30. What will be the tas on $3758, at the rate of 4 mills on the dollar? Ans. $15, 03, 2. 31. A certain work can be raised in 12 days by working 4 hours each day: how long would it require to raise the work by working 6 hours per day? Ans. S days. 32. What quantity of corn can I buy for 90 guineas, at the rate of 6 shillings a bushel? Ans. 315 bushels. 33. A person failing in trade owes £977, at which time he has in money, goods, and recorerable debts £420 6s. 31d.: now supposing an equal divi. sion among his creditors how much will they get on the pound? Ans. &s. 74d. 34. A pasture of a certain extent having supplied a body of horse, consisting of 3000, with forage for 18 days, how many days would the same pasture have supplied a body of 2000 horse ? Ans. 27 days. 35. Suppose a gentleman's income to be 600 guineas a year, and that he spends 25s. 6d. per day, one day with another; how much will he have at the end of the year? Ans. £164 12s. 6d. 36. What is the cost of 30 pieces of lead, each weighing lcut. 1216, at the rate of 16s. 4d. the cwt. ? Ans. £27 2s. 6d. 37. The governor of a besieged place has provisions for 54 days at the rate of 2b. of bread per ration, but is desirous to prolong the siege to 80 days, in expectation of succour: in that case, what must be the ration of bread ? Ans. 171l. 38. If a person pays half a guinea a week for hoard, how long can he be boarded for £21 ? Ans. 40 weeks. per bottle ? 39. What is the value of a year's rent of 547 acres of land at the rate of 15s. 6d. the acre ? Ans. £423 18s. 6d. 40. If a person drink 20 bottles of wine per month, when it costs 2s. per bottle, how much can he drink without increasing the expense when it costs 2s. 6d. Ans. 16 bottles. 41. A merchant bought 21 pieces of cloth, each containing 40 yards, for which he paid $1260; he sold the cloth at $1,75 per yard: did he make or lose by the bargain? Ans. he gained $210. 42. A cistern containing 200 gallons is filled by a pipe which discharges 3 gallons in 5 minutes: but the cistern has a leak which empties 1 gallon in 5 minutes. Now if the water begins to run in, when the cistern is empty, how long will it be in filling? Ans. 8 hours 20 minutes. 43. What will be the cost of 895 feet of timber, at $6 per hundred feet? 100 895 6 answer.. 6 100)5370 53,70 Ans. $53,70. In this example, 100 feet of timber, is to the given quantity 895 feet, as $6, the cost of 100 feet, to $53,70, the cost of 895 feet. If the timber had been sold at the rate of $6 per thousand feet, the cost of 895 feet would have been $5, 37, for we should have divided by 1000, instead of 100; that is, we should have removed the separating point in the product three places to the left. Hence, to find the cost : of things sold by the 100, or 1000, we have the fol. lowing RULE. Multiply the number by the price, and if the things Ar reckoned by the 100, cut of two places from the right, and if reckoned by the 1000, cut off three, and the figures to the left will be the answer in the sume denomination as the given price. 44. What will be the cost of 1350 feet of boards at $11 per hundred! Ans. $148,50. 45. What will be the cost of 36578 bricks at $6,50 per thousand ? Ans. $237,75, t. 46. What will be the cost of 6359 feet of boards at $9, 25 per 100 feet? Ans. $588, 20, t. 47. What will be the cost of 13918 feet of timber at $14, 37 per thousand ? Ans. $200,00, +. 48. What will 18759 oranges cost at $5,50 per hundred ? Ans. $1031, 74, +. OF QUESTIONS REQUIRING TWO STATEMENTS. The answer to each of the above questions has been found by a single statement. Questions, however, frequently occur in which two or more statements are necessary. In most Arithmetics, such cuestions are arranged under a rule called Compound n, or the Double Rule of Three. They want, be answered by the rules already Ec. 1. If 16 men build 18 feet of wall in 12 days, how many men must be employed to build 72 feet in 8 days, working at the same rate ? The first question is, how long would it take feet. feet. days. days. 18 : 72 : : 12 : answer. the 16 men to build the 72 72 feet of wall ? It is evident that 18 24 feet of wall, is to 72 feet, 84 as 12 days, the time ne 18)864(48 days. cessary to build 18 feet, 72 to 48 days, the time ne 144 cessary to build 72 feet. 144 men. The second question days. days. men. is, if 16 men can build 8: 48 : : 16 : answer. 72 feet of wall in 48 48 days, how many men 128 are necessary to build it 64 in 8 days? Make 16 men the 8)7681 third term. 96 men. Then as Ans. the same work is to be done in a less time, more men will be necessary ; then the fourth term will be greater than the third, and hence 8 days are placed in the first term. § 109. 2. If a family of 6 persons expend $300 in 8 months, how much will serve a family of 15 persons for 20 months ? First question. If $300 will support a persone, persons. 15 300 : ans. family of 6 persons 15 for 8 months, how many dollars will support 6)4500 15 persons for the Ans. $750 6 : same time? : Second question. If months. months. $750 will support a 8 20 :: 750 : ans. family of 15 persons 20 for 8 months, how 8)15000 much will serve them Ans. $1875 for 20 months ? 3. If a man travel 217 miles in 7 days, travelling 6 hours a day, how far would he travel in 9 days, if he travelled 11 hours a day. 1st. 2d. days. days. miles. miles. hours. hours. miles. miles. ņ: 9:: 217 : 279 6 : 11 :: 279 : 511% 9 11 7)1953 6)3069 279 5113 Ans. 5114 miles. 4. If the wages of 6 men for 14 days be $84, what will be the wages of 9 men for 11 days? Ans. $99. 5. If 154 bushels of oats serve 14 horses for 44 days, how long would 406 bushels last 7 horses ? Ans. 232 days. 6. If 25 men can earn $6250 in 2 years, how long will it take 5 men to earn $11250 ? Ans. 18 years. 7. If a barrel of beer last 7 persons 12 days, how much will be drank by 42 persons in a year? Ans. 182bar. 18gal. 8. If 9 men can cut 36 acres of grass in 4 days, how many acres will 19 men cut in 11 days? Ans. 209 acres. 9. If 25 persons consume 300 bushels of corn in ona vear, how much will 139 persons consume in t the same rate ? Ans. 11676bu. |