LESSON 16. If a pound of tobacco cost 18d. what will 300 weight of 112 lb. each come to? Answer, £25 4s. Reduce the tobacco to pounds for a third term. If 1 pound of sugar cost 9 pence, what is the cost of How much in length that is of a yard wide will make a piece 1 yard wide and 2 yards long? Ans. 2 yds. 6 in. There are 8 quarters in a piece 2 yards long, and at the same time the piece is 4 quarters wide. Then say, if 4 qrs. wide, require 8 qrs. in length, what will 3 qrs. wide require? This appears to be less requires more, or inverse proportion. 10 and 2 qrs. over 18 inches. 3 in 18? 6 times. 10 qrs. 6 in. = 24 yds. 6 inches. LESSON 19. If when wheat is at 175 cents a bushel, the baker gives 22 ounces Avoirdupois in a loaf for 12 cents, how many ounces can he give in the loaf without loss, when the wheat is at 150 cents a bushel? Answer, 25 oz. 10 drams. 100 of a dram. cents. oz. cents. In this case the third term is less 175 : 22 :: 150 || than the first, and requires the fourth to be greater than the second: For, the cheaper the wheat is, the larger the loaf can be for the same money. And if the third term be less than the first, and requires the fourth to be greater than the second, then, less requires more; therefore the proportion is inverse. If I borrow 540 dollars for 160 days, how long must I lend 800 dollars, to pay the interest? If a yard of cambric cost 12s. what will 4 pieces cost, each piece containing 20 yards? Answer, £48. If a dozen caseknives cost 4s. 4d. what will 49392 cost? If a board be 8 inches wide, how much in length will make a foot square? in w. in l. in w. 12 12 12 8)144 8 Answer, 18 inches. Here we say, if 12 inches in width, require 12 inches in length, to make a foot square, then 8 inches wide will require more in length. Therefore as the third term is less than the first, and requires the fourth to be greater than the second, less requires more. We will now make a memorandum which must be learned so perfectly, that it will always be ready in the mind; that is to say, DIRECT PROPORTION is known by, more requires more, or, less requires less. AND, INVERSE PROPORTION is known by, less requires more, or, more requires less. However nice these distinctions may appear, they must be observed by all expert arithmeticians. LESSON 24. A merchant has owing to him £1000, and the debtor 6d. on the pound; how much will be agrees to pay 12s. the payment? Answer, £625. 1 : 12.5 :: 1000 1000 12s. 6d. 12.5s. 2,0)12500.0 shillings for the fourth term. £625 Answer in pounds. The third term is greater than the first, and requires the fourth to be greater than the second. LESSON 25, If a pint of wine cost 10d. what will 189 gallons cost? Answer, £63. 8 pints make 1 gallon. Multiply 189 gals. by 8. 8 210)126,0 £ 63 1512 pints. LESSON 26. A grocer bought 3 hogsheads of sugar, each 10 cwt. 3 qrs. 12 lb. gross, tare 26 lb. in each hogshead, at 7d. 2q. a pound; what was the price of the 3 hhds.? Answer, £111 11s. 3d. 78 lb. of tare in the whole, which must be subtracted from the gross, the remainder will be neat. 3570 lb. neat, after the tare is deducted. Now state the question. If a cistern of water in a city be sufficient to supply 615 persons 30 days, how many must move out that the water may last 45 days? Answer, 205. REMARKS. If 615 persons will use the water in 30 days, then it will require a less number in 45 days. Say, if 30 days require 615 persons,what number will 45 days require? 45 will require 410 persons. Subtract 410 from 615, the difference will be the number to move out. |