 4 per cent. ? 3. What must I pay annually for an insurance of $900 upon my life, at 2'J per cent. ? 4. What must be paid for insuring a case of cloths, valued at $600, at If per cent, premium ? 5. What is the annual premium of insurance, at I per cent., on a building valued at $4000 ? 6. If a merchant has his stock of goods insured for $2500, at | of 1 per cent., what is the premium ? 7. A man owns f of a boat load of grain, valued at $1600, and insures his interest at If per cent ; what premium does he pay ? 8. At 2 per cent., what amount of insurance can I obtain for $18 premium ? Analysis. Si7ice 2 per cent, premium is y§^, or -^-^ of the amount insured, $18, the given premium, will he equal to -1^ of the required amount of insurance ; $18 is ^^ of 50 times $18, equal to $900. TJierefore, Sfc. 9." At 3 per cent., what amount of insurance can be obtained on a house for $75 ? 10. At ^ per cent., what amount of insurance can be obtained on a boat load of flour, for $24 ? 11. What amount of insurance can be had for $45, upon a car load of horses, at 4~|^ per cent. ? 12. If the rate is If per cent., and the premium paid is $91, what will be the amount of insurance obtained on a store and its contents ? * The sum paid for insurance is called the premium. 124 INTELLECTUAL ARITHMETIC. [82. 8S. 1. If a man buy a horse for |90, for how much must he sell him to gain 20 per cent. ? Analysis. Since he c/ains 20 per cent., or y^.o^, equal to ^ of what the horse cost hi)7i, he must sell him for f o}' what he cost; -i of $90 is $18, and | of $90 is 6 times $18, or $108. Therefore, S)'C. 2. A sleigh was bought for |50, and sold for 8 per cent, more than it cost ; what was it sold for ? 3. Bought a quantity of sugar for $84, and sold it at an advance of 12|^ per cent ; what was it sold for ? 4. A grocer bought some tea for $45, but finding it damaged, he was obliged to sell it at a loss of 10 per cent. ; what did he sell it for ? 5. Paid $12 for 15 yards of cloth ; what must it be sold for a yard to gain 25 per cent. ? 6. A drover bought 60 sheep for $180, and sold them at a loss of 20 per cent, on the cost ; what did he receive per head for them ? 7. A grocer bought 440 lemons for $12, and after throwing away 10 per cent, of them, lacking 4, as worthless, he sold the remainder so as to gain 88|- per cent, on the cost of the whole ; what did he sell them for apiece ? 8. Bought 6 barrels of flour for $40 ; for what must it be sold a barrel to gain 5 per cent, on the cost ? '9. If I buy eggs at 10 cents a dozen, how must I sell them to gain 30 per cent. ? 10. A speculator bought a quantity of pork for $500, and sold it at a loss of 7 per cent. ; with the proceeds he bought another quantity, upon which lie gained 20 per cent. ; what wa his gain on the whole ? 11. Bought hay at $14 dollars a ton, which was 12| per cent, less than the market price ; what was the market price ? 83.] INTELLECTUAL ARITHMETIC. 125 83. 1. What is gained per cent, by selling clover seed for |6, that cost |4 ? Analysis. The whole gain is equal to the difference between $6 and $4, which is $2. Since $4 gain S$2, or -^ of Itself, equal to Y^gV? ^^^^ ^«ui will be 50 per cent. There- fore, ^c. 2. What per cent, is gained by selling pork for $7 a hundred weight, that cost |6 ? 3. What will be gained by expending $500 for sugar, when it can be bought for 8 cents, and sold for 8|- cents a pound ? 4. "if I buy 1300 worth of sheep, and sell them for $375, what do I gain per cent. ? 5. Mr. C. bought a horse for $153, and sold him for $128 ; what per cent, did he lose ? 6. A grocer bought eggs for 9 cents a dozen, and sold them for 12 cents ; what per cent, did he gain ? 7. What per cent, is lost in buying corn at 50 cents a bushel, and selling it at 45 cents ? 8. If a house bring |- of its value every 4 years in rent, what is the gain per cent, each year ? 9. Bought a horse for 20 per cent, less than $150, and sold him for 10 per cent more than $150 ; what per cent, was gained ? 10. A peddler bought oranges for 18 cents a dozen, and sold them for 2 cents each ; what per cent, did he gain ? 11. A farmer refused to sell his barley for 75 cents a bushel, and was afterwards obliged to take 60 cents a bushel for it ; what per cent, did he lose ? 12. Bouglit cotton cloth at 7-|- cents a yard, and sold it for 9 cents a yard ; wha"t was the gain per cent. ? 13. Sold damaged cloth so as to lose J of what it cost ; what per cent, was lost ? 126 INTELLECTUAL ARITHMETIC. [84. 84. 1. A tailor sold a coat for 124, b J whicli he gained 20 per cent, on the first cost ; what was its cost ? Analysis. Since he gained 20 per cent, or ^ of the cost, l^'l^ is f of the cost ; since $24 is f, ^ o/$24, or $4, is -^ of the cost, and $4 is i of 6 times $4, or $20. There- fore, S^c» 2. A hatter sold a hat for $3-J-, which was 12J- per cent, above cost ; what did it cost : 3. A jeweler sold a watch for $Q5, thereby gain- ing 30 per cent, on its cost ; what was its cost ? 4. A mechanic sold a carriage for $108, which was 10 per cent, less than it cost ; how much would he have received for it had he sold it so as to gain 20 per cent. ? 5. If 16| per cent, is gained by selling flour at $1 a barrel, what did it cost ? 6. A merchant sold 2 barrels of sugar for $24 each ; on one barrel he gained 20 per cent, and on the other he lost 20 per cent. ; did he gain or lose by the bargain, and how much ? 7. A grocer bought coffee so that he could sell it for 18 cents a pound, and make a profit of 33-^- per cent. ; what did it cost him ? 8. A man bought a horse and carriage ; he sold them both at 8 per cent, above cost, receiving $81 for the horse, and $108 for the carriage ; what was the cost of both ? 9. A fruit dealer sold pine-apples at 96 cents a dozen, thereby losing 4 per cent. ; what did they cost apiece ? 10. B sells a horse to C, and gains 12|- per cent. ; C sells him to D for $118, and thereby gains 18 per cent. ; how much did the horse cost B ? 85.] INTELLECTUAL ARITHMETIC. 127 8d. 1. Sold Avheat so as to gain 16 cents on a bushel, which was 12|- per cent, of what it cost ; what did it cost ? 2. A broker exchanged $150 at ^ per cent. ; how much brokerage did he receive ? 3. A man, having a farm of 200 acres, sold 75 acres of it; what per cent, of the whole remains unsold ? 4. What per cent, does William gain by selling apples at |- of the cost ? 5. If I buy stoves at $12 each, and sell them at S^ per cent, profit, what Avill I gain on 1 stove ? 6. If a broker buy $800 worth of bank stock for me, and charge ^ per cent, brokerage, how much will he receive ? 7. Sold butter so as to gain | as much as it cost ; what per cent, was gained ? 8. Mr. A. lends his money so as to receive a sum equal to -^q of it for its use ; Avliat per cent, does he receive ? 9. A brewer sends a person $520 with which to purchase barley, after deducting his commission of 4 per cent. ; how much does he expend, and how much does his commission amount to ? 10. The cost of building a town house, and paying collector's fees of 5 per cent., was $945 ; what was the cost of the house ? 11. Hiram agrees to dig farmer F.'s potatoes for 8 per cent, of what should be put into the farmer'^ cellar ; he digs 324 bushels ; how many bushels should be put into the cellar, and how many bushels should Hiram receive ? 12. Bought $200 worth of dry goods, and $300 worth of groceries ; on the dry goods I lost 20 per cent., but on the groceries I gained 15 per cent. ; did I gain or lose on my whole capital, and how much ? 128 INTELLECTUAL ARITHMETIC. [85. 13. A merchant bought 40 bushels of grass seed, at the rate of 4 bushels for $6, and sold it at the rate of 5 bushels for $8 ; what was his whole gain, and what his gain per cent. ? 14. A drover bought 20 sheep for $50, and sold them so as to gain 20 per cent. ; how much did he receive a head for them ? 15. A man bought 60 cords of wood for |200, and sold it at a loss of 5 per cent. ; at what price did he sell it per cord ? 18. If I buy rice at 4 cents a pound, and sell it at 5 cents, what is my gain per cent. ? 17. Sold a cow at auction for $18 that cost $20 ; what was the loss per cent. ? 18. A boy bought peaches at the rate of 3 for 2 cents, and sold them at the rate of 9 for 7 cents, what was his gain per cent. ? 19. A tailor sold two coats for $26 each ; on one he gained 30 per cent., and on the other he lost 30 per cent. ; did he gain or lose on both, and how much ? 20. A music dealer sold a piano-forte for $230, which was 8 per cent, less than its value ; had he sold it for $300, what Avould have been his gain per cent. ? 21. Two men buy a lot of pork together ; A fur- nishes $200, and B $150 ; their profits are $70 ; what is their gain per cent., and what is each one's share of the gain ? 22. If a ton of hay is bought for | of the market price, and sold for 5 per cent, more than the market price, what per cent, is gained ? 23. A person engaged in speculation sold out his interest for $2100, which was 30 per cent, less than twice as much money as he began with ; how much did he begin with, and what was his gain ? §0,] INTELLECTUAL ARITHMETIC. 129 §@, Interest is a sum paid for the use of borrowed money, or on demands after they become due. The PiiiNCiPAL is the money lent, or the sum for which interest is paid. The Amount is the sum of the principal and interest. The Rate per Cent, is the sum paid for the use of SlOO or 100 cents for one year. Thus, if $6 be paid for the use of $100 one year, the rate is 6 per cent, per annum. The interest on any sum for one year is always a certain number of hundredths of the principal. Thus, the interest of any sum for one year, at 5 per cent., is 5 hundredths (tub) or ^V of the principal ; at 8 per cent, it is 8 hun- drcdtiLS (xf xr) or -^-^ of the principal. Practically., SO days are considered a month, and 12 months a year, in computing interest. When no time is named, one year is always understood. The rate of interest is established by law; and taking more than such rates is termed usury. 1. What is the yearly interest of ^80, at 5 per cent. ? Analysis. Sinc^. the interest is 5 per cent., or y^^, equal to -'^ of the princ^'pal, the interest of $80 is -^\y of $80, or $4. Therefore, SfC. Or tlius : Siy^ne the interest of $1, or 100 cents, is 5 cents for one year, the interest of $80 is 80 twies 5 cents, or 400 cents, equal to $4.* 2. What is the yearly interest of $200, at 6 per cent. ? 3. What is the yearly interest of $125, at 4 per cent. ? 4. What is the annual interest of $80, at 7 per cent. ? 5. What is tho annual interest of $95, at 5 per cent. ? * The fractio'Hf^ method is considered preferable in mental exercises. 9 130 INTELLECTUAL ARITHMETIC. [87. 6. What is the annual interest of $26, at 10 per cent. ? 7. What is the annual interest of |228, at 12|- per cent. ? 8. What is the annual interest of 196.32, at 6| per cent. ? 9. What is the annual interest of 8144.60, at 8J per cent. ? 10. What is the annual interest of $400, at 15 per cent. ? 