6. If 8 yards of cloth cost $31, how many yards can be bought for $50? Ans. 1144 yd. 7. If 7 pounds of sugar cost 75 cents, how many pounds can be bought for $9? Ans. 84 lb. 8. What will 11 lb. 4 oz. of tea cost, if 3 lb. 12 oz. cost $3.50? Ans. $10.50. 9. If a staff 3 ft. 8 in. long casts a shadow 1 ft. 6 in., what is the height of a steeple that casts a shadow 75 feet at the same time? Ans. 183 ft. 4 in. 10. At $2.75 for 14 pounds of sugar, what will be the cost of 100 pounds? Ans. $19.644. 11. How many bushels of wheat can be bought for $51.06, if 12 bushels can be bought for $13.32 ? 12. What will be the cost of 281 gallons of molasses, if 15 hogsheads cost $236.25? Ans. $7.121. 13. If 7 barrels of flour are sufficient for a family 6 months, how many barrels will they require for 11 months? 14. At the rate of 9 yards for £5 12s., how many yards of cloth can be bought for £44 16s.? Ans. 72 yd. 15. An insolvent debtor fails for $7560, of which he is able to pay only $3100; how much will A receive, whose claim is $756? Ans. $310. 16. If 2 pounds of sugar cost 25 cents, and 8 pounds of sugar are worth 5 pounds of coffee, what will 100 pounds of coffee cost? Ans. $20. 17. If the moon moves 13° 10′ 35′′ in 1 day, in what time will it perform one revolution? 18. If 84 bushels of corn cost $ 4.20, what will be the cost of 131 bushels at the same rate? Ans. $6.48. 19. If 1 yards of cloth cost 6 pence, how many yards can be bought for £10 6s. 8d.? Ans. 694 yd. '20. If 12 cwt. of iron cost $424, what will 48% cwt. cost? 21. What quantity of tobacco can be bought for $317.23, if 83 lb. cost $14? Ans. 15 cwt. 22.7+ lb. seed cost $1561, how 22. If 15 bushels of clover much can be bought for $95.75? Ans. 9 bu. 2 pk. 2 qt. 23. If of a barrel of oil costs $99, how much will of a barrel cost? Ans. $ 24. If a piece of land of a certain length and 4 rods in breadth contains of an acre, how much would there be if it were 113 rods wide? Ans. 2 A. 28 sq. rods. 25. If 13 cwt. of iron cost $424, what will 12 cwt. cost? 26. A grocer has a false balance, by which he sells 12 oz. for a pound. What is the real value of a barrel of sugar that sells for $28? Ans. $21. 27. A butcher in selling meat sells 141 oz. for a pound. Of how much does he cheat a customer who buys of him to the amount of $30? Ans. $2.46+. 28. If a man clears $750 by his business in 1 yr. 6 mo., how much would he gain in 3 yr. 9 mo. at the same rate? 29. If a certain business yields $350 net profits in 10 mo., in what time would the same business yield $1050 profits? 30. B and C have each a farm; B's farm is worth $25 an acre, and C's $30. If, in trading, B values his land at $28 an acre, what value should C put upon his ? Ans. $34.16. 31. If I borrow $500, and keep it 1 yr. 4 mo., for how long a time should I lend $240 as an equivalent for the favor? Ans. 2 yr. 9 mo. 10 da. 32. How many days will 12 men require to do a piece of work that 95 men can do in 7 days? 33. When 10 barrels of flour cost $112.50, what will be the cost of 476 barrels ? COMPOUND PROPORTION. 400. Compound Proportion embraces that class of questions in which the causes, or the effects, or both, are compound. The required term may be a cause, or a single element of a cause; or it may be an effect, or a single element of an effect. EXAMPLES. 1. If 16 horses consume 128 bu. of oats in 50 days, how many bushels will 5 horses consume in 90 days? 16 x 50 : 5 × 90 OPERATION. 9 8 5 × 90 × 128 = 72 bu. :: 128 : ( ) SOLUTION. - In this example the required term is the second effect; and the question may be read: If 16 horses in 50 days consume 128 bushels of oats, 5 horses in 90 days will consume how many, or (blank) bushels? Dividing the product of the means by the extremes, we have 72 bu. These examples are most readily performed by cancellation. 2. If $480 gains $84 interest in 30 months, what sum will gain $21 in 15 months? what principal in 15 months will gain $21? Dividing the product of the extremes by the means, we have $240. 3. If 7 men dig a ditch 60 feet long, 8 feet wide, and 6 feet deep, in 12 days, what length of ditch can 21 men dig in 23 days, if it is 3 feet wide and 8 feet deep? Or, 7 × 12:21 × :: 60 × 8 × 6: ( ) × 3 × 8. OPERATION. 5 2 7 21 × 8 × 60 × 8 × 6 = 7 × 12 × 3 × 8 × 3 example the required term is the length of the 80 ft., Ans. ditch, and is an element of the second effect. The question, as stated, will read thus: If 7 men, in 12 days, dig a ditch 60 feet long, 8 feet wide, and 6 feet deep, 21 men, in 23 days, will dig a ditch how many, or (blank) feet long, 3 feet wide, and 8 feet deep? Dividing the product of the means by the extreme, we have 80 ft. RULE. -I. Of the given terms, select those which constitute the causes, and those which constitute the effects, and arrange them in couplets, putting () in place of the required term. II. Then, if the blank term () occurs in either of the extremes, make the product of the means a dividend, and the product of the extremes a divisor; but if the blank term occurs in either mean, make the product of the extremes a dividend, and the product of the means a divisor. The causes must be exactly alike in the number and kind of their terms; the same is true of the effects. The same preparation of the terms by reduction is to be observed as in simple proportion. 4. If $320 will pay the board of 4 persons for 8 weeks, for how many weeks will $800 pay the board of 15 persons? 5. If a man walks 192 miles in 6 days, walking 8 h. a day, how far can he walk in 18 days, walking 6 h. a day? Examples in Compound Proportion may also be solved by the Second Method in Simple Proportion (399). 6. If 18 men can build 42 rods of wall in 16 days, how many men can build 28 rods in 8 days? SOLUTION. In this example all the terms appear in couplets, except one, which is 18 men, and that is of the same kind as the required answer. Since compound proportion is made up of two or more simple proportions, if this third or odd term is divided by the compound ratio, or by the simple ratio of each couplet successively, the product will be the required term. By comparing the terms of each couplet with the third term we may readily determine whether the answer, or term sought, will be greater or less than the third term; if greater, then the ratio will be less than 1, and the divisor a proper fraction; if less, the ratio will be more than 1, and the divisor an improper fraction. First we will compare the terms composing the first couplet, 42 rods and 28 rods, with the third term, 18 men. If 42 rods require 18 men, how many men will 28 rods require? Less men: hence the ratio is greater than 1, and the divisor an improper fraction, 1. Next, if 16 days require 18 men, how many men will 8 days require ? More men: hence the ratio is less than 1, and the divisor a proper fraction, f. Regarding the third term as the antecedent of a couplet, the consequent being the term sought, if we divide this third term by the simple ratios, or by their product, we shall have |
