Sum 288 Proof 19 0 0 2. Two merchants traded in company; A put iņ 21 duls. for 6 months, and B 390 dols. for 9 months, but by misfortune they lose 200 dols. ; how must they share the joss?. Aus. A's loss 853, 15cts. B's $148, 25cts. 5. Three persons had received 663 dals. interest: A had put in 4000 dols. for 12 months, B 3000 dols. for 15 months, and C 5000 dols. for 8 months ; how much is each man's part of the interest ? Ans. A 8240, B 8225 and C 8200 4. Two partners gained by trading 1101. 12s. : A’s stock was 1201. 20s. for 4 months, and B's 2001, for 63 months; what is each man's part of the gain? Ans. A's part £29 18s. Sid. 139. B's £80 135. 811.446. 5. Two merchants enter into partnership for 18 months. A at first put into stock 500 dollars, and at the end of 8 months lie put in 100 dollars more; Bat first put in 800 dollars, and at 4 inonth's end took out 200 dols. At the expiration of the time they find they have gained 700 dolLars; what is each man's share of the gain? Ans. 210 $375, 92 5+B's. do 6. A and B companied ; A put in the first of January, 1000 dols.; but B could not put in any till the first of May; what did he then put in to have an equal share with A at the year's end ? No. $ Mo... ma DOUBLE RULE OF THREE. THIS Rule, teaches to resolve at once such questions as require two or more statings in simple proportioil, whether direct or inverse. In this rule there are always five terms given to find a sixth; the three first terms of which are a supposition, the two last a demand. RULE. * In stating the question, place the terms of the supposition so that the principal cause of loss, gain or action possess the first place; that which signifies time, distance of place, &c. in the second place; and the remaing term In the third place. Place the terms of demand, under those of the same kind in the supposition. If the blank place or term sought, fall under the third term, the pro proportion is direct, then multiply the first and second terms together for a divisor, anu the other three for a dividend: but if the blank fall under the first or second term, the proportion is inverse; then multiply the third and fourth térms together for a divisor, and the other three for a dividend, and the quotient will be the answer. EXAMPLES. 1. If 7 men can build 36 rods of wall in 3 days; how many rods can 20 men build in 14 days? 7:3 : 36 Terins of supposition. .: 20 : 14 Terms of demand 1:36. -7X3=21)10080(480 rods, Ans. . 2. If 1001. principal will gain 6l. interest in 12 months what will 4001. gain in 7 months ? Principal 1001. : 12mo. : : 61. Int. 400 : 7 : Ans. 141 400 : 7 :: 14 3. If 1001. will gain 61. a year ; in wnat time wili 4001. gain 141. £ no. £o 100 : 12 : : 6 400 : : : 14: Ans. 7 months, 4. If 4001. gain 141. in 7 months; what is the rate per cent. per annum?; mo. Int. 100 : 12 Ans. 66. 5. What Principal at 6l. per cent. per annum, will gain 141. in 7 months. f. mo. Inte 100 : 12 : : 6 7:: 14 Ans. £400 , 6. An usurer pre out 861. to receive interest for the sanie; and when it had continued 8 months, he received principal and interest, 881. 17$. 4d.; I demand at what rate per cent. per ann. he received interest ? Ans. 5 per ct. 7. If 20 bushels of wheat are sufficient for a family of 8 persons 5 months, how much will be sufficient for 4 persons 12 months ? Ans. 24 bushels. 30 : 20 :: 1. Ans. 600. Ans. $14, 08cts. 6m. + 10. If 8 men can build a wall 20 feet long, 6 feet high and 4 feet thick, in 12 days ; in what time will 24 mon build one 200 feet long, 8 feet high, and 6 feet thick? 8: 12 : : 20x6x4 the tel Ele 2016 of the time? mount CONJOINED PROPORTION, Is when the coins, weights or measures of several countries are compared in the same question; rr it is joining many proportions together, and by the nation which Si 14 DOUBLE RULE OF THREE. THIS Rule teaches to resolve at once such questions 28 require two or more statings in simple proportioil, whether direct or inverse. In this rule there are always five terms given to find a sixth; the three first terms of which are a supposition, the two last a demand. RULE. In stating the question, place the terms of the supposiion so that the principal cause of loss, gain or action posess the first place; that which signifies time, distance of alace, &c. in the second place; and the remaing term n the third place. Place the terms of demand, under hose of the same kind in the supposition. If the blank vlace or term sought, fall under the third term, the pro wroportion is direct; then multiply the first and second erms together for a divisor, anu the other three for a Lividend : but if the blank fall under the first or second erin, the proportion is inverse; then multiply the third nd fourth térms together for a divisor, and the other saree for a dividend, and the quotient will be the answer. EXAMPLES. 1. If 7 men can build 36 rods of wall in 3 days; how any rods can 20 men build in 14 days? 7 : 3 • ; 56 Terms of supposition. 20 : 14 Terms of demand 36 7x3=21)10080(480 rods, Ans. 2. If 1001. principal will gain ol. interest in 12 months, at will 4001. gain in 7 months ? Principal 1001. : 12mo. :: 61. Int. 400 ; 7. Ans. 141. 3. If 1001. will gain 61. a year ; in wnat time v 4001. gain 141. £. mo. £.. · 100 : 12 : : 6 400 : : : 14 Ans. 7 months 4. If 4001. gain 141. in 7 months; what is the rate cent. per annum? £. mo. Int. 400 : 7 :: 14. 100 : 12 .3 Ans. 66. - 5. What Principal at 61. per cent. per annum, will ga 141. in 7 months :: fon mo. Int. 100 : 12 : : 6 on : : 14 Ans. £,400 6. An usurer pit out 861. to receive interest for t sanie; and when it had continued 8 months, he receive principal and interest, 881. 178. 4d.; I demand at wh: rate per cent. per ann. he received interest ? Ans. 5 perc 7. If 20 bushels of wheat are sufficient for a family 8 persons 5 months, how much will be sufficient for 4 per sons 12 months ? Ans. 24 bushels. 8. If 30 men perform a piece of work in 20 days; how many men will accomplish another piece of work 4 time as large in a fifth part of the time? i 90 : 20 :: 1 2 4 ::4 . Ans, 600. 9. If the carriage of 5 cwt. 3 qrs. 150 miles, cost 2 dollars 58 cents; what must be paid for the carriage o: 7 cwt. 2 grs. 35 lb. 64 miles at the same rate ? Ans. $14, 08cts. 6m. + 10. If 8 men can build a wall 20 feet long, 6 feet hig! and 4 feet thick, in 12 days; in what time will 24 mor build one 200 feet long, 8 feet high, and 6 feet thick ? 8: 12 : : 20x6x4 20 CONJOINED PROPORTION, Is when the coins, weights or measures of several countries are compared in the same question; rr it is joining many proportions together. and by the relation which |