11. What is the annual interest of $500, at 7 per cent. ? 12. What is the annual interest of 1120.80, at 7| per cent. ? 13. What is the annual interest of $1000, at 9 per cent. ? 14. What is the annual interest of $150, at 3 per cent. ? 87. 1. What is the interest of $150 for 3 years, at 8 per cent. ? Analysis. Since the interest for 1 year at 8 per cent, is jf^, equal to ^2_, of the principal, for 3 years it is 3 times 4^, or -S^, of the principal. ^^ ^f ^^^^ ** ^^j ^"^ ^6- o/*'$150 Is 6 times $6, or $36. Therefore, Sfc. Or thus : Siiice the interest of $150 for 1 year at 8 per cent, is $12, (86,) for 3 years it is 3 times $12, or $36. 2. What is the interest of $30 for 2 years, at 5 per cent. ? 3. What is the irnterest of $50 for 4 years, at 6 per cent. ? 4. What is the interest of $90 for 5 years, at 7 per cent. ? 5. What is the interest of $75 for 3 years, at 12 per cent. ? 88.] INTELLECTUAL ARITHMETIC. 131 6. What is the interest of 864.96 for 2 years, at 6| per cent. ? 7. A's note of |25 has been due 2 years ; what is the interest, at 6 per cent. ? 8. Borrowed 8-300 for 3 years, at 7 per cent. ; what will be the interest ? 9. What is the interest on a note of $16.50, for 5 years, at 10 per cent. ? 10. I owe two notes, one for 8145, due in 2 years, at 5 per cent., and the other for 8200, due in 3 years, at 6 per cent. ; what will be the sum of the interest that I must pay ? 11. What is the interest of 8225 for 2 years, at 7 per cent. ? 12. What is the interest of 850 for 8 years, at 6 per cent. ? 13. What is the interest of 8400 for 2 years, at 5J- per cent. ? "14. Gave a note for 888.96, due in 3 years, at 6| per cent ; what will be the interest ? 15. Gave a note due at date, for 845.50, but did not pay it until the end of 5 years ; what was the interest due, at 8 per cent. ? 88. 1. At 8 per cent., what part of 81 equals the use of it for 3 years 9 months ? Analysis. Since there are 12 months in 1 year^ 9 months is y^^* or ^ of \ year, and 3 years 9 months are equal to 3|^, or ■'^-^- years. Since the interest of %\ for 1 year at 8 per cent, is y^^y, equal to ^t; of the principaU for 3 years 9 months, it is 3|- ti?nes, or -y^-, of -^^^ equal to -^^ of the principal^ or %y^. Therefore, ^-c. 2. At 6 per cent., what part of 81 equals the use of it for 2 years 8 months ? 132 INTELLECTUAL AEITHMETIC. [88. 3. At 5 per cent., what part of any sum equals the use of it for 2 years 6 months ? 4. At 7 per cent., what part of any sum equals the interest of it for 1 year 8 months ? 5. What part of any sum equals the interest of it for 3 years 2 months, at 4 per cent. ? 6. What part of any sum equals the interest of it for 5 years 4 months, at 9 per cent. ? 7. At 6^ per cent., for 3 years 4 months, what part of the interest equals the principal ? 8. At 8 per cent., for 5 years 5 months, what part of the principal equals the interest ? 9. At 7^- per cent., for 2 years 11 months, what part of the principal equals the interest ? 10. At 6 per cent., for 2 years 1 month, what part of the principal equals the interest ? 11. At 10 per cent., for 4 years 10 months, what part of the principal equals tlie interest ? 12. At 8 per cent., for 3 years 3 months and 18 days, what part of the principal equals the interest ? Analysts. Since 30 days make a. month, 18 days are 4^8., or ^ of a month ; and since 12 months make a year, 1 month is yV of a year ; ^ of 1 month is ^ of yV, or ^\j of 1 year, and 3| months, equal to ^^-, is 18 times -^^j, or y^^ of a year. Hence the interest of $1 for Sy^^y, or ^^ years, at 8 per cent., is y^^\ of it. (8Sj Ex. 1.) There* fore, ^c. 13. What part of the principal equals the inter- est, for 2 years 5 months and 10 days, at 6 per cent. ? 14. Wliat part of the principal equals the interest, for 1 year 8 months and 25 days, at 7 per cent. ? 15. What part of the iH'incipal equals the interest, for 2 years 3 months and 6 days, at 6 per cent. ? 16. What part of the principal equals the interest, for 2 years 11 months and 6 days, at 5 per cent^ ? 89.] INTELLECTUAL ARITHMETIC. 133 17. At 7|- per cent., for 8 months 10 days, v/liat part of the principal will equal the interest ? 18. At 6 per cent., for 5 years 7 months and 15 days, ^vhat part of the principal will equal the interest ? 19. At 8 J per cent., for 3 years 5 months and 12 days, what part of the principal equals the in- terest V 20. At 7 per cent., for 11 months 3 days, what part of the principal will equal the interest ? 21. At 4 per cent., for 8 years 6 months and 15 days, what part of the principal will equal the in- terest ? §9, 1. What is the interest of 840 for 3 years 4 months, at 6 per cent. ? Analysis. 3 years 4 months equals 3^, or ^^- years ; and the interest of any sum for ^^- years, at 6 j^e?' cent.^ equals ^ of it. (88.) -5- of $40 is $8, the required in^ terest. Therefore, ^c. Or thus : Since the interest of $1 for 1 year, at G per cent., is 6 cents, for $40 it is 40 times 6 cents, or $2.40, and for 3^ years it is 3^- times $2.40, equal to $8. 2. What is the interest of 8150 for 2 years 10 months, at 8 per cent. ? 3. What is the interest of 880.40 for 4 years 2 months, at 7 per cent. ? 4. What is the interest of 8240 for 1 year 9 Months, at 5 per cent. ? 5. What is the interest of 8120 for 5 years 8 months, at 1\ per cent. ? 6. What is the interest of 890 for 4 years 7 months, at 4 per cent. ? 7. What is the interest of 8500 for 10 months, at 6 per cent. ? 134 INTELLECTUAL APJTHMETIC. l& 8. What is the interest of $128 for 2 years 9 months, at 6|- per cent. ? 9. What is the interest of $125 for 1 year 4 months, at 7 per cent. ? 10. What is the interest of |300 for 8 months, at 6 Der cent. ? 11. What is the interest of |50 for 5 years 7 months and 15 days, at 8 per cent. ? Analysis. The interest of any sum for 5 years 7 months and 15 days, at 8 per cent., equals -^^ of it, (885 Ex. 12 ;) 2-V of $50 is $2^, and ^% of $50 is 9 times $2^-, equal to $22i. Therefore, ^c. 12. What is the interest of 175.60 for 4 years 5 months and 10 days, at 9 per cent. ? 13. What is the interest of $50 for 6 years 4 months and 24 days, at 5 per cent. ? 14. What is the interest of $300 for 4 years 7 months and 15 days, at 8 per cent. ? 15. What is the interest of $288 for 8 months 10 days, at 7 J per cent. ? 16. What is the interest of $1200 for 20 days, at 6 per cent. ? 17. What is the interest of $40 for 9 months 5 days, at 4^- per cent. ? 18. Wiiat is the interest of $36.72 for 5 years 6 months and 20 days, at 7 per cent. ? 19. Wliat is the interest of $120 for 2 years 1 month and 6 days, at 12|- per cent. ? 20. What is the interest of $24 for 11 months and 20 days, at 15 per cent. ? 21. What is the interest of $2000 for 18 days, at 5 per cent. ? 22. What is the interest of $1500 for 2 months and 24 days, at 6 per cent. ? ,] INTELLECTUAL ARITHMETIC. 135 1. Yvliat will be the amount of $60 for 2 years 6 months, at 6 per cent. ? Analysis. Since the interest is equal to ^^^ of the prin- cipal^ (^^5) and the amount is equal to the principal and interest, it folloivs that %%, the principal, added to ^^g-, the interest, equals §3', ^^^^ amount, ^^u" ^f ^^^ is $3, arid f ^- of $60 is 23 times $3, or $69, the amouyit. Therefore, ^c, Note. "When more convenient, the interest may first be found, to which add the principal, and the result will be the amount. 2. What is the amount of $36 for 4 years 2 months, at 7 per cent. ? 3. What will $120 amount to in 2 years 11 months, at 8 per cent. ? 4. What will $96.48 amount to in 3 years 4 months, ac 6^ per cent. ? 5. What will $80.50 amount to in 6 years 8 months, at 4| per cent. ? 6. What will $20.25 amount to in 12 years, at 5 per cent. ? 7. What will $1500 amount to in 10 months, at 10 per cent. ? 8. What will $150 amount to in 6 months and 20 days, at 6 per cent. ? 9. What will $250 amount to in 9 months and 18 days, at 7^ per cent. ? 10. What is the amount of $480 for 1 year 10 months and 25 days, at 5 per cent. ? 11. What is the amount of $500 for 3 years 4 months and 24 days, at 6 per cent. ? 12. What is the amount of $240 for 2 years 7 months and 6 days, at 7 per cent. ? 13. What is the amount of $1000 for 5 years 1 month and 6 days, at 4 per cent. ? 14. What is the amount of $120 for 10 years 6 months and 20 days, at 3 per cent. ? 136 INTELLECTUAL ARITHMETIC. [91. 1. What principal in 3 years 9 months, at 8 per cent., will give $90 interest ? Analysis. Since the interest for 3 years 9 months, at 8 per cent., is -^^ of the principal, (S85) $90 must be -^-q- of the required principal. Since $90 is y^^, ^tt is ^ o/$90jO/ $30, and $30 is y^ of 10 times $30, or $300, the principal Therefore, S)-c. 2. What principal, in 1 year 8 months, at 9 per cent., will give 836 interest? 8. What principal in 11 months, at 6 per cent., will give $22 interest ? 4. What principal in 7 months 15 days, at 8 per cent., Avill give $40 interest? 5. A rents a store to B for the yearly rent of $300, which is 12 per cent, of its cost ; what did it cost ? 6. A gentleman bonght 6 horses, for which he paid a sum of money which in 2 years 6 months, at 4 per cent., would have given him $90 interest; what did he pay apiece for the horses ? 7. A person deposits | of his money in the bank, which brings him an annual income of $1500, at 10 per cent. ; the remaining | he invests in business which yields him 20 per cent, profit ; what are his entire capital and his yearly income ? 8. Two persons engaged in trade ; A furnished | of the capital, and B | ; at the end of 3 years and 4 months they found that they had made a clear profit of $5000, which is 12^^ per cent, per annum on the money invested ; how much capital did each furnish ? 9. A capitalist invested | of his money in railroad stock, which depreciated 5 per cent, in value ; the remaining | he invested in bank stock, which at the end of 1 year had gained $1200, which was 12 per cent, of the investment ; what was the whole amount of his capital, and what was his entire loss or gain ? SJ3.] INTELLECTUAL ARITHMETIC. 137 92, 1. What principal will, in 3 years 4 months, at 5 per cent, amount to $700. Analysis. Since the interest for 3 years 4 months, at 5 per cent., is ^ of the principal, (88,) the principal |, added to the interest ^, equals the amount \ ; hence $700 is \ of the principal Since $700 is f, ^ is } of $700, or $100, and $100 is ^ of 6 times $100, or $600. Therefore, ^c. 2. What principal in 5 years, at 6 per cent., will amount to $1300 ? 3. What principal in 1 year 6 months, at 8 per cent., will amount to $280 ? 4. What principal in 4 years 2 months, at 3 per cent., will amount to $630 ? 5. What principal in 10 years, at 7 per cent., will amount to $340 ? 6. What principal in 9 months, at 10 per cent., will amount to $172 ? 7. What principal in 18 months, at 4 per cent., will amount to $530 ? 8. The amount due on a bond and mortgage is $2900, it having been on interest 7 years 6 months, at 6 per cent. ; what was the principal ? 