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. lb. d. Ib. 112 lb.x3=336 lb. 1 : 18 : : 336 The fourth term is 6048 18 pence=£25 4s. 12)6048d. 2688 210)504 336 £ 25 4s. 6048 LESSON 17. If 1 pound of sugar cost 9 pence, what is the cost of 17 hundred, 2 quarters ? Answer, £73 10s, lb. d. lb. 17 2 1: 9:: 1960 qrs. in a hundred. 9 cwt. qrs. quarters. 28 12)17640 £ 73 10s. 1960 lb. LESSON 18. 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 3 qrs. in length, what will 3 qrs. wide require ? This appears to be less requires more, or inverse proportion. gr.w. gr.l. qr.w. 8 :: 3 4 3)32 10 and 2 qrs. over = 18 inches. 3 in 18? 6 tines. 10 10 qrs. 6 in. = 2, 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. 19. of a dram. 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. OPERATION. 175 cents the 1st term. 850 continued. 22 oz. the 2nd term. 750 350 350 100 ounces remain. 150)3850(25 oz. 150)1600(10 drams. 1500 300 850 continued. . 100 189 of a dr. rem. LESSON 20. If I borrow 540 dollars for 160 days, how long must I lend 800 dollars, to pay the interest ? Answer, 108 days. dol. d. dol. 540 : 160 : : 800 If 540 dollars require 160 540 days to make a sum of inte64 rest, then 800 dollars will 80 require a less time. This is 8,00)864,00 more requires less. Ans. 108 days. LESSON 21. If a yard of cambric cost 12s. what will 4 pieces cost, each piece containing 20 yards ? Answer, £ 48. £ 48 yd. S. yds. 4 pieces x20=80 for the 1 : 12 : : 80 third term. The third term 80 is greater than the first, and requires the fourth to be 210)96|0s. greater than the second. This proportion is of more requires more; consequent ly, direct. LESSON 22. If a dozen caseknives cost 45. 4d. what will 49392 cost ? Answer, £ 891 16s. k. d. k. 12 : 52 : : 49392 52d. second term or 4s. 4d. 98784 246960 12)2568384 £891' 16s. LESSON 23. If a board be 8 inches wide, how much in length will make a foot square? Answer, 18 inches. in w. in l. in will Here we say, if 12 inches in width, re12 : 12 : : 8 | quire 12 inches in length, to make a foot 12 square, then 8 inches wide will require more in length. Therefore as the third 8)144 term is less than the first, and requires 18 in. 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 agrees to pay 128. 6d. on the pound; how much will be the payment? Answer, £ 625. £. £. 12s. 60.-12.5s. 2,0)125010.0 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. pints. d. pints. 8 pints make 1 gallon. 1: 10 : : 1512 Multiply 189 gals. by 8. 12)15120*d. 210) 126,0 £ 63 1512 pints. 8 LESSON 26. 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. Note.-Tare is an allowance for waste. 26 lb. tare in each hogshead. 3 hhds. from the 78 lb. of tare in the whole, which must be subtracted gross, the remainder will be neat. lb. quarters 1 hundred. Continued. * A cipher annexed, multiplies by 10. 43 quarters. 356 1216 pounds in 1 hogshead, gross. 3 hhds. 3648 lb. gross in 3 hogsheads. . 78 lb. tare in the whole. 7d. 29. = 30 farthings. Ib. 1 : 30 :: 3570 As the second term is in 30 farthings, so the fourth term must be farthings; divide 4)1071009 them by 4, by 12 and 20, to 12) 26775d. make pounds. LESSON 27. 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. d. P d. 30 : 615 :: 45 615 persons for 30 days. 30 410 for 45 days. 45)18450(410 persons. 205 the difference, which 180 number must move out. ...45 45 |