101. Miscellaneous Problems. 1. A merchant bought 4 pieces of cloth, the first containing 271 yd., the second 283 yd., the third 285 yd., and the fourth 271 yd. How many yards did they all contain ? 2. I bought three yards of cloth at $34 per yd., 2 pairs of shoes at 17 per pair, and a hat for $35, giving in payment a twentydollar bill. How much change ought I to receive ? 3. I bought of a bushel of meal at § of a dollar per bu., giving in payment a quarter-eagle. How many dollars and cents ought I to receive back? 4. A lady went a shopping, and after paying $14. for a dress, $83 for a shawl, $75 for a bonnet, $1} for a collar, and of a dollar for incidental expenses, she had $5; left. How much money had she at first? 5. A, B, C & D together own a ship. A owns f of her, B , C., and D the remainder. What part does Down ? 6. A person on a journey travelled is of the distance the first day, it of it the second, & the third, \ the fourth, the fifth, is the sixth, and the rest the seventh. What part of the whole distance did he travel the seventh day? 7. How much more will 7ş bu. of corn cost at of a dollar per bu., than 9 bu. of oats at of a dollar per bu. ? 8. How much will it cost to build a rod of wall at is of a dollar per foot ? 9. How many solid feet in a block of stone 44 ft. long, 1; ft. thick, and if ft. wide; and how much will it cost at $2% per cubic foot? 10. If the sum of two fractions is ļ, and one of them is , what is the other? 11. George has of a dollar. How much more money must be get, to be able to buy 2 knives at tg of a dollar each? 12. A boy who had a quarter-eagle bought 3 books with it, and received in change a quarter-dollar, 4 half-dimes, 7 three-cent pieces, and 4 cents. How much did the books cost each, they being of equal value ? 13. What is the least common multiple of 18, 24, 36, 42, 54, and 60 ? 14. How many days will it take a man who earns $1; per day to earn $100 ? 15. If a man can earn $17 per day, and a boy can earn } of a dollar per day, how much can 1 man and 2 boys earn in a week, there being 6 working days in a week? 16. If a man can earn $1 in of a day, how much can he earn in a week? 17. A farmer cuts ã of a ton of hay from of an acre of land. How much will he cut from a field containing 7} acres, the crop being uniform ? 18. A young man who had inherited a large estate, spent of it in dissipation, when he had $2582.52 left. How much had he spent in dissipation, and what was the original value of the estate? 19. After spending ļ and ß of my money, I had $13.58 left. How much money had I at first? 20. What number multiplied by 3} equals 14 times the quotient obtained by dividing 21 by 9 ? 21. An estate of $8539.16 was divided among 2 sons and 3 daughters, in such a way that each son had twice as much as each daughter. What was the share of each ? 22. If $18000 is to be divided between two persons in such a way that the first will have three times as much as the second, what will be the share of each? 23. When pears are worth three times as much per bushel as apples, a person bought a bushel of pears and a bushel of apples for $5. What was the price of each per bushel ? 24. A person bought a yard of silk and a yard of muslin for $24. Now, allowing that the muslin was worth only 4 as much per yard as the silk, how many dollars was each worth per yard ? 25. How much will it cost to build 23.86 miles of railroad at $23463.75 per mile? 26. How much will 7.5 yards of ribbon cost at $.125 per yard ? 27. A man who owned a cotton factory sold $ of it to A, of what remained to B, of what remained to C, and the rest to D. How many dollars ought each man to pay for his share, if the factory was worth $50000 ? 28. What will 27 tons of English bar-iron cost at £1 138. 6d. per ton ? 29. Mr. Ball's farm contained 67 A. 3 R. 15 sq. rd., and I bought of it. How many A. R. and sq. rd. did I buy? 30. George started from home to go to school, a distance of of a mile. After walking of a furlong, he met James. How many furlongs, rods, etc. were the boys from the school-room when they met? 31. I bought a gold pen and case for of a £, a bottle of ink for of a shilling, and a box of wafers for 3% pence. What was the amount of my purchase ? 