9. Two men bought 200 acres of land, and at the end of 2 years sold it for $1500, which was an ad- vance of 12^ per cent, per annum on its cost ; what did it cost an acre ? 10. A man invested J of all he was worth in the lumber trade, and at the end of 2 years 8 months sold out his entire interest for $3100, whicli was a yearly gain of 9 per cent, on the money invested ; how much was he worth vrhen he commenced trade ? 11. A's money is to B's as 2 to 3 ; if J of A's money be put at interest for 3 years 9 months, at 10 per cent., it will amount to $550 ; how much money has each ? 188 INTELLECTUAL ARITHMETIC. [93. 9S. 1. Ill what time, at 5 per cent., will |60 gain $15 interest ? Analysis. 77^6 gain, or interest, is ^^-, or ^ of the prin- cipal, equal to 25 per cent, of the principal. (7T^ Ex. 7.) Jf a given principal gain 5 per cent, in 1 year, it will re- quire as many years to gain 25 per cent, as 5 per cent, is contairied times in 25 per cent., or 5 years. Therefore, ^c. Or thus : Since $60 in 1 year, at 5 per cent., will gain S3 interest, it will require as many years for $60 to gain $15 interest, as $3 is contained times in $15, which is 5 times. 2. How long will it take $120 to gain |24 interest, at 6 per cent. ? 3. In what time will $500 gain $35, at 7 per cent. ? 4. In what time will $120 gain $40, at 10 per cent. ? 5. In what time will $80 gain $6, at 3 per cent. ? 6. In what time will $300 gain $84, at 7 per cent. ? 7. In what time will $160 gain $20, at 6^ per cent. ? 8. In what time will $49 gain $12.25, at. 5 per cent. ? 9. In what time will any given principal douhle itself at 4 per cent. ? Analysis. Since, to douhle itself, any sum of money must gain 100 per cent., at 1 per cent., it loill require 100 years, at 4 per cent., ^ of 100 years, or 25 years. There- fore, ^'C. 10. In what time will a given principal double it- self at 5 per cent. ? 11. In what time will a given principal double it- self at 7 per cent. ? 94.] INTELLECTUAL ARITHMETIC. ISO 12. In what time will a given principal double it- self at 6 per cent. ? 13. In what time will a given principal double it- self at 10 per cent. ? 14. In what time will 1500 double itself, at 12J per cent. ? 15. In what time will |175 double itself at 20 per cent. ? 16. In what time will a given principal treble it- self at 5 per cent. ? Analysis. A given principal ivill treble itself at 1 per cent, in 200 years ; at 5 per cent, in \ of 200 years, or 40 years, 17. In what time will 8100 treble itself at 6 per cent. ? at 7 per cent. ? at 8 per cent. ? at 10 per cent. ? 1^4. 1. A man loaned 875 for 4 years, and re- ceived $18 interest ; what was the rate per cent. ? Analysis. Since tlic gain, or interest^ for 4 years, is rh ^^ i^b ^f ^^'^ principal, for 1 year it is ^ of ^^, or ^fg- of the principal, equal to 6 per cent. Therefore, ^c. Or, thus : At 1 per cent., the interest of $1 for 4 years is 4 ce?its, and of $75 it is 75 times 4 cents, which are 300 cents, equal to $3. Since $3 interest is 1 per cent, of $75 for 4 years, $18 interest is as many per cent, as $3 is contained times in $18, which is 6 times, equal to G per cent. 2. At what per cent, will $200 gain $49 interest in 3|- years ? 3. At what per cent, will $60 gain $25 interest in 4J years ? 4. At what per cent, will $90 gain $27 in 6 years ? 140 INTELLECTUAL ARITHMETIC. 5. At what per cent, will $12 gain $5 in 10 years ? 6. At what per cent, will $400 gain $55 interest in 2|- years ? 7. At what per cent, will $150 gain $44 interest in 3| years ? 8. At what per cent, will $125 gain $37.50 interest in 5 years ? 9. At what per cent, will $800 gain $75 interest in 1 year and 3 months ? 10. At what per cent, will $180 gain $45 interest in 3 years and 9 months ? 11. At what per cent, will $1250 gain. $312.50 interest in 2 years 6 months ? 12. At what per cent, will $2500 gain $200 in- terest in 1 year and 4 months ? 13. At what per cent, will a given principal double itself in 5 years ? Analysis. Since a given principal must gain 100 per cent, to double itself in 1 year, to double itself in 5 years ivill require ^ of 100 per cent., or 20 per cent. Therefore, SfC. 14. At what per cent, will a given principal double itself in 10 years ? 15. At what per cent, will a given principal double itself in 12 years 6 months ? 16. At what per cent. Avill $200 double itself in 4 years ? 17. At what per cent, will $100 double itself in 8 years ? 18. At what per cent, will $150 double itself in 15 years ? 19. At what per cent, will $300 double itself in 16 years 8 months ? 20. At what per cent, will $175 double itself in 2 years 6 months ? 95>.] INTELLECTUAL ARITHMETIC. 141 05. The 2^^'<^sent worth of a note payable a*: a future time is such a sum a?, put at interest at the given rate per cent, until it becomes due, will amount to the face of the note. Discount is an allowance made for the payment of money before it becomes due, and is obtained by subtracting the ■present worth from the given sum or face of the note. 1. What is the present worth of $180 payable in 8 years 4 months at 6 per cent, 'i Analysis. Since the interest for 3 years 4 months at 6 per cent, is \ of the principal, (^^j) ^^^^ amount, $180, is equal to the principal, |^, added to the interest, \, equal to f of the principal. Since $180 is f of the principal, ^ of $180, or $30, is \, and $30 is \ of 5 times $30, or $150. Therefore, SfC. Note. The discount is the difference between ^180 and $150, which is $30. 2. What is the present worth of a note for $36.90, payable in 2 years 6 months, at 5 per cent. ? 3. What is the present value of a note for 854, due in 5 years, and bearing interest at 7 per cent. ? 4. What is the present value of a debt of 8124.40, due in 4 years 2 months, at 8 per cent, interest ? 5. What is the discount of 82100, due in 1 year 3 months, at 4 per cent. ? 6. What is the discount on a note of 8560, paya- ble in 2 years, at 6 per cent, interest ? 7. What is the difference between the interest and the discount of 8130, due 10 months hence, at 10 per cent. ? 8. A man, having a span of horses for sale, offered them for 8480 cash in hand, or a note of 8550 due in 1 year 8 months without interest. The buyer accepted the latter offer ; did the seller gain or lose by his offer, and how much, allowing the money to be worth 6 per cent. ? 142 INTELLECTUAL ARITHMETIC. [S$6. 1. B sold a horse for | of 1| times the cost ; what was the gain per cent. ? 2. A cow purchased for ^28 in the spring was sold for $21 in autumn ; what was the loss per cent. ? 3. An old lady bought 80 apples of John at the rate of 2 for a cent, as many more of William at the rate of 3 for a cent, and sold the whole at the rate of 5 for 2 cents ; did she gain or lose, and at what rate per cent. ? 4. Did she gain or lose on the purchase made of John or William, and at v/hat rate per cent, on the amount of the purchase ? 5. A hogshead of molasses was bought for $20 ; 11-J per cent, of it leaked out ; how must the re- mainder be sold per gallon to gain 40 per cent, on the cost ? 6. A manufacturer sold 2 machines for $391 each ; on one he gained 15 per cent., on the other he lost 15 per cent. ; did he gain or lose on the sale of both, and how much ? 7. How much wheat must be taken to mill, that 6 bushels may be retained after giving toll of 6 pounds per bushel, or 10 per cent, for grinding ? 8. A man brought home 1500 feet of lumber after giving 37 J per cent, of the whole for sawing ; how much lumber did he have sp.wod ? 9. A farmer sold 2 horses for $150 apiece ; on one he gained 25 per cent., on the other he lost 25 per cent. ; did he gain or lose on both, and how much ? 10. For hulling barley, 36 per cent, is taken for pay ; at this rate, how many bushels must be taken that 32 bushels be returned after hulling ? 11. In a school district $57 was to be collected for teacher's wages ; the collector was to have 5 per cent, on all moneys collected ; how much must he collect to pay his fee and the teacher ? 96.] INTELLECTUAL ARITHMETIC. 143 12. How much plaster must A have ground, to bring home 14 tons, after the miller has taken 12^- per cent, of all he has ground ? 13. In how many years, at 5 per cent., will a given principal amount to the same as it would at 7 per cent, in 3 years ? 14. At what rate per cent, in 12 years will a given principal amount to the same as at 7 per cent, for 8 years ? 15. A farm rents for $500 a year, which is 6J per cent, on the purchase money, at $40 per acre ; how many acres in the farm ? 16. Mr. Jones paid $44 interest on a note running 4 years 4 months and 24 days, at 5 per cent. ; what was the face of the note ? 17. A's note of 8200 was given for a carriage ; 5 years 7 months and 6 days afterwards, $256 was given for the note ; what rito p^^r cent, was paid ? 18. A note of $300 on interest at 6 per cent, was given for a span of horses ; when the note was taken up, $330 was paid for it ; how long did it run ? 19. B, on being asked how much he owed for his farm, replied, " I pay 9 per cent, on the debt ; if I paid but 7 per cent., it would be $60 in my favor yearly." What did he owe ? 20. If Aaron had purchased his horses for 5 per cent, less than he did, they would have cost him $190 ; how much did he pay for them ? 21. If I had purchased my farm for 6 per cent, less than I paid for it, it would have made a differ- ence in the purchase money of $120 ; what did the farm cost me ? 22. A speculator sold wheat for 90 cents a bushel, and in so doing lost 10 per cent. ; what should he have sold it for, to have gained 15 per cent. ? 23. A nurseryman sold apple trees at $15 per 144 INTELLECTUAL ARITHMETIC. [06, thousand, and cleared | of Ms receipts ; what per cent, profit did he make ? 24. B pays ^400 a year for the use of 100 acres of land, giving 8 per cent, of its value ; what is it worth per acre ? 25. I bought a stock of goods for $800, and paid •$15 for store rent, $8d for clerk hire, and sold them at the end of 6 months ; wliat per cent, must be made on the goods to cover expenses ? 26. In how maiiy years will a man, paying inter- est at 7 per cent, on a debt for land, pay the amount of the debt in interest ? 27. A. bought a farm for 13000 ; he reahzed $700 from the sale of wheat, $200 from corn and barley, and $100 from fruit, and then sold the farm at a dis- count of 25 per cent. ; did he gain or lose, and how much ? 28. B bought a horse for $60, then sold him for $100, and repurchased him for $80 ; what was the gain per cent, on the c.ri;??r^'J inve^Lment ? 29. A milkman sold milk for 4 cents a quart, by which he cleared ^ c£ the i ccei(.'te ; b\t milk becoming, scarce, he sold for 5 cents ; what per cent, did he make at the latter price ? SO. A walked 5 per cent, of a journey of 300 miles ; 20 per cent, of the remainder he rode in the stage, and the rest of the way in the cars ; how far did he ride in the cars ? 31. A mechanic sold a buggy for $54, and gained 20 per cent. ; he then sold another for $54, and lost 10 per cent. ; did he gain or lose, and how much ? 