WRITTEN EXERCISES. 49. I am offered $ 7000 cash for my house or $7700 in a year without interest. I can get 10 % for my money. Which is the better offer? 50. I buy butter for 32 cents, and am obliged to sell it for 28 cents. What % do I lose ? 51. A suit of clothes marked to sell at $ 40 is sold at 10% discount, and yet the seller makes 25%. What did it cost him ? 52. What is 33}% of the square of the cube root of ? 53. What is the entire surface of a 14-foot cube? 54. When Washington was inaugurated there were 13 States in the Union, and, March 4, 1881, there were 38. Required the rate per cent of increase. 55. I lost 16% of my property by fire and 20% by failures. How much had I originally if $ 5700 remained ? 56. I buy books at 80 cents, 20% off, and sell for $1.00, 15% off, and 5% off the remainder. How much do I gain ? 57. Received a consignment of 2000 barrels of flour, which I sell at $ 8.50, paying $ 74 storage and $27 cartage. My commission is 14 %. How much do I remit? 58. My insurance at $ % cost me a premium of $ 62.40, and is of the value of my house. What do I lose in case of its total destruction by fire ? 59. Received a remittance of $ 25375 for the purchase of cotton at 12}! per pound after deducting my commission of 1} %. How many pounds do I purchase ? 60. I buy 6 % stock at 112. What per cent do I receive on my investment ? 61. What sum will cancel a note of $ 892, Dec. 24, 1881, dated May 30, 1878, drawing 41 % interest ? · 62. Sold two pianos for $600 each, gaining 20% on one and losing 20% on the other. Required my gain or loss. 63. What is the compound interest, payable Jan. 1 and July 1 of each year, of $ 1200 at a yearly rate of 4% for 1 y. 9 mo. 18 d. ? 64. Robert Burns owes me $ 1500 due 9 mo. hence without interest. What will be a fair deduction for present payment if the current rate for money is 8 % ? 65. How long will $ 1000 be in amounting to $ 1500 at 7 %? 66. A note for $ 1600 dated Jan. 1, 1879, has three indorsements of $ 200 each, - July 10, 1879, Aug. 15, 1880, and May 12, 1881. What was due at settlement, Jan. 1, 1882 ? 67. Bought 624 yards of carpet at $ 1.87}, receiving a discount of 15%. What was my bill ? 68. Sold an estate which cost me $ 8000, 1 % for insurance, $64 taxes, and $ 1260 for repairs, for a 2-month note of $ 11000, which I had immediately discounted at a bank at 5%. Did I gain or lose, and how much? · 69. What is the face of a 4-month note which will yield $ 800 when discounted at 4 %? 70. What cost 125 shares of N. Y. Central R. R. stock at 143] and brokerage ? 71. May 14, I get a 90-day note for $ 1292 discounted, which was dated April 10, 1882. What were the proceeds ? 72. Exchange on Paris is quoted at 5.14. What will a bill of exchange for 8500 francs cost me ? 73. Find the missing term : V.0625 : (1)2 = x : 15.625. 74. Find a mean proportional to 816 and 97}. 75. If of a pound cost $ , what will of an ounce cost ? 76. If an 8-cent loaf weighs 10 ounces with flour at $ 8.50 per barrel, what will a 12-cent loaf weigh with flour at $ 10 ? 77. If my gas-bill is $4 for the month of January, 1881, when I use 4 burners 3 hours each evening, what will it be for the month of February, when I use 3 burners 4 h. 20 min. each evening? 78. Three children, aged 14, 12, and 7 respectively, share a bequest of $ 7000 in proportion to their ages. What is the share of the youngest ? 79. Ames and Stevens form a partnership January 1, Ames furnishing $ 8000 capital and Stevens $ 6000. May 1st, they take Conant into the firm with a capital of $ 5000, and August 1, Hubbell joins them with $ 3000. How shall the gain of $ 12000 be divided at the end of the year? 80. If it costs $ 320 to fence a rectangular lot 120 rods long and 80 rods wide, what will it cost to fence an equal square lot at the same rate ? 81. If it is 90 feet between the bases of a ball ground, what is the shortest distance from the second base to the home plate ? 82. What is the diagonal of a section of land in rods ? 83. How long a cube contains 25934.336 cu. ft. ? 84. Grandmother Gray lives in the center of a square farm containing a quarter-section of land. How far must she walk by the shortest route to visit her four children, one of whom lives at each corner of the farm, and return home? 85. How large a cubical pile will 32 cords of wood make ? 