DOUBLE RULE OF THREE. THE Double Rule of Three teaches to resolve at once such questions as require two or more statings in simple proportion, 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 remaining 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 proportion is direct; then multiply the first and second terms, together for a divisor, and 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 terms 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 Terms of supposition. 20: 14 Terms of demand. 36 84 42 504 20 7x3=24)10080(480 rods Ans. 2. If 100l. principal will gain el. interest in 12 months, what will 4001. gain in 7 months? Principal 1001.: 12mo. : : 6l. Int. 3. If 100l. will gain 67. a year; in what time will 4001. gain 147. £• 100 147. in 7 months; what is the rate per 400 : £. mo. Int. 400: 7 :: 14 100 : 12 Ans. £6. will gain 5. What Principal at 67. per cent. per anirum, 14/. in 7 months ? £. 100 mo. Int. 12: 6 7 :: 14 Ans. £400. 6. An usurer put out 861. to receive interest for the same; and when it had continued 8 months, he received principal and interest, 881. 17s. 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 perAns. 24 bushels. 8. If 30 men perform a piece of work in 20 days; how many men will accomplish another piece of work 4 times as large in a fifth part of the time? sons 12 months? 30 20:1 Ans. 600. 9. If the carriage of 5 cwt. 3 qrs. 150 miles, cost 24 dollars 58 cents; what must be paid for the carriage of 7 cwt. 2 qrs. 25 lb. 64 miles at the same rate? 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 men build one 200 feet long, 8 feet high, and feet thick? 8 12 24 : 20×6×4 200×8×6 80 days, Ans. CONJOINED PROPORTION, Is when the coins, weights or measures of several countries are compared in the same question; or it is joining many proportions together, and by the relation which several antecedents have to their consequents, the proportion between the first antecedent and the last consequent is discovered, as well as the proportion between the others in their several respects. NOTE. This rule may generally be abridged by cancelling equal quantities, or terms that happen to be the same in both columns: and it may be proved by as many statings in the Single Rule of Threc, as the nature of the question may require. CASE I. When it is required to find how many of the first sort of coin, weight or measure, mentioned in the question, are equal to a given quantity of the last. RULE. Place the numbers alternately, beginning at the left hand, and let the last number stand on the left hand col umn; then multiply the left hand column continually for a dividend, and the right hand for a divisor, and the quolient will be the answer. EXAMPLES. 1. If 100lb. English make 95lb. Flemish, and 19lb. Flemish 251b. at Bologna; how many pounds English are equal to 50lb, at Bologna ? lb. lb. 100 Eng.95 Flemish. 25 Bologna. 19 Fle. 50 Bologna. Then 95x25-2375 the divisor. 95000 lividend, and 2575)95000(40 Ans. 2. If 40lb. at New-York, make 48lb. at Antwerp, and 50lb. at Antwerp, make 361b. at Leghorn; how many b. at New-York are equal to 144b. at Leghorn? Ans. 100lb. S. If 70 braces at Venice be equal to 75 braces at Leghorn, and, braces at Leghorn be equal to 4 American vards; how many braces at Venice are equal to 64 Amctan yards? Ans. 104 CASE II. When it is required to find how many of the last sort of coin, weight or measure, mentioned in the question, are equal to a given quantity of the first., RULE Place the numbers alternately, beginning at the left hand, and let the last number stand on the right hand; then multiply the first row for a divisor, and the second for a dividend. EXAMPLES. 1. If 24lb. at New-London make 201b. at Amsterdam, and 50lb. at Amsterdam 60lb. at Paris; how many at Paris are equal to 40 at New-London ? Left. Right. 2. If 50lb. at New-York make 45 at Amsterdam, and 80lb. at Amsterdam make 103 at Dantzic; how many lb. at Dantzic are equal to 240 at N. York? Ans. 278% 3. If 20 braces at Leghorn be equal to 11 vares at Lisbon, and 40 vares at Lisbon to 80 braces a Lucca; how many braces at Lucca are equal to 100 braces at Leghorn 2 Ans. 110 EXCHANGE. By this rule merchants know what sum of money ought to be received in one country, for any sum of different specie paid in another, according to the given course of exchange. To reduce the monies of foreign nations to that of the United States, you may consult the following TABLE: Showing the value of the monies of account, of foreign nations, estimated in Federal Money.* & cts. Pound Sterling of Great-Britain, Pound Sterling of Ireland, Livre of France, Guilder or Florin of the U. Netherlands, 4.44 4 10 *Laws U. S. A. Mark Banco of Hamburgh, Rix Dollar of Denmark, 1. In 45l. 10s. sterling, how many dollars and cents? A pound sterling being 444 cents, Therefore-As 11.: 444cts. : : 45,5l.: 20202ets. Ans. 2. In 500 dollars how many pounds sterling? As 444cts. 1.:: 50000cts. 112l. 12s. 3d. Ans. II. OF IRELAND.. EXAMPLES. 1. In 90l. 10s. 6d. Irish money, how many cents P 11. Irish-410cts. £. cts. £• cts. 8 cts. Therefore-As 1: 410 :: 90,525 : 371151=371, 151 Accounts are kept in livres, sols and deniers. EXAMPLES. 1. In 250 livres, 8 sols, how many dollars and cents ř 1 livre of France 184 cts. or 185 mills. £. m. m. S. cts. m. As 1: 185:: 250,4 : 46324-46, 32 4 Ans. 2. Reduce 87 dols. 45 cts. 7 m. into livres of France. mills. liv. mills. liv. so. den. As 185 1: 87457 : 472 14 9 Ans. IV. OF THE U. NETILERLANDS. Accounts are kept here in guilders, stivers, groats and phennings. 8 phennings make 1 groat. |