82. A dealer sold a melodeon for $190, and lost 5 per cent, on it ; he then sold another for the same money, but made enough to balance the loss on tho first ; what per cent, did he make on the second ? 97.] INTELLECTUAL ARITHMETIC. 145 CHAPTER IX. MISCELLANEOUS EXAMPLES. 97. 1. A gentleman, owning | of a vessel, sold I of his share ; what part of the vessel does he still own ? Analysis. Since he sold | of his share, he would have i left, and ^ of ^ is ^. Therefore, ^c, 2. A man, owning ^ of a share in the Central Rail- road, sold I of it ; what part of a share has he left ? 3. A man, having |^ of a barrel of flour, gave \ of it to a poor neighbor ; what part of a barrel has he left ? 4. Harry, having | of a dollar, gave |- of it for a knife ; what part of a dollar has he left ? 5. A man sold a watch for 818, which was | of what it cost him ; how much did he lose ? 6. A grocer sold a quantity of cheese for $45, which was | of what it cost him ; how much did he gain ? 7. A threshing machine was sold for 1120, at a sacrifice of | of the cost ; what was the loss on it ? 8. Henry having lost | of his money playing cards, lent \ of the remainder, when he found he had 822 left ; how much had he at first ? 9. A horse was sold for 880, which was |- of | of twice the cost ; what was lost on the horse ? 10. A man bought a wagon for 854, which was |- of twice as much as he sold it for ; what did he gain ? 11. Homer had 15 marbles, which was | of 3 times as many as Henry had ; how many had Henry ? 12. Thomas gave 4 cents for a top, which was f times ^ of what money he had ; how many marbles, at 2 for a cent, could he buy with what he had left ? 10 146 INTELLECTUAL ARITHMETIC. [97. 13. A farmer, after selling | of his flock of sheep, had 20 left ; how many had he at first ? 14. A pole was standing | of its length in the air, 1^ of the remainder in the water, and 3 feet in the mud ; how many feet in the air ? 15. If from my age you take J and | of my age,^ the remainder will be 4 years ; how old am I ? 16. If to I of the cost of A's coat you add $12 the sum will be $20 ; what was the cost of the coat ? 17. A drover, being asked how many sheep he had, replied, " If to |- my number you add 80 sheep, the sum will be 5 more than 3 times my number ; '^ how many had he ? 18. John and James play at marbles ; John wins 16, which is | of twice as many as James now has ; when they began, | of John's equaled |- of James's ; how many had each when they began ? 19. 1^ of Herbert's age, increased by 10 years, equals 1^ times his age ; how old is he ? 20. A cow cost $40 ; | of this sum was -^j of 2| times ^ of the cost of a horse ; what was tlie cost of the horse ? 21. A. was 25 years of age when he was married, and his age was |- times | of his wife's age ; how old was she ? 22. A post-office Avas robbed by a clerk, who took I of the money in the drawer ; when he was arrested, he had made away with | of it, and had $10 left ; how much was in the drawer at first ? 23. A's farm cost $1500 ; | of this is | of 4 time& the cost of the barn ; wliat did the barn cost ? 24. At the battle of Long Island, the Americans lost 500 men ; | of this number was | of --^^Q of their force ; how many men had they in the field ? 25. At Ridgefield, 100 Americans were killed ; | of the slain was 7-|- times j^-^ of the men on duty ; how many on duty ? 98.] INTELLECTUAL ARITHMETIC. 14T 26. The American loss at the battle of Trenton, m killed, frozen, and wounded, was 60 men ; ^ of this number was 2^- times yI-q ^^ ^^^^ number en- gaged ; how many men in the engagement ? 27. At the assault on Quebec, the Americans had 100 killed ; | of this number was If times ^V of the men sent, and 6 more ; how many men in the de- tachment ? 28. The American loss in the battle of Port Royal Island was 80 men ; 2^ times this number was 8-i- times yV of the number in the field ; how many in the field ? 29. At Germantown, the American loss, in slain, wounded, and prisoners, was 1200 ; |- of this num- ber was 8-1- times yoo of i of the army, lacking 1000 men ; how many in the army ? 98. 1. Divide 28 into two numbers that shall be to each other as 5 to 2. Analysis. Since the nnmhers are to each other as 5 to 2, the given sum must be divided into 7 equal parts, and 5 of those parts will equal one of the mmibers, and 2 of them the ither ; the numbers will be ^ of 28 and S of 28, equal to 20 wtd 8. Therefore, Sfc. 2. Two men bought 40 bushels of potatoes ; one paid $6, and the other -$4 ; how many bushels should each have ? 3. Two travelers, 49 miles apart, approach each other ; one traA'cls 4 miles an hour, the other 3 miles an hour ; how many miles will each travel ? 4. A and B hired a horse and buggy for ^25 ; A used it 3 weeks, B 2 weeks ; Avhat should each pay ? 5. Two men hired a pasture for f 24 ; one put in 5 cows, the other put in 3 cows ; what should each pay? 148 INTELLECTUAL AEITHMETIC. [98, 6. Two men hired a field for $12 ; one put in 2 horses for 2 weekSj the other two horses for 4 weeks ; what shoukl each pay ? 7. John had 9 cents, and Jay had 7 ; they gave them all for 32 figs ; how many should each of them liave ? 8. A and B enter into partnership ; A invests §10 for 5 months, B invests ^5 for 8 months ; they gain $15 ; what is each man's share of the gain ? 9. A, B, and C bought a horse ; A paid $5 as often as B $1 and C $3 ; tliey gained $21 in selling him ; wliat is each man's share of the gain ? 10. Taree men agree to mow a field for $10 ; A sends 2 men three days, B sends 3 men three days, C sends 2 men two and a half days ; what shoukl each receive ? 11. A, B, and C traded in company ; A put in $30, B $50, and C such a sum that he took $10 of the $12 gained during the year; what was the gain of A and B, and what C's stock ? 12. An ignorant partner, who furnished $500 of a capital ot* $800, on which $240 had been gained, took $145 for his share of the profits ; did he gain or lo33, and how much ? 13. Two men paid $11 for the use of a pasture; the first put in 5 calves, the second 4 colts ; what shoiild each pay, provided 2 colts consume as much as 3 calves ? 14. A, B, and C hire a field for $42 ; A puts in 5 cows, B 3 cows, and C pays | of the rent ; how much must A and B pay, and how many cows docs C put in ? 15. Three men paid $56 for a pasture ; the first put in 9 oxen, the second 8 cows, and the third 10 calves ; what should each pay, if 4 cows eat as much as 3 oxen, and 5 calves as much as 4 cows ? 99.] nsTELLECTUAL AEITHMETIC. 149 16. Mary and Melissa wrote 60 lines in a copy book ; Mary wrote i as many lines as Melissa ; liow many lines did eacli y\'rite ? 17. A gardener gave 24: pears to some scliool children, giving each girl 4 pears, and each boy 3; the boys received as many pears as the girls ; how many children were there 'i 18. A flither divided -$96 among his two sons and 8 daughters, giving each son ^ as much as each dauo-hter ; how much did each receive ? 99. 1. Three boys have 76 marbles: the second has 2 more than the first, and the third has 6 more than the second ; how many has eacli ? 2. James, Henry, and Joseph, together, have 72 apples ; Henry iias 2 more than James, and Joseph 2 more than Henry ; if each had no more than James, how many would all have ? 3. If each had as many as Joseph, h.ow many would all have ? 4. How many must Joseph give James tha^t each may have the same number ? How many lias each ? 5. A, B, and C built a warehouse for $300 ; B paid 8100 more than A, and C paid as much as A and B ; how much did each pay ? 6. William bought a ride, a watcli, and a drum, for $4:2 ; for the rifle he gave twice as much as for the drum, and for the watch twice as much as for the rifle ; what did he give for each ? 7. A span of horses, wagon, and harness cost $225 ; the difference between the cost of the horses and wagon was 1^ times the cost of the liarness, and the cost of the horses was 4 times tlie cost of the harness ; what was the cost of each ? 8. B traveled 114 miles in 3 days ; the first day 150 INTELLECTUAL ARITHMETIC. [99. he traveled J as far as on the last 2 days, and the last day I' as far as on the first two days ; how far did he travel each day ? 9. A laborer in one week dug 5 rods more than -J the length of a ditch, and the next week he dug the remaining 20 rods ; how long was the ditch ? Analysis. Since he dug 5 rods more than ^ of the ditch the first week, the remainder, 20 rods, increased by 5 rods, must equal ^ the ditch ; 20 rods + 5 rods = 25 rodsy which is i of twice 25, or 50 rods. Therefore, S^c, 10. A farmer, owing a store debt, paid at one time $10 more than -^ of it, at another $20 more than i of the remainder, and gave a note of |20 for the balance of the debt ; what was the amount of the debt ? 11. Arthur gave 2 more than -| of his pennies for a top, 1 more than | of the remainder for a wliip, and had 4 left ; how many pennies had he at first ? 12. A grocer, selling beer, drew ^ a gallon more than l the contents of a keg one day, the next day he drew J a gallon more than -| of the remainder, and the third day, when he went to draw, he found the keg was empty ; how many gallons in the keg at first ? 13. A and B have $55 ; -I- of A's money equals -| of B's ; how many dollars has each ? Analysts. Since ^ of A's money equals f of B's, 2 halves, or all of A's, ivill equal 2 times f , or f of B's ; then A has 6, and B 5 equal parts of the money, and both have 11 parts ; -^\ of $55 is $5, or "l part ; G times $5 are $30, or A's share ; and 5 times $5 are $25, or B's share. TJiere- fore, ^c. 14. If 34 apples he divided between John and Mary, so that | of John's may equal | of Mary's, how many will each have ? .] INTPXLECTUAL ARITHMETIC. 151 15. A and B have together 83 sheep ; f of A's flock, increased by 8 sheep, is equal to B's flock ; how many sheep has each ? 16. If 10 cents be taken from 4 of Mary's money, the remainder will be equal to Susan's ; the girls, together, have 39 cents ; how many cents has eacli ? 17. Homer has 3 marbles more tlian Silas, and ^ of Homer's marbles equal | of Silas's ; how mani" has each ? 100. 1. One man will drink a gallon of beer in 3 days ; another will drink a gallon in 4 days ; how long will a gallon last both of them ? 2. Julia can do the washing in 7 hours ; with Jane's assistance she can do it in 1 hours ; in what time can Jane do it ? 3. Two boys can pitch a quantity of hay in 5 hours ; the first can do it in 9 hours ; in what time can the second do it ? 4. A cistern can be emptied by 2 pipes in 3| hours, but 1 pipe will empty it in 7^ hours ; in how many hours will the other empty it V 5. A can make a vest in | of a day, B in |, and C in I of a day ; hoAV many more vests can A and B make in a day than C can ? 6. Susan can knit a pair of mittens in | of a day, and Sarah can knit a pair in | of a day ; how many pairs can both knit in a day ? 7. What part of a day must Sarah assist Susan that Susan may complete 2 pairs ? 