5. If bushels of oats cost $8, what will of a bushel bu. will cost 5 times less, or $; and bu. will cost 4 times as much asbu., or 1 × 4: = $184 RULE 1.—I. With the two given numbers which are of the same name or kind, form a ratio greater or less than 1, according as the answer is to be greater or less than the third given number. II. Find the fourth term by dividing the product of the means by the known extreme. RULE 2.-So arrange the terms that the causes shall form one couplet, and the effects the other. Then find the unknown cause or effect as indicated above. 6. When 12 barrels of apples cost $37.50, what will 165 barrels cost? Ans. $515.63. 7. What is the cost of 36 hhd. of molasses, if 9 hhd. cost $180? 8. If 16 bushels of wheat make 3 barrels of flour, how many barrels of flour will 120 bushels make? Ans. $720. Ans. 224 bbl. 9. How many men will it take to do a piece of work in 15 days, if 30 men require 10 days to do it? Ans. 20 men. 10. If 45 oxen eat 72 acres of grass in a month, how many oxen will 288 acres keep for the same time? Ans. 180 oxen. Ans. $16. 11. If $200 gain $10 in 18 months, how much will $320 gain in the same time? 12. If 15 gallons of wine cost $35, what will 75 gallons cost? Ans. $175. 13. Two numbers are to each other as 5: 40, and the less is 136.25; what is the greater? Ans. 1090. 14. If 39 men earn $312 in two weeks, how many men can earn $504 in the same time? Ans. 63 men. 15. If 63 cords of wood cost $236.25, what will 25 cords cost? Ans. $93.75. 16. If 23 horses consume 46 bundles of hay in 2 weeks, how many bundles will 32 horses consume in the same time? Ans. 64 bundles. 17. How much will 35 cwt. 25 lb. of sugar cost, at the rate of 12 cwt. 75 lb. for $68 ? Ans. $188. 18. If a pole 18 feet high cast a shadow 22 feet long, what must be the length of a pole to cast a shadow 110 feet long? Ans. 90 ft. 19. In what time will a train run from New York to Washington, 236 miles, at the rate of 6 miles in 12 min. 15 sec.? Ans. 8 hr. 1 mi. 50 sec. 20. In what time can a man pump 60 barrels of water, if he pumps 35 barrels in 1 hr. 45 mi.? Ans. 3 hr. 21. At the rate of 10 yards for $28.50, how many yards of cloth can be bought for $179.55? Ans. 63 yd. 22. What quantity of sugar can be bought for $256.25, if 5 lb. cost 62 cents Ans. 2050 lb. of an 23. If a piece of land 10 rods wide, contain acre, how much would there be if it were 16 rods wide? Ans. 1 A. 24. If a cistern containing 2500 gallons, leak 2 gal. 3 qt. a minute, how long will it take to empty it? Ans. 15 hr. 9+ min. 25. If a certain quantity of provisions will supply a garrison of 520 men 9 months, how long will it last 3640 men ? Ans. 14 mo. 26. If $630 purchase 420 hats, how many hats can be purchased for $75 ? Ans. 50 hats. 27. If it requires 75 men, working 8 hours a day, to do a piece of work, how many men working 12 hours a day, will it require to do the same work? Ans. 50 men. 28. If of a yard of cloth cost $33, what will 12§ yd. cost? Ans. $12.30. 29. What will 162 bushels of wheat cost, if 80 bushels cost $97.60 ? Ans. $197.64. 30. How long will it take 60 men to dig a well, if 10 men can do it in 32 days? Ans. 5 days. COMPOUND PROPORTION. 164. Compound Proportion is that proportion in which one or both ratios are compound. It embraces all those problems in which the unknown quantity depends upon the ratios of two or more pairs of similar quantities. Find the unknown term in each of the following compound proportions: 1. 10 x: (3:5) 14: S = 10 x 12 : 30. 1. If 6 men can earn $36 in 9 days, how much can 15 men earn in 8 days? STATEMENT. men men 6: 15 da. da. 9: 8 :: $36: $x. OPERATION. 5 24 8 = X × 36 = $80. SOLUTION.-The required term is the number of dollars that 15 men can earn in 8 days. If the number of men be increased, the number of dollars will be increased in direct proportion. And if the number of days be diminished, the number of dollars will also be diminished. Hence the ratio of the given sum to the required sum is in proportion to the combined ratios of the given number of men and days. From these relations, expressed as a compound proportion, we obtain by the operation in the margin, the required sum, $80. 2. How many horses will be required to plow 66 acres in 36 days, if 24 horses plow 22 acres in 10 days? acres, to plow 66 acres in 36 days, will require fewer horses, that is, the number of days is inversely proportional to the number of horses. These relations may be expressed in the form of a compound proportion, from which we will obtain the unknown term, x, 20 horses. 3. If 12 men working 10 hours a day for 5 days, earn $50, in how many days of 9 hours each, can 5 men earn $180 ? 12 men working 10 hours a day, earn $50 in 5 days. |