3. Mary gave of her money for a silk dress and for a cloak, and had $10 remaining; how much had she at first? 4. Frank, after spending of his money, found that $16 was of what he had remaining; how much money had he at first? . 5. If of an army were killed, taken prisoners, and 800 men escaped, of how many men did the army consist? 6. What number is that which being increased by its, and that sum diminished by of the number, the remainder is 50? 7. When E was married he was 27 years old, and of his age was 4 years more than of bis wife's age; required the age of his wife. 8. A boy, after spending of his money for candies and for peaches, found that 20 cents was of what remained; how much money had he? 9. A thief stole of Harry's money, and before he was caught spent of it; the remainder, which was $20 less than he stole, was given back; how much money had Harry? WRITTEN EXERCISES. 2. A invested of his money in bank stock, and had $6045 remaining; how much money had he? Ans. $24,180. 3. A drover sold of his cows, and then had 210 remain- ing; remaining 1463 shares; how many shares each, and how many had he at first? Ans. 270. to D, and had did he sell to Ans. 3135. 5. A gave of his fortune for a farm, and paid of the remainder for building a house, and then had $4671 remaining; how much had he at first? Ans. $46,710. 6. A father gave of his fortune to his daughter, to his wife, and the remainder, which was $6720, to his son; what did the wife and the daughter receive? Ans. W., $5376; D., $4032. 7. One-third of the trees in an orchard bear apples, 4 bear peaches, and the remainder, which is 100, bear plums; required the number of trees in the orchard. Ans. 240. 8. A boy lost of his kite string, and then added 53 feet, when he found that it was just of its original length; what was its original length? Ans. 129 feet. MENTAL EXERCISES. MISCELLANEOUS EXAMPLES. 1. If a barrel of apples cost $54, how many "quarters" does it cost? 2. If 4 boys can earn $63 in a week, how much does each boy earn? 3. If I buy at the mint 125 " 'quarters" for change, how many dollars must I pay? 4. What cost 8 barrels of apples, at the rate of $33 per barre. ?` 5. of $40 is 2 times what A gave for a bureau; what was the cost of the bureau ? 6. of of a dollars of the cost of a watch; how much did the watch cost? 7. A man owning of the stock of a bank sold of his share; how much did he sell? 8. Jane bought a slate for of a dollar, and an arithmetic for § of a dollar; what was the cost of both? 9. If of a number, increased by of the number, equals 50, what is the number? 10. Maria owes a store bill of $; if she hands the clerk $3, how much change would she receive? 11. If of a pole is in the air, in the water, and the rest in the mud, how much is in the mud? 12. How much will 4 yards of muslin cost, at the rate of 12 cents a yard? 13. How much will 10 pounds of sugar cost, at of a dime a pound? 14. If a yard of flannel costs $, how many yards can you buy for $12? 15. Mrs. Brown exchanged 10 pounds of butter, at 15 cents a pound, for calico worth 64 cents a yard; how many yards did she receive? 16. How much will 14 pounds of cloves cost, if 3 pounds can be bought for 50 cents? 17. If 24 yards of muslin cost 30 cents, how much will 10 yards cost, at the same rate? 18. How far will a man drive in 5 hours, at the rate of 21 miles in 3 hours? 19. If of a ton of hay is worth $43, what cost 73 tons of hay at the same rate? 20. John found 60 cents, which is § of 3 of what he then had; how much had he at first? 21. Henry gave his sister 20 cents, which is of what he had at first, and of what his sister now has; how much had each at first? 22. Amanda, having 50 pins, lost ‡ of them, and then found f as many as remained; how many had she then? 23. A gave B 48 cents, and of this is 4 times as much as he had remaining; how much had he at first? 