8. What part of a day must Susan assist Sarah that Sarah may complete 3 pairs ? 9. Jason can hoe 10 rows of corn in | of an hour, and Jesse can hoe them in | of an hour ; in what time can both together hoe them ? 152 INTELLECTUAL ARITHMETIC. 10. In what time can Jason hoe what remains after Jesse has hoed |- an hour ? 11. In what time can Jesse hoe what remains after Jason has hoed ^ of an hour ? 12. How many rows can both hoe in 1 hour ? 13. A and B can clear a field in 15 days ; with the help of C they can do it in 9 days ; in how many days can C do it ? 14. A and B can dig a well in 6 days, A and C in 8 days, and B and C in 9 days ; in how many days can each dig it, working alone ? 15. In how many days can they do it working together ? 16. Patrick, Peter, and Pliilo can dig 40 rods of ditch in 10 days ; Patrick and Peter can do it in 15 days ; Peter and Philo can do it in lo^ days ; in how many days can Patrick and Philo dig 28 rods ? 17. How long will it take each man to dig 30 rods ? 18. Henry and Harlan can cut a field of corn in 6| days ; Harlan's day's work exceeds Henry's by I oi* Henry's ; in how many days can each cut the field ? 19. Three men can do a piece of work in 10 days ; the first does | as much as the second, the third does -| as much as the first and second; in how many days will each do it ? 20. In how many days will the first and second doit? 21. In how many days will the first and third do it ? 22. In how many days will the second and third doit? 23. A, B, and C can do a piece of work in 8 days ; B and C can do it in 12 days, and A and B in 10 days ; in how many days can each, working separately, doit? 24. A cistern can be discharged by 3 pipes in 4 hours ; the first and second pipes will discharge it in 101.] INTELLECTUAL ARITHMETIC. 153 8 hours ; the first and third in 6 hours ; in what time will each pipe discharge it ? 25. Three men can trench a field in 10 days ; A and B can do it in 20 days ; B and C can do it in 15 days ; in how many days can A and C trench the same field ? 26. A barrel of flour would last a brother, sister, and servant 30 days ; when tlie brother Avas absent it would last 60 days ; when the sister was absent it would last 45 days ; how long would it last the sistei" after all had iised from it 20 days ? 101. 1. Benjamin, meeting some beggars, gave each of them 5 cents ; had he given them 7 cents apiece, ir would have taken 8 cents more ; how many beggars were there ? Analysis. Since 2 cents was the increase paid to 1 beggar^ and 8 cents the increase paid to all, there were as many beggars as 2 is contained times in 8, which is 4 times, llierefore, S^c. 2. Edward gave 6 plums to each of his playmates, and had 9 remaining ; had he given each of them 8, he would have had but 1 left ; how many playmatecs had he ? 3. Three times a certain number is 15 less than 6 times the same numl^icr ? what is tlie number ? 4. SiTsan, purchasing calico, found that if she took that at 8 cents a yard she would liavc 11 cents left ; ]nit if she took that at 12 cents a yard she would need 17 cents to pay for it ; how many yards did she want ? 5. 4 times a number is 15 less than 6|- times the same number ; what is tlie number ? 6. John, being asked how many marbles he had, replied, " f of them exceed J of them by 4." How many had he ? 154 INTELLECTUAL ARITHMETIC. [101. 7. 5^- times a number is 21 greater than 3| times the same number ; what is the number ? 8. If 24 chestnuts be divided among some boys, giving 4 apiece to -|- of them, and 2 apiece to the others, how many boys are there ? Analysis. Smce one hoy received 4 chestnuts as often as another received 2 chestnuts^ 2 hoys received 6 chestnuts; there were as many times 2 hoys as 6 is contained times in 24, which is 4 times, and 4 times 2 hoys are 8 hoys» Therefore, ^c, 9. Mary gave her chickens 26 grains of corn ; J of them had 5 grains each, the others but 3 each; how many chickens had she ? Note. The above gives the following question : — 10. 5 times |- of a certain number, phis 3 times -J of the same number, is 26 ; what is the number ? 11. A class received 29 merit marks ; -J of them received 5 apiece, -| of the remainder 3 apiece, |- of the remainder 2 apiece, and the rest 1 apiece ; how many scholars in the class ? 12. 26 melons were stolen, | of the party getting 4 each, the rest 3 apiece, except 2, who obtained but 2 apiece ; how many were there in the party ? Analysts. Had the last 2 ohtained 3 each, there would have been 28 melons ; then 4 times ^ of a number, plus 3 times ^ of the some number, or ^, woidd equal 28. Since 28 is J of a number, J- of 28, or 4, is ^, and 4 is ^ of 2 times 4, or 8. Therefore, S^c. 13. 4 times ^ of a number, plus 3-|- times the same number, is equal to 28 plus 5 ; what is the number ? 14. Henry said that 4 years more than J of his age, increased by 5 times ^ of it, and that sum by 4 times \ of his age less 4, would make the siuii 50 years ; how old was he ? 1®!.] INTELLECTUAL ARITHMETIC. * 155 15. A drover paid $5 a head for -J of his flock, $4 a head for as many more, -fo a head for -| of the remainder, and ^2 a head for the rest ; the flock cost $115 ; how many sheep had he ? 16. A grocer received -flO for a lot of baskets ; for ^ of them he had 6 dimes each, for ^- of the re- mainder plus 3, 4 dimes each, for -J of the rest plus 2, 3 dimes each, and for the rest 2 dimes each ; lidKv many baskets did he sell ? 17. 5 times Henry's age is 3 more than 4 times ^ of it increased by 6 times ~ of it ; how old is he ? Analysis. 5 ti77ies Henrxfs age equals ^^-^ 4 times § of it^ plus 6 ti?7ies ^ of it, equals -'5*-, a7id ^-^ less ^-^- equals ^ of it, which, according to the conditions of the question, is 3 ; and 3 is -^ of 3 times 3, or 9. Therefore, ^t. 18. 6 times a number is 4 less than 7 times | of it, plus 5 times \ of the same number ; what is the iiumber ? 19. Bridget, wishing to get a certain number of pounds of meat, found, if she took beef at 5 cents, slie would have 4 cents left ; if pork at 7 cents, she had not money enough to pay for it ; and therefore she took |- of the quantity in beef, the rest in pork, and paid for it ; how many pounds did she get ? 20. Four times a number is 6 greater than 5 times |- of the same number ; what is the number ? 21. A farmer, wishing to buy a flock of sheep, found, if he paid $2 a head, he would have $80 left ; if he paid ^h a head, he had not enough to pay for them ; if he took |- the number at each price, he could just pay for them ; how many sheep would his money buy ? 22. Twice f of a number equals the number plus 8 ; what is the number ? 156 INTELLECTUAL ARITHMETIC. I® 2!. 1. The sum of two numbers is 27 ; their difterence 5 ; what are the numbers ? Analysis. Since 27 is the sum of two numbers v:hose difference is 5, 27 less 5, or 22, would be twice the less num- ber ; ^ of 22 is 11, the less number, which increased by equals IG, or the greater number. Therefore, S^c. 2. James and John together have 19 peaches ; John has 3 more than James ; how many lias each ? 3. Hobart has 9 marbles more than Herbert, and together they have 31 ; how many has each ? 4. Two men are 37| miles apart, and trayel toward each other ; when they meet, one has trav- eled 5|- miles more than the other ; how far has each traveled ? 5. Horace, finding he had 5 more apples than Homer, gave him 3, when they together had 21 ; how many had each then ? 6. Mary has twice as many berries as Martha, and together they have 12 quarts ; how many quarts has each ? 7. A farmer had 47 sheep in two fields ; in one field there were 5 more than twice as many as in the other ; how many were there in each field ? 8. There are 54 bushels of corn in two bins ; in one bin there are 6 bushels less than half as many as there are in the other ; how many bushels in each ? 9. A man bought a watch" and chain for $96 ; the watch cost $4 less than 3 times the cost of the chain ; what was the cost of each ? 10. Hiram and Harvey built wall 11 days ; Hiram received 2 dimes a day more than Harvey, and they both received $25.30 ; what did each receive, and how much per day ? 11. The sum of A's and B's ac-cs is 60 years ; 6 years ago, A's age was ^ of B's ; what are their ages now ? II O^.] INTELLECTUAL ARITHMETIC. 157 12. A horse and cow cost $124 ; the horse cost '$4 more than 3 times the cost of the cow ; what was the cost of each ? 13. A farmer paid $24 for a colt and cow ; | the cost of the colt, multiplied by j the cost of the cow, equaled the cost of the cow ; what did he pay for each ? ^ 14. A lady purchased a dish and cover for 24 dimes; -J of the cost of the dish, increased by the difference between the cost of the dish and cover, equals the cost of the cover ; what was the cost of each ? 15. A grocer purchased 25 pounds of butter of two women ; |- of the number of pounds he took of one, increased by the difference between tlio amounts purchased of both, equals the number of pounds he took of the other ; how many pounds did each sell ? 16. The sum of two numbers is 10 ; their differ- ence is equal to J of the greater number ; what are the numbers ? 17. A Avagon cost 838 ; -^j of the cost of the wood work exceeds the cost of ironing it by ^ of the dif- ference between the expense of the two ; what was the cost of each ? 18. Emily purchased some lace and some ribbon for 30 cents ; l- the cost of the lace, increased by -i- the difference between the cost of the lace and rib"- bon, equals the cost of the ribbon ; what did she pay for each ? 19. Wilber paid 20 shillings for a pair of skates ' and a knife ; twice the difference between the cost of the two, plus J the cost of the knife, equals the cost of the skates ; what did he pay for each ? 20. , A horse and harness cost $34 ; |- of the cost of tlie horse is $1 more than the cost of the harness ; what was the cost of each ? 158 INTELLECTUAL ARITHMETIC. [ 1. A grocer paid 112.60 for 30 bushels of potatoes, giving 50 cents a bushel for good ones, and 20 cents a bushel for poor ones ; how many bushels were good ? Analysis. If all had heen good, he woidd have paid $15, or $2.40 more than he did; each bushel of poor ones made a difference of 30 cents; hence there were as many bushels of poor ones as 30 cents (the difference on 1 bushel) is contained times in $2.40, {the difference on all,) which is 8 times, equal to 8 bushels of poor ones ; the difference be- tween 30 bushels and 8 bushels is 22 bushels, equal to the good ones. Therefore^ ^c. 2. A farmer bought 28 sheep for $76, paying |3 for old sheep, and $2 for yearlings ; how many old sheep ? 3. A flour merchant paid $82 for 20 barrels of flour, giving $4.50 for first quality, and $3.50 for second quality ; how many barrels were first quality ? 4. Henry sold his watch for $18, and by so doing lost I of what it cost ; what did it cost ? 5. A man, employing an equal number of men and boys, paid each boy 5 dimes, and each man 7 dimes, and to them all he paid $7.20 ; how many were there of both ? 