COR. — When a given number of articles of the same value costs a certain sum of money, in order to find the cost of one article, divide the certain sum by the given number, whether integral or fractional ; and in order to get the cost of any required number, multiply the cost of one article by the required number. 29. If one acre of land is worth $371, what is the cost of 1251 acres? Ans. $46961 30. If of a farm cost $4250, what did the whole farm cost? Ans. $6375. 31. If j of a house is worth $4949, what is of it worth? What is the whole house worth? Ans. J is worth $707, and the house $6363. 32. A watch and chain are worth $150, and the chain is worth of the price of the watch ; what is the value of each? Ans. Watch $105, chain $45. 33. Two-thirds the value of the house is equal to the value of the lot; both are worth $8500; what is the value of each ? Ans. House $4500, lot $4000. 34. One-third of A's money is equal to of B's; both have $160; how many has each? Ans. A has $90 and B $70. 35. If of a yard of cloth cost $24, how many yards can be bought for $1431 ? Ans. 34 yd. 36. If a man travel 31 miles an hour, how long will it take him to travel 481 miles ? Ans. 13 hours. 37. A cistern has two pipes of 'supply and one for discharge; the first alone will fill it in 5 hours, the second in 8 hours, and the third will empty it in 9 hours; in what time will it be filled if all run together? Ans. 4 hours. 38. What number is that from which if of 1 of itself be subtracted, the remainder will be 25? Ans. 50. 39. A father bequeathed to his eldest son $12000, which was I of his estate; what was the value of his estate? Ans. $20000. 40. A, B, and C owned a section of land (640 acres); A owned of it, which was of what B owned, and o the remainder; how many acres did each own? ans. A owned 256 A., B 288 A., and C 96 A. 41. The part of a pole above the water was of the part under the water; what part of the pole was above the water and what part under the water ? Ans. & above and under. 42. Find the sum, difference, and product of and $; also the quotient, making the larger fraction the divisor? Ans. Sum 178, diff. de, prod. #, and quo. 36 43. What number must be divided by } of 36f to produce 4 times 61 ? Ans. 1834. 44. What is the least common multiple of 74 and 9 ? Ans. 43). 45. What is the greatest common divisor of 243 and 273? Ans. 46. A farmer has three separate parcels of land which he wishes to divide into lots of equal size and as large as possible ; the first parcel has 54 acres, the 2d 44 acres, and the 3d 23 acres. What will be the size of each lot ? Ans. į acre. 47. A can mow 3 acres of grass in 4 days, and B can mow 4 acres of grass in 5 days; how long wili it take both to mow 12 acres? Ans. 731 days. 48. A and B together can perform a piece of work in 9 days; A alone can do it in 15 days ? How long would it take B to do it ? Ans. 221 days. 49. A and B can do a piece of work in 5 days, C in 6 days, and B and C in 8 days; in what time will each one alone do it ? Ans. A in 8% days, B in 1214 days, and C in 21*1 days. 50. A merchant bought goods at } less than cost, and sold them at first cost; what part of the money he paid was his profit? Ans. 1. 51. A and B bought 1000 acres of land, of which A is to have 11 acres as often as B 9 acres ; how much does each get ? Ans. A 550 acres, B 450 acres. 52. A merchant sold of his stock for what the whole cost; what was the rate of profit? Ans. 4 year? 53. A, B, and C engage in business ; A puts in $9, to B $8 and C $7; what is each one's part of the stock? Ans. A , B3, C4 54. The profits of a firm this year is $4875%, which is one-fourth more than last year; what were they last Ans. $39003 55. If á of a cord of wood cost $5, what will be the cost of 25 cords? Ans. $155. 56. If 25% cords of wood cost $155, what will of a cord cost? Ans. $4. 57. Reduce 11 x 1} x 13 x 14 = H x 14 x 13 x 19 to a simple fraction. Ans. xf x 58. Reduce to a simple fraction, #xfx Ans. 16 whole 59. Reduce to a simple fraction. Ans. $. 용 60. What is the value of 8 x 12 x 16 x 18 x 24 ; 4 x 6 x 32 x 9 x 48? Ans. 2. 61. The difference between fand of a number is 21; what is the number? Ans. 90. 62. is of what number? Ans. 14. 63. If a pole 64 ft. long cast a shadow 94 ft., what is the height of a tree that casts a shadow 903 ft. ? Ans. 60ft. 64. What is the least common multiple of 1, $, , and ? Ans. 30. 65. What is the greatest common divisor of , }, /, Ans. 4: 66. A and B bought goods for $1200; A paid as much as B; what did each pay? Ans. A $450, B $750. and ? 67. Divide $12000 among 4 persons; the first to have $$ as often as the second $4, the third $4, and the fourth $}; what part does each get? 1, 3, 4, * = 48, 48, 46, 4%; } 30 +- 20 + 15 + 12 = 77. The first to have 14, the second 44, the third H, and the fourth 14. 68. A, B, and C traded together. A put in $64 as often as B $81 and C $93 ; the amount of their stock was $2890; what was each one's share ? Ans. A $750, B $1000, C $1140. 69. The sum of two fractions is 17, their difference is B; what are the fractions ? Ans. 4 and 70. Multiply 37 by 25. 37 x 100 = 3.700 = 925 71. Multiply 37 by 21. 37 x 12 = 370 = 921 72. Multiply 37 by 250. 37 X 1900 33400 = 9250 73. Multiply 49 by 225. 49 x 200 = 11025. 74. Multiply 49 by 3331. 49 X 1900 = 163335. 75. Multiply 49 by 275. 49 x 110 = 13475. = = |