32. I bought 31 yd. of ribbon at of a £ per yd., and 5 yd. at Í of a shilling per yd. What was the amount of my purchase ? 33. How many miles of furrow will be turned in ploughing an acre, if the furrows are it of a foot wide ? 34. What is the value of 23 acres of land at $465 per acre ? 35. How much will a square rod of land cost at $1.35% per square yard ? 36. What must be paid for a piece of cloth containing 771 yards at $21} per yard ? 37. How much will a nail of cloth cost at is of a dollar per inch? 38. I bought 8f bushels of wheat at $1} per bushel, and sold it at $15 per busbel. How much did I gain by the transaction ? 39. What will be gained by purchasing 157 barrels of apples at $1% per barrel, and selling them at $21per bbl.? 40. I bought 27} bbl. of apples at $1.624 per bbl. It cost me $.184 per bbl. to have them carried to market, and I sold them for $2.163 per bbl. What did I gain on them ? 41. If Charles can do a piece of work in 9 days, and Joseph can do it in 10 days, what part of it can both together do in 1 day? How many days will it take both to do it? 42. If Mr. Stone can reap a field in 5 days, and Mr. Gray can reap it in 6 days, in how many days can both together reap it? 43. Mr. French can do a piece of work in 20 days, Mr. Thompson can do it in 25 days, and Mr. Ellis can do it in 30 days. In how many days can all do it? 44. When of a barrel of crackers cost $2.37, how much will 3 barrels cost ? 45. When a man can earn $10.50 in of a week, how much can he earn in 3 weeks ? 46. If a ship sails 4.25 miles in .51 of an hour, how many miles will she sail in 1 day? 47. If .09 of a man's estate is worth $854.82, how much is the whole of it worth? 48. If .75 of an acre of land costs $98.55, how much will 3.4 acres cost? 49. If .005383 is the product and .07 is the multiplier, what is the multiplicand ? 50. = of what number? 51. If ý of a yard of cloth is worth $16, how much are 24 yd. worth? 52. When $4} will pay for 224 melons, how many melons will $45 pay for ? 53. If 229 melons cost $4, how much will 25% melons cost ? 54. If $4; will pay for 25} melons, how many melons will $44 pay for ? 55. If a man can earn $21% in 15 days, how many dollars can he earn in 2 days? 56. If 18 horses can be kept 11} days on 12} bu. of corn; how many days can 14 horses be kept on 20 bu.? SOLUTION. As the answer is to be in days, we first write the 1 iš days = it of a day. If 18 horses can be kept so many days, 1 horse can be kept 18 times as many days, expressed by making 18 a factor of the numerator, thus, 28 X 18 15 If 123 bushels, or 3 of a bushel will keep a horse so many days, f of a bushel will keep him o'z of this number of days, expressed by making 63 a factor of the denominator, and of a bushel will keep him 5 times the last 28 X 18 X 5 result, expressed by making 5 a factor of the numerator, thus, 15 X 63 If 1 horse can be kept so many days, 14 horses can be kept 7 as many 28 X 18 X 5 days, expressed by making 14 a factor of the denominator, thus, 15 X 63 X 14. If 14 horses can be kept so many days on 1 bushel of grain, they can be kept 20f or times as many days on 204 bushels, expressed by making 81 a factor of the numerator, and 4 a factor of the denominator, thus, 28 X 18 X 5 X 81 15 X 63 X 14 X 4 In practice, the written work would take the following form: 3 X 9 9 3 9 15 X 69 X 14 X 4 days 39 days. 7 NOTE. — In solving such problems, each condition may be considered by itself, without reference to the other conditions, and the problem considered as though made up of several simple problems. For instance, the above problem was solved as though composed of the following: 1. If 18 horses can be kept 113 days on a given quantity of grain, how many days can 1 horse be kept on the same quantity ? 2. If 1 horse can be kept so many days (the number obtained as the answer to the preceding question) on 127 or 63 bu., how many days can he be kept on { of a bushel? How many days on a bushel ? 3. If 1 horse can be kept so many days (the last answer) on a bushel of grain, how many days can 14 horses be kept on it? |