6. An old lady sold an equal number of chickens and turkeys for $4, receiving for chickens 3 dimes each, and for turkeys 5 dimes each ; how many fowls did she sell ? 7. A speculator bought an equal quantity of wheat and berans, giving $1.50 per bushel for wheat, and $1 for beans ; the wheat cost $7 more than the beans ; how many bushels of beans did he buy ? 8. A man engaged to Avork 25 days, on condition that he should receive $2 for every day's labor, and 103.] INTELLECTUAL ARITHMETIC. lo9 pay $1 for board every day lie was idle ; he received at settlement ^38 ; how many days was he idle V Analysis. As mcmy days as $3, (the difference made hy 1 idle day^') is contained times in $12, {the difference made hy all the idle days,) which is 4 times, llierefore he was idle 4 days. 9. A man was engaged for 20 days to copy, re- ceiving $2.50 for every day's labor, and forfeiting $>1 for every day he was idle ; he received $48 ; how many days did he copy ? 10. Job, having some chestnuts, gave | of them to John, who, after eating 6, gave -| of what remained to his sister, and still had 5 left ; how many had Job ? Analysis. If John gave f to his sister, the 5 left was { ; 5 is ^ of 4: times 5, or 20, a?id 20, plus the Q he ate, make 26, which is f of Job's, ^c. 11. Mary gave | of her flowers to her playmates^ I of the remainder to her teacher, and had 2 left ; how many had she at first ? 12. A farmer sold | of 1\ times his flock, and had 12 sheep remaining ; how many sheep had ha at first ? 13. A man paid $5 more than f of his grocer' et bill ; soon after he paid -| of what remained unpaid^ when he found 83 was still due ; what was the amount of his bill ? 14. John paid $10 more than J of his year's waores for clothes, $12 for a watch ; he then lent 1^ of what he had left, and having paid $3 for a pair of boots, had $5 left ; what were his wages ? 15. A laborer engaged to work 20 days, on con- dition that he should have 12 dimes for a day's labor, and pay 2 dimes for every idle day for board ; he received as many dollars as he worked days ; how many days was he idle ? 160 INTELLECTUAL ARITHMETIC. [fi©4, l®4. 1. A rope 28 feet in length was broken so that |- of the longer piece was equal to the shorter ; what was the length of each piece ? Analysis. Tlie longer 'piece is divided into 5 equal parts, 2 of which equal the shorter ; the sum of the 2 pieces is 7 equal parts, one of which equals 4- of 2S feet, or 4 feet ; 2 parts equal 2 times 4 feet, which are 8 feet, the shorter piece ; 5 parts equal 5 times A feet, which are 20 feet, the longer piece. 2'hertfore, Sfc. 2. A tree 56 feet high was broken in a storm ; | of the part standing was equal to the part broken off; what was the length of each part ? 3. Henry and Horace have 45 marbles ; Horace has I as many as Henry ; how many has each ? 4. A grocer, having opened a barrel containing 160 pounds of sugar, took out | as much as he left ; how many pounds were left in the barrel ? 5. A traveler paid Go cents for his supper and lodging, paying | as much for his supper as for his lodging ; what did he pay for his supper ? 6. A horse and wagon cost $170 ; the liorse cost 11 times as much as the wagon ; what Avas tiie cost of each ? 7. Henry traveled 140 miles in 2 days ; the first day he traveled 1 1 times as far as he did the second ; liow far did he travel each day ? 8. From BuffyJo to Bergeo k 50 miles, from Bergen to Utica is 1|- times as far as from Utica to Schenec- tady, which is 280 miles from Buffalo ; how many miles from Buffalo to Utica ? 9. David caught a trout 17 inches long ; the tail was I as long as the body, and the head was 3 inches long ; how long was the tail ? 10. Divide 36 into 2 such parts that 1| times one shall equal the other. 104.] INTELLECTUAL ARITHMETIC. 161 11. Homer and Harlan have 48 apples ; -| of Homer's, plus 6, equal the number Harlan has ; how many has each V Analysis. Harlan has 6 more than |- as many as Ho- mer, which makes the sum 48, 6 greater than if he had but ^ as many ; Homer's are divided into 4 parts, of ichich 3 parts plus 6 apples are equal to Harlan's ; then 4 parts plus 3 parts, plus 6 apples, equal 48, 7 parts equal 42, and y of 42, or 6, equals 1 part. 3 parts plus 6 equal 24, the number Harlan has, and 4 parts equal 24, the num- ber Homer has. Therefore, S^c. 12. Rochester is 52 miles from Geneva, via Vic- tor ; -j^Y of the distance from Geneva to Victor, plus 4 miles, equals the distance from Victor to Rociies- ter ; how far is Victor from each place ? 18. From the ground to the top of a church steeple is 146 feet ; | of the height of the steeple above the church, plus 6 feet, is equal to the heiglit of the church ; wliat is the height of the steeple above the church ? 14. A jar and cover weigh 18 pounds ; |- of the weight of the cover, increased by 12 pounds, equals the weight of the jar ; Avhat is the weight of each ? 15. A coat and vest cost $19 ; ^ of the cost of the coat, plus 83, equals the cost of the vest ; what is the cost of each ? 16. Wilson has 15 oranges and lemons ; -J- of the oranges equals \ of the lemons ; how many of each has he ? Analysis. Since ^ of the oranges equals ^ of the lemons, f , or all the oranges, equcd § of the lemons ; we then have the oranges and lemons divided into 5 equal parts, 2 parts of which equal the oranges, and 3 tlie lemons, ^c. 17. A father gave his 2 sons 50 cents ; ^ of George's money was equal to | of Abel's ; how many cents had each ? 18. Andrew has 34 marbles ; | of the gray ones 11 16^ INTELLECTUAL ARITHMETIC. [S04» equal j- of the black ones ; how many of each kind were there ? 19. The sum of two numbers is 62 ; -| of one equal | of the other ; what are the numbers ? 20. A purse and contents are valued at 46 shil- lings ; I of the value of the purse is equal to | of the value of what is in it ; what is the purse worth ? 21. A person, being asked the time of day, replied, *' The time past noon is equal to ^ of the time to midnight." What was the hour ? Analysis. The time to midnight is divided into 5 equal parts, one of which equals the time past noon ; then 5 parts plus 1 part equals 6 paints; and 12 hours, the time from noon to midnight, must he ^ of the time it lached of being Tnidnight ; since 12 is f, \, which is ^ o/*|, ivill be ^ of 12 hours, which is 2 hours. Therefore the hour was 2 o'clock, P.M. 22. What was the time, provided | of the time past midnight equaled the time to 10 o'clock, A. M. ? 23. f of the time from this instant to 5 o'clock, P. M., equals ^ of the time past midnight; what is the time of day ? 24. Peter said to John, " 1| times my age is If times your age, and the sum of our ages is 36 years." What was the age of each ? 25. A bin whose capacity was 44 bushels was partly filled with grain ; 2^ times wliat was in it was 2-|- times what it would take to fill it ; how many more bushels would fill it ? 26. A person, inquiring the distance to Cincinnati, was told that 3| times what it lacked of being 88 miles was 1| times what it exceeded 39 miles ; how far was he from Cincinnati ? 27. The number of miles that the distance from Charleston to Columbia exceeds 100 miles equals 1^ times the distance it lacks of being 150 miles ; how far is it from Charleston to Columbia ? lOo.] INTELLECTUAL ARITHMETIC. 163 lOo. 1. Two pieces of cloth contain 88 yards ; I of the first piece equals | of the second, phis 4 yards ; how many yards in each piece ? Analysis. If § equal f -|- 4, ^ will equal h of ^ -\- 4, which is 4^ -j- 2, this is -^ of 3 times ^ -\- '1, or f -[" ^ > then we have 1 piece equal to ^ the other plus 6 yards^ or 1 •piece divided into 5 parts, and 3 of these parts plus 6 yards equal the other piece ; hence 5 parts plus 3 parts plus 6 yards equal 38 yards, or 8 parts and 6 yards, equal 38 yards ; 38 yards minus 6 yards equal 32 yards, or 8 parts, S^-c. 2. A lad inquiring his mother's age, his father replied, " | of my age is 9 years more than |- of your mother's, and the sum of our ages is 72 years." How old was his mother ? 3. Two men built 38 rods of wall ; | of what one built, plus 4 rods, is equal to |- of wdiat the other built ; how many rods did each build ? 4. Hiram and Richard sheared 67 sheep ; -^ of the number Hiram sheared was 4 more tlian |- of the number Richard sheared ; how many did each shear ? 5. What is the time, providing | of the time past midnight, plus 1^^ hours, equals | of tlie time to midnight ? 6. A, being asked his age, replied, " 1\ times what I lack of being a hundred years old is 9 years more than 1|- times what my age exceeds 64." What was his ao'e ? 7. A rope was cut into 3 pieces ; the first piece was 5 feet long, the second was as long as the first plus -|- of the third, and the third was as long as the other two ; wiiat was the length of the rope ? Analysis. Since the third piece is as long as the other two, it must he ^ of the rope ; the second piece, being J- as long, is i; and the o feet which the second exceeds J-, with the ^ feet of the first piece, make 10 feet, which must he the other fourth ; 4 times 10 is 40. Tlierefore, S)C. 164 INTELLECTUAL ARITHMETIC. [Mt^, 8. The Lead of a fish is 7 inches long, the tail is as long as the head and | of the body, and the body is as long as the head and tail ; what is the length of the fish ? 9. A piece of steel was broken into 3 pieces; the first piece was |- of the whole, the second weighed o pounds, and the third weighed as much as tlie other two ; what was the weight of the whole ? 10. Three men dig potatoes ; the first digs ^ of the whole, lacking 2 bushels, the second digs 5 bush- els, and the third digs as many as the other two ; how many bushels did all dig ? 11. From Batavia to Avon is 21 miles ; this dis- tance, plus the distance from Bath to Corning, and 12 miles more, equals the distance from Avon to Bath ; from Bath to Corning is |- of the whole dis- tance ; how far from Batavia to Corning ? 12. A farmer took money for stock, as follows : S18 for swine, $3 more than -J of the whole for sheep, and for cattle $1 less than | as much as for sheep and swine ; liow many dolia/s did he receive ? 13. A third and ^ a third of 12 is | of twice wha^t number ? 14. Stephen spent | of his money, and afterward earned f as much as he had spent, when he bad $16.50 l2S3 than at first ; how much had he at first ? 15. If I of a ton of hay cost |- of an eagle, how many dollars vfill J of a ton cost ? 16. A is 6 years more than -J as old as B, C is §■ as old as A, and B's age is equal to the sum of A's and C's ; what is the age of each ? 17. A owns 12 more than | as many acres as B, C owns -}j as many as A, and B owns 24 acres loss than A and C ; how many acres has each.. 106.] INTELLECTUAL ARITHMETIC. 165 1^6. 1. Malcom is 8 years old, and Martin 25 ; in how many years will Malcom be -|- as old as Martin ? Analysis. 