24. If 4 horses eat 2 tons of hay in 8 weeks, how long will it require 5 horses to eat the same? 25. Fanny's number of roses, increased by and of her number, equals 55; how many roses has she? of this is 4 times what he paid chin. 26. A gave $24 for a watch, and for the chain; required the cost of the 27. A boy having 36 marbles, lost of them, and then found § as many as he had at first; how many had he then? 28. $60 is of what B gave for a horse, and the cost of the horse, increased by its , is 5 times what he paid for a sleigh; required the cost of the sleigh. 29. A has 40 fruit trees, of which bear apples, of the remainder bear pears, and the rest bear peaches; how many trees of each kind has he? 30. Janson's age, diminished by its and, is 22 years, and his age is of his uncle's age; required the age of each. 31. Annie, having } of a pound of candies, shared them equally with 5 of her schoolmates; what part of a pound did each receive? 32. Peter gave of his marbles to Samuel, and 2 times of them to Anson; how many had he at first, if he gave away 14 marbles? 33. A boy divided 14 apples equally among his companions, giving to each 3 apples; required the number of his companions. 34. Harry bought 8 bushels of potatoes, worth $§ a bushel, and paid for them with eggs, worth $3 a dozen; how many eggs did it take? 35. If 3 boxes of starch cost $51, how much will 10 boxes cost at the same rate? 36. Hannah's wedding dress cost $50, and # of this is 4 times the cost of her bonnet, and also of the cost of her cloak; required the cost of the bonnet and cloak respectively. 37. Mary gave of her money to the poor, and then found as much as she gave away, and then had $30; how much had she at first? 38. William borrowed of Emily's money, and after spending of it, returned the remainder, which was $20; how much money had Emily? 39. A kite in the air fell of the distance to the ground, then arose of the distance it was from the ground, and then fell of the distance it arose; what part of the whole distance was it from the ground? WRITTEN EXERCISES. MISCELLANEOUS PROBLEMS. 1. Reduce 457 to an improper fraction. 2. Reduce 385 to an improper fraction. Ans. 387. Ans. 5014. Ans. 173. Ans. 38. Ans. Ans. H Ans. 1. 7. Reduce of 18 of 18 of 25 to a simple fraction. 8. Reduce of 18 of 20 of 4 of go to a simple fraction. Ans. 432 1876. 9. Reduce, 4, 5, 7, to a common denominator. 80 90 Ans. 12%, 120, 128, 125, 128. 10. Reduce, 5, 7, 11, 14, 15 to a common denominator. 1575 1560 Ans. 181, 188, 1478, 1548, 1888, 1678. 1400 680 1680 11. Reduce 1 of 17 of 25 of 3 of 7 of of 34 from & of 16 of 93. 17. Add to } of $ 14. Subtract 15. Multiply 16. Divide of 27 of 5 168 Ans. 8 9 23. Divide 33 by of Ans. 37. 4 24. Divide & of & of 312 by 4 of 14 of 19 Ans. 41g. 25. What cost 45 yards of muslin at 12 cents a yard? 26. What cost 967 tons of coal, at $12 per Ans. $5.713. ton? Ans. $1162. 27. What cost 1963 pounds of meat, at 63 cents a pound? Ans. $13.27. 28. What cost 327 yards of cloth, at 62 cents a yard ? Ans. $204.79. 29. What cost of a barrel of flour, if 1 barrel cost $8? Ans. $63. 30. What cost of a yard of cloth, if 2 yards cost $18? Ans. $8.05. 31. What cost 23 tons of hay, if 3 tons cost $48 ? Ans. $40. 32. If 1 yard of cloth cost $11, what will 53 yards cost? Ans. $6.50. 33. If tons of hay cost $30, what will 57 tons cost? Ans $693. 34. If 1 yard of cloth cost $8.014, what will 141 yards cost? Ans. $117. 35. A has of $8560, which is 21 times B's money; how much money has B? Ans. $2568. 36. B has 725 acres of land; 23 times B's equals 3 times C's; how much has C? Ans. 507 acres. 37. If 4 be added to both terms of the fraction §, will the value of the fraction be increased or diminished? 38. If 4 be subtracted from both terms of the fraction, will the value of the fraction be increased or diminished? 39. Will the value of the fraction be increased or diminished if 4 be added to both terms? If 4 be subtracted from both terms? 40. Mr. Mann bought a tract of land for $6500, and sold of it to Mr. Chase, and of the remainder to Mr. Colburn; what was the cost of the remainder? Ans. $7429. days, and after paying his board of his earnings, he had $12.36 daily wages? Ans. 80 cents. 41. A man worked 25 and other expenses with remaining; what were his |