86. Find the diagonal of a rectangular solid 60 inches long, 40 wide, 20 high. 87. How many feet long is a square containing an acre ? 88. What will it cost at $ 0.75 per rod to fence eight equal rectangular lots made from a square ten-acre field ? 89. The roof of how high a building can be reached by a 40-foot ladder, the bottom of which is 12 feet from the building ? 90. A certain cube contains 175616 cu. in. Find the diag. onal of one of its faces. 91. If 5184 is the square of a number, what is its cube? 92. How long are the rafters of a house 40 feet wide, the ridge-pole being 12 feet above the attic floor ? 93. What is the ratio of V 27 to ♡ 417. 94. What is the entire area of a cube containing 592704 cubic inches ? 95. If 8 men can make 300 pairs of shoes in 6 days, how many men must be added to their number in order that twice as much may be done in half the time? 96. There are two numbers in the ratio of 6 to 11, and the larger is 1671. What is the smaller ? 97. Reduce the ratio 1: 3 to the smallest integral terms. 98. If 4 pounds of coffee cost $ 1.38, what will 113 pounds cost ? 99. If 24 men can build 405 yards of wall in 24 days, how many men will it require to build it in 8 days ? 100. A and B are in partnership for one year. January 1, A put in $ 2000, but B did not put in any until April 1. What did he then put in to have an equal share with A at the end of the year ? 101. A and B start from the same place, and travel the same road. A goes 5 days before B, at the rate of 20 miles a day. B follows at the rate of 25 miles a day. In what time and at what distance will he overtake A ? 102. A cistern has 3 pipes: the first will empty it in 2, hours, the second in 3 hours, and the third in 4 hours. In what time would they together empty the cistern? 103. A certain piece of labor was to have been performed by 144 men in 36 days, but a number of them having been sent away, the work was performed in 48 days. What number of men was sent away ? 104. If 15 carpenters can build a bridge in 60 days by working 15 hours a day, how long will it take 20 men to build the bridge by working only 10 hours a day? 105. Divide $ 2000 among A, B, and C, so that for every $3 given to A, B is to receive $ 5, and C $8. What sum did they each receive ? 106. How many inches in the diagonal of a square whose side is 24 feet ? 107. What is the cube root of %, to the nearest hundredth ? 108. The side of a square is 8 feet 6 inches. What is the side of a square having 25 times the area ? 109. How many gallons per minute will a 2-inch faucet discharge, if a z-inch faucet discharges 30 gallons ? 110. One person owes another $ 150 payable in six months, $ 180 payable in 8 months, and $ 270 payable in 4 months. Find the equated time of payment. 111. Three towns are to provide, according to their population, a contingent of 182 men. The population of the first town is 2456, of the second 735, and of the third 436. Find as exactly as possible the number of men to be provided by each town. 112. How many square yards in the area of the sides of a square pyramid, whose slant height is 100 feet and the perimeter of whose base is 54 feet ? 113. How many globes 4 inches in diameter are equal in volume to ono that is 12 inches in diameter ? REVIEW QUESTIONS. 134. How is the part that one number is of another found ? 338. What is ratio ? How is it determined ? 345. What is proportion ? 349. What is a simple proportion ? 351. A compound proportion ? 161. What is a line? 164. What is an angle? 165. What is a right angle ? 179. How many degrees in a right angle ? 163. What is a surface ? 166. What is a rectangle ? 167. A square ? 391. A quadrilateral ? 219. What is a triangle ? 387. A right-angled triangle? The hypothenuse ? The perpendicular ? 177. What is a circle ? The circunference of a circle ? The diameter? 222. The ratio of the cicumference to the diameter ? 169. What is a solid, or volume ? 223. A rectangular solid ? 170. A cube ? 399. A prism ? 225. A cylinder ? 401. A pyramid ? 402. A cone? 406. A sphere ? |