8 years since, 3farfin was 17 years of age; ith 17 years from that time, or, since 3Ialcom is 8 years old, in 17 less 8, or 9 years from this time, Malcom will be 11 years old, and Martin will he twice 17, or 34 years old. Therefore, ^-c. 2. A father is 22 years older than his son, and the son's age is |- of the father's ; how many years since the son's age was |- the father's ? 3. Helen is 9 years old, her sister is 22 ; in how many years will Helen be ^ as old as her sister ? 4. Henry played at marbles with Charles, who had 45 : Henry won as many as he had to commence with ; when they quit, each had the same number ; how many had both ? Analysis. Since Henry won as many as he had. he left of playing with twice as many as he began with ; and Charles, novj having the same raimber, must have had 3 times as many as Henry when they commenced playiny. 45 is 3 tijnes -i of 45, or 15, and 45 -|- 15 is 60. Therefore, Sjc. 5. A farmer, having 60 sheep in one field, took as many from them as he had in another field, and put them with the others, when tlio Locks were equal ; how many sheep had he ? 6. From a bin containing 52 bushels, 2 more than as many bushels as were in another bin were taken and put in the other bin, when both contained the same quantity ; how many bushels in both bins ? 7. Uncle Simon's age, increased by the difference between \ and -J of his age, is 6 more than \ times his age ; how old is he ? 8. Henry earned 20 dollars in the spring ; in the fall he earned as much as in the spring and \ as 16G INTELLECTUAL ARITHMETIC. much as in the summer, and in the summer as much as in the spring and fall ; how much did he earn in all ? 9. A has 10 sheep, C has as many as A and |- as many as B, and B has as many as A and C ; how many sheep have they all ? Analysis. Since B has as many as A and 0, lie must have ^ of the ivliole ; then 10 sheep ^ plus \0 + f ^/ l* plus J-, equals f -j- 20, or the whole number of sheep ; hence 20 equals ^ the numher^ and 20 is \ of 6 times 20, or 120 sheep. Therefore^ ^c^ 10. A, owning 74 acres of land, sold B | as much as B owned ; then B's farm was \ as large as A's ; how many acres in each farm ? 11. Mary has 10 more chickens than turkeys, yet I of the turkeys equal | the chickens ; how many chickens has she ? 12. Heman's coat cost |15 less than his whole suit ; \ of the price of the suit equaled | of the price of the coat ; what did the suit cost ? 13. Daniel caught 14 pigeons more than his brother, and 2-| times his brother's equaled | of his ; how many did each catch ? 14. One number is 3|^ times another ; if 15 be added to each, one is just |- of the other; what are the numl^ers ? 15. The difference between the cost of a horse andabuggy is$40 ; I of the cost of the buggy equal 3§5 of the cost of the horse ; what is the value of uach ? 16. Alice is \ as old as her mother ; 5 years since she was but \ as old ; in how many years will she be \ as old ? 17. Ilobart, having 20 marbles more than Dwight, plays with him ; D wight wins \ as many as l>.e had 107.] INTELLECTUAL ARITHMETIC. 167 at first, when Hobart lias -| as many left as he com- menced with ; how many had each at first ? 18. The difference between two numbers is 16 ; , f if 4 be taken from the larger and added to the less, \|^ 2 1 times the larger will equal 3 J times the smaller; what are the numbers ? 19. Jason bought a watch, and had $20 remain- .^ ing ; he then gave 2 times the cost of the watch for fv a rifle, and had ^ of his money left ; what did the rifle cost ? 20. Find the ages of A, B, and C, by knowing that C's age at A's birth was b\ times B's, and now is equal to the sum of A's and B's ; also that if A were now 3 years younger, or B 4 years older, A's age would be equal to \ of B's. 107. 1. Two boys are running in the same direction ; one is 27 rods in advance of the other in pursuit, who gains upon the foremost 3 rods in a minute ; in how many minutes will he be overtaken ? Analysis. In as many minutes as 3, the number of rods gained in one minute^ is contained times in 27, the number of rods to be gained. 2. A, after traveling 2 hours, at the rate of 5 miles an hour, was followed by B, at the rate of 7 miles an hour ; in how many hours would B over- take A ? 3. A dog in pursuit of a hare which has 28 rods the start, runs 9 rods while the hare runs 7 ; how far will the dog run to catch the hare ? 4. Henry saves 85 while John saves 87 ; how much will each have when the difference between what each has saved is $30 ? 5. A and B started from the same point to run a race ; A ran 84 rods and gave out, when \ of the 168 INTELLECTUAL ARITHMETIC. [107. distance B had run equaled the distance he was ahead of A ; how far did B run ? 6. Three men bought a horse ; A paid ^25, which was |- of what B and C paid ; B paid |- as much as A and C ; what did B and C pay ? 7. The hour and minute hands of a watch are together at 12 o'clock ; when will they next be to- gether ? Analysis. Since the minute hand passes the hour hand 11 times in 12 hours, if both are at 12, the minute hand will pass the hour hand the jirst time in -^^ ^f ^^ hours, or in 1-jY hours, equal to 5y\ minutes past 1 o'clock. There" fore, S^c, 8. A gentleman, being asked the time, replied, " It is between 3 and 4 o'clock, and the hands are directly opposite." What was the time ? 9. A fox is 40 leaps ahead of a hound, and takes 7 leaps to the hound's 4 ; but 3 of the hound's leaps equal 6 of the fox's ; how many leaps will the fox take before being caught ? 10. A wolf ran 80 rods to catch a sheep ; | of the distance the sheep ran was equal to the distance be- tween them when the chase commenced ; what was the distance ? 11. The sum of | of A's and f of B's money, being on interest 2 years 7 months and 6 days, at 5 pei- cent., amounted to 82260 ; | of B's money was 1-|- times I of A's ; how much had each ? 12. B's fortune is 1^ times A's ; the interest of | of A's fortune and 1 of B's for 5 years, at 6 per cent., is 1600 ; what is the fortune of each ? 13. A drover paid f 76 ibr calves and sheep, pay- ing 83 apiece for calves and $2 for sheep ; he sold \ of his calves and | of his sheep for |23, and in so doing lost 8 per cent, on their cost ; how many of §ach did he purchase ? APPENDIX. The author desires to call the attention of teachers to the numher auQ variety of chamjes that may be wrought upon the examples of the Sec- tions from which the following have been selected, as well as upon many others of the same class, and which may appropriately be termed " Hing- ing the Changes." It is not recommended that these changes be ap- plied to all the examples, but used as an occasional exercise, and limited according to the time and convenience of the teacher. It is recommended to teachers to exercise their classes in these " changes," not so much for the novelty of them, as for the enlivening effect produced upon the class, and especially for the peculiar facilities they afford for thorough mental discipline ; and while, at first, to some they may appear severe and too mathematical, they "will very soon become easy and comprehensible. To aid beginners, the blackboard maybe used to advantage; and to illustrate, take the example which has been written out in full in Section 71, page 171-3: — ^ of 35 is I of how manj thirds of 18 ? which may be written on the board thus : — f X 35 = f X TT X 18? Call upon some pupil to read the question according to i\\e first form, and to solve the question according to the form of analysis given ; and the answer, if correct, placed over the 3, will fulfill the conditions of the question; substitute this number, and erase another, thus : — *X35 — fXfX ? which is read 4. of 35 is f of f of what number ? Solve this as before, and so continue until all the numbers have been erased, and replaced by solution. When the class have become familiar with the exercise, the use of thi blackboard should be dispensed with, and the pupil be required to " ring the changes " by simply hearing the first form of the question read. Each question, and its form of solution, should be given by the pupil, but he may be allowed to give results in the solution that have been 2)reviously determined by analysis, in order to shorten the work and avoid monotonous repetition. Msmbers of the class should be called upon promiscuously, and en- couraged to ask questions, and to detect errors either in the statement or solution of questions. The teacher should re'ad an example once, slowly and distinctly, then call upon some one of the class who shall commence operations, and continue to give questions, forms, solutions, and conclu- sions, until signaled to sit, or another pupil detecting an error, raises the hand, when some other one should be called upon, who should re- sume where the last one left off; and so on. A teacher who has not practiced a class upon these changes, cannot conceive of the interest, close attention, and perfect enthusiasm that may be created, as well as the thorough mental discipline attained, by thi^^ exercise; and it is firmly believed that, upon trial, it will commend itself to the judgment and approval of every live teacher. (160) 170 APPENDIX. 67. 1. 24 is I of how many times 10 ? 24 is i of as many times 10 as 10 is contained times in 5 times | of 24 ; ^ of 24 is 6, and 5 times 6 is 30 ; 10 is contained in 30, 3 times. Therefore 24 is i of 3 times 10. 2. 24 is f of 3 times what number ? 24 is 4 of 3 times J of 5 times ^ of 24 ; | of 24 is 6, and 5 times G is 30 { I of 30 is 10. Therefore 24 is 4 of 3 times 10. 3. 24 is how many fifths of 3 times 10 ? 24 is as many fifths of 3 times 10 as i of 3 times lOjjis contained times in 24. 3 times 10 is 30, and 4 of 30 is ^, and 6 is contained in 24, 4 times. Therefore 24 is 4 of 3 times 10. 4. 24 is 4 times what part of 3 times 10 ? 24 is 4 times such a part of 3 times 10 as 3 times 10 is contained times in | of 24. 3 times 10 is 30, and ^ of 24 is 6 ; 30 is contained in 6, 3% or i times. There- fore 24 is 4 times 4, or 4, of 3 times 10. 5. What number is | of 3 times 10 ? 4 times i of 3 times 10. 3 times 10 is 30, l of 30 is 6, and 4 times 6 is 24. Therefore 24 is 4 of 3 times 10. 70. 1. I of 56 is f of 3 times what number ? I of 56 is f of 3 times | of 9 times 5 of 4 times ^ of 56 ; 4 of 56 is 8, and 4 times 8 is 32 ; ^ of 32 is 4, and 9 times 4 is 36 ; -| of 36 is 12. Therefore, 4 of 56 is I of 3 times 12. 2. 4 of 56 is I of how many times 12 ? 4 of 56 is I of as many times 12 as 12 is contained times m 9 times g of 4 times -| of 56 ; -} of 56 is 8, and 4 times 8 is 32 ; i of 32 is 4, and 9 times 4 is 36 ; 12 is contained in 36, 3 times. Therefore | of 56 is | of 3 times 12. 3. 4 of 56 is how many ninths of 3 times 12 ? 4 of 56 is as many ninths of 3 times 12 as ^ of 3 times APPENDIX. 171 12 is contained times in 4 times ^ of 56. ^^ of 56 is 8, and I of 56 is 4 times 8 ; 4 times 8 is 32 ; 3 times 12 is 36, ^ of 36 is 4, and 4 is contained in 32, 8 times. Therefore 4 of 56 is f of 3 times 12. 4. I of 56 is 8 times Avhat part of 3 times 12 ? Siicli a part of 3 times 12 as 3 times 12 is contained times in ^ of 4 times ^ of 5G. '^ of 56 is 8, and 4 times 8 is 32 ; | of 32 is 4 ; 3 times 12 is 36, and 36 is con- tained in 4, -2% or i times. Therefore ^ of 56 is 8 times i, or I, of 3 times 12. 5. I of 3 times 12 is -f of what number ? I of 3 times 12 is 4 of 7 times | of 8 times ^ of 3 times 12 ; i of 36 is 4, and 8 times 4 is 32 ; J^ of 32 is 8, and 7 times 8 is 56. Therefore f of 3 times 12 is -j of 56. 6. f of 3 times 12 is how many sevenths of 56 ? As many sevenths of 56 as 4 of 56 is contained times in 8 times ^ of 3 times 12. 3 times 12 is 36, ^ of 36 is 4, and 8 times 4 is 32 ; 4 of 56 is 8, and 8 is contained in 32, 4 times. Therefore f of 3 times 12 is 4 of 56. 7. f of 3 times 12 is 4 times what part of 56 ? Such a part of 56 as 56 is contained times in | of 8 times i of 3 times 12 ; 3 times 12 is 36 ; i of 36 is 4, and 8 times 4 is 32 ; :J of 32 is 8, and 56 is contained in 8, ^Q or 4 times. Therefore f of 3 times 12 is 4 times J, or 4, of 56. 71. 1. 4 of 35 is f of how many thirds of 18 ? Expressed by signs on the bkickboard thus : — 4x35 = f X 3 X 18 ? Of as many thirds of 18 as ^ of 18. is contained times in 9 times i of 4 times 4 of 35 ; 4 of 35 is 5, and 4 times 5 is 20 ; 4 of 20 is 4, and 9 times 4 is 36 ; ^ of 18 is 6, and 6 is contained in 36, 6 times. Therefore 4 of 35 is I of 6 thirds of IS. 2. 4 of 35 is f of f of what number ? X oO=:§ X^ X I of 35 is 4 of I of 3 times i of 9 times 4 of 4 tnnes 172 APPENDIX. 4 of 35 ; } of 35 is 5, and 4 times 5 is 20 ; 4 of 20 is 4, and 9 times 4 is 36 ; J of 30 is 6, and 3 times 6 is 18. Therefore ^ of 35 is | of | of 18. 3. I of 35 is f of G times what part of 18 ? ^4 x35i=|x-^xl8? I of 35 is f of 6 times such a part of 18 as 18 is con- tained times in J of 9 times i of 4 times ^ of 35. 4 ^^ 35 is 5, and 4 times 5 is 20 ; |- of 20 is 4, and 9 times 4 is 30 ; J of 36 is 6, and 18 is contained in 6, j% or ^ times. Therefore 4 of 35 is f of 6 times -J, or -g, of 18. 4. -i of 35 is how many ninths of f of 18 ? 4x35=r^x| Xl8? 4 of 35 is as many ninths of | of 18 as ^ of 6 times | of 18 is cont'iined times in 4 times ^ of 35. | of 35 is 5, and 4 times 5 is 20 ; J of 18 is 6, and 6 times 6 is 36 ; ^ of 36 is 4, and 4 is contained in 20, 5 times. There- fore 4 of 35 is § of I of 18. 5. 4 of 35 is 5 times what part of f of 18 ? 4 x35=-^x| xl8? 4 of 35 is 5 times such a part of | of 18 as 6 times ^ of 18 is contained times in i of 4 times ^ of 35. ^ ^^' 35 is 5, and 4 times 5 is 20 ; i of 20 is 4 ; ^ of 18 is 6, and 6 times 6, is 36 ; 36 is contained in 4, ^\ or ^ times. Therefore ^ of 35 is 5 times -1, or |, of | of 18. G. f of f of 18 is 4 of what numher ? f X ^ xl8 = 4x ? I of I of 18 is 4 of 7 times | of 5 times -g of 6 times I of 18 ; ^ of 18 is 6, and 6 times 6 is 36 ; -i of 36 is 4, and 5 times 4 is 20 ; | of 20 is 5, and 7 times 5 is 35. Therefore f of | of 18 is ^ of 35. 7. f of f of 18 is how many sevenths of 35 ? |x| X 18=3.7X35? I of I of 18 is as many seinenths of 35 as ^ of 35 is contained times in 5 times ^ of 6 times -J of 18 ; -J of 18 is 6, and 6 times 6 is 36 ; ^ of 36 is 4, and 5 times 4 APPENDIX. 173 is 20 ; 4 of 35 is 5, and 5 is contained in 20, 4 times. Therefore | of | of 18 is ^ of 35. 8. i of I of IS is 4 times ^vliat part of 35 .^ a x|x 183=^x35? I of I of 18 is 4 times such a part of 35 as 35 is con- tained times in ^ of 5 times ^ of 6 times I of 18. -J of 18 is 6, and 6 times 6 is 36 ; ^ of 36 is 4, and 5 times 4 is 20 ; -] of 20 is 5, and 35 is contained in 5, f-^ or 4 times. Therefore f of f of 18 is 4 times 4, or 4, of 35. 7S. 1. f of 36 is f of how many times f of 42 ? Of as many times f of 42 as 2 times -} of 42 is con- tained times in 9 times | of 4 times ^ of 36 ; ^ of 36 is 12, and 4 times 12 is 48 ; 4 of 48 is 12, and 9 times 12 is 108 ; 4 of 42 is 6, and 2 times 6 is 12, and 12 is con- tained in 108, 9 times. Therefore | of 36 is | of 9 times f of 42. 2. f of 36 is f of 9 times f of what rmmber ? -J of 36 is 4 of 9 times ~ of 7 times J- of i of 9 times | of 4 times -J of 36 ; -J of 36 is 12, and 4 times 12 is 1^ ; ^ of 48 is 12, and 9 times 12 is 108 ; 1 of 108 is 12, 4 of 12 is 6, and 7 times 6 is 42. Therefore 3^ of 36 is ^ of 9 times § of 42. 3. I of 36 is f of 9 times how many sevenths of 42 ? I of 36 is ^ of 9 times as many sevenths of 42 as 4 of 42 is contained times in i of 9 times 4 of 4 times | of 36 ; I of 36 is 12, and 4 times 12 is 48 ; 4 of 48 is 12, 9 times 12 is 108 ; 1 of 108 is 12 ; 4 of 42 is 6, and 6 is con- tained in 12, 2 times. Therefore 4 of 36 is 4 of 9 times f of 42. 4. I- of 36 is ^ of 9 times 2 times what part of 42 ? I of 36 is 4 of 9 times 2 tnnes such a part of 42 as 42 is contained times in 4 of ^ of 9 times j of 4 times 4 of 36 ; 4 of 36 is 12, and 4 times 12 is 48 ; 4 of 48 is 12, and 9 times 12 is 108 ; 4 of 108 is 12, and A of 12 is 6 ; 42 is 174 APPENDIX. contained in G, 4% or ~\ times. Therefore j of 36 is | of 9 times 2 times ^, or f, of 42. 5. f of 36 is how many ninths of 9 times f of 42 ? I of 36 is as many ninths of 9 tnnes f of 42, as -i of 9 times 2 times | of 42 is contained times in 4 times I of 36 ; I of 36 is 12, and 4 times 12 is 48 ; J of 42 is 6, and 2 times 6 is 12 ; 9 times 12 is 108, and 1 of 108 is 12 ; 12 is contained in 48, 4 times. Therefore -| of 36 is I of 9 times f of 42. 6. I of 36 is 4 times what part of 9 times f of 42 ? I of 36 is 4 times such a part of 9 times 5 of 42, as 9 times 2 times ^ of 42 is contained times in ^ of 4 times -J of 36 ; J of 36 is J 2, and 4 times 12 is 48 ; | of 48 is 12''; 4 of 42 is 6, 2 times 6 is 12, and 9 times 12 is 108; 108 is contained in 12, j^~^^ or ^ times. Therefore | of 36 is 4 tunes, i or |, of 9 times f of 42. 7. f of 9 times f of 42 is J of what number .? -| of 9 times f of 42 is | of 3 times | of 4 times -g of 9 times 2 times 4 of 42. i of 42 is 6, 2 times 6 is 12, and 9 times 12 is 108 ; i of 108 is-12, and 4 times 12 is 48 ; I of 48 is 12, and 3 times 12 is 36. Therefore | of 9 times § of 42 h j of 36. 8. t of 9 times f of 42 is how many thirds of 36 ? I of 9 times f of 42 is as many thirds of 36, as -J of 36 is contained tim'es in 4 times ^ of 9 times 2 times ^ of 42; 4 of 42 is 6, 2 times 6 is 12, and 9 times 12 is 108 ; i of 108 is 12, and 4 times 12 is 48 ; ^ of 36 is 12, and 12 is contained in 48, 4 times. Tlierefbre J of 9 times f of 42 is j of 36. 9. f of 9 times f of 42 is 4 times what part of 36 ? ^ of 9 times f of 42 is 4 times snch part of 36 as 36 is contained times in | of 4 times ^ of 9 times 2 times 4 of 42 ; 4 of 42 is 6, 2 times 6 is 12, and 9 times 12 is 108; 1 of 108 is 12, and 4 times 12 is 48 ; { of 48 is 12, and 36 is contained in 12, Jg or ^ times. Therefore -J of 9 times f of 42 is 4 times, 4 or |, of 36. INTELLECTUAL ARITHMETIC. 1T5 MULTIPLICATION TABLE. Once 1 2 3 4 5 6 Twice are o are 4 are 6 are 8 are 10 are 12 3 times are 3 are 6 are 9 are 12 are 15 are 18 4 times are 4 are 8 are 12 are are 16 20 are 20 are 24 5 times are 5 are 10 are 15 are 25 are 30 6' times are 6 are 12 are 18 are 24 are 30 are 36 7 times are 7 are 14 are 21 are 28 are 35 are 42 8 times are 8 are 16 are 24 are 32 are 40 are 48 9 times are 9 are 18 are 27 are 36 are 45 are 54 10 times are 10 are 20 are 30 are 40 are 50 are 60 11 times are 11 are 22 are 33 are 44 are 55 are 66 12 times are 12 are 24 are 36 are 48 are 60 are 72 Once 7 8 9 10 11 12 Twice are 14 are 16 are are 18 "27~ are 20 are 22 are 24 3 times are 21 are 24 are 30 are 33 are 36 4 times are 28 are 32 are 36 are 40 are 44 are 48 5 times are 35 are 40 are 45 are 50 are 55 are are are 60 6 times are 42 are 48 are 54 are 60 are 66 72 7 times are 49 are 58 are 63 are 70 are 77 84 8 times are 56 are 64 are 72 .are 80 are 88 are are 96 9 times are 63 are 72 are 81 are 90 are 99 108 10 times are 70 are 80 are 90 are 100 are 110 are are 120 11 times are 77 are 88 are 99 are 110 are 121 132 12 times are 84 are 96 are 108 are 120 are 132 are 144 1 2 3 4 5 6 13 times are 13 are 26 are 39 are 52 are are 65 70 are 78 14 times are 14 are 28 are 42 are 56 are 84 15 times are 15 are 30 are 45 are 60 are are 75 80 are 90 16 times are 16 are 32 are 48 are 64 are 96 17 times are 17 are 34 are 51 are 68 are 85 are 102 18 times are 18 are 36 are 54 are 72 are 90 are 108 19 times are 19 are 38 are 57 are 76 are 95 are 114 20 times are 20 are are 40 42 are 60 are 80 are 100 are 12) 21 times are 2] are 63 are are 84 88 are 105 are 126 22 times are 22 are 44 are 66 are 110 are 132 23 times are 23 are 46 are 69 are are 92 96 are 115 are are are 138 24 times are 24 are 48 are 72 are 120 144 25 times are 25 are 50 are 75 are 100 are 125 150 176 INTELLECTUAL ARITHMETIC. 1 7 8 9 10 11 12 13 times are 91 are 104 are 117 are 130 are 143 are 156 14 times are 98 are 112 are are 126 "l35 are 140 are 154 are 168 15 times are 105 are 120 are 150 are 165 are 180 16 times are 112 are 128 are 144 are 160 are 176 are 192 17 times are 119 are 136 are 153 are 17j are 187 are 204 18 times are 126 are 144 are 162 are 180 are 198 are 216 19 times are 133 are 152 are 171 are 190 are 209 are 238 20 times are 140 are are 160 168 are 180 are 200 are 220 are 240 21 times are 147 are 189 are 210 are 231 are 252 22 times are 154 are 176 are 198 are 220 are 242 are 264 23 times are 161 are 184 are 207 are 230 are 253 are 276 24 times are 168 are are 192 200 are 216 are 240 are 264 are 288 25 times are 175 are 225 are 250 are 275 are 300 1 o 14 15 16 17 18 13 times are 169 are 182 are 195 are 208 are 22J aie 238 are 234 14 times are 182 are 196 are 210 are 224 are 252 15 times are 195 are 210 are 225 are 240 are 255 are 270 16 times are 208 are 224 are 240 are 256 are 272 are 288 17 times are 221 are 238 are 255 are 272 are 289 are 306 18 times are 234 are 252 are 270 are 288 are 306 are 324 19 times are 247 are 266 are 285 are 304 are 323 are 342 20 times are 260 are 280 are 300 are 320 are 340 are are 360 21 times are 273 are 294 are 315 are 336 are 357 378 22 times are 286 are 308 are 330 are 352 are 374 are 396 23 times are 299 are 322 are 345 are 368 are 391 are 414 24 times are 312 are 336 are 360 are 384 are 408 are 432 25 times are 325 are 350 are 375 are 400 are 425 are 450 19 20 21 22 23 24 13 times are 247 are 260 are 273 are 286 are 299 are 322 are 312 14 times are 266 are 280 are 294 are 308 are 336 15 times are 285 are 30J are 315 are 330 are 345 are 3G0 16 times are 304 are 320 are 336 are 352 are 368 are 384 17 times are 323 are 340 are 357 are 374 are 391 are 408 18 times are 342 are 360 are 378 are 396 are 414 are 432 19 times are 361 are 380 are 399 are 418 are 437 are 456 20 times are 380 are 400 are 420 are 440 are 460 are 480 21 times are 399 are 420 are 441 are 462 are 483 are 504 22 times are 418 are 440 are 462 are 484 are 506 are 528 23 times are 437 are 4 are 483 are 506 are 529 are 552 24 times are 456 are 480 are 504 are 528 are 552 are 576 25 times are 475 are 500 are 525 are 550 are 575 are 600 OfV!D3 K(Oc^. 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