« ΠροηγούμενηΣυνέχεια »
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 first three terms of which are a supposition, the last two 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 un. der 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 di vidend, and the quotient will be the answer.
1. If 7 men can build 36 rods of wall in 3 days; hov many rods can 20 men build in 14 days ?
7: 3 :: 36 Terms of supposition. 20 : 14 Terms of demand.
7x3=21)10080(480 rods. Ans.
2. If 1001. principal will gain 61. interest in 12 montba, what will 4001. gain in 7 months ? Principal 1001. : 12 mo. : : 61. interest. 400 ; 7
3. If 1001. will gain 6l. a year; in what time will 4001. gain 141.
£ 100 : 12 : : 6
:14 Ans. 7 months. 4. If 4001. gain 14l. in 7 months : what is the rate per cent. per annum? £.
Int. 400 :
7:: 14 100 : 12
Ans, £6. 3. What principal at 6l. per cent. per annum, will give 141. in 7 months ? £.
Int. 100 : 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 ct. per ann. he received interest?
Ans. 5 per cent. 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. 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?
80 : 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 qre. 25 lb. 64 miles, at the same rate ?
Ans. $14,08 cts. 6m. + 10. 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 6 feet thick ?
8 : 12 : : 20 x 6x4
CONJOINED PROPORTION, IS when the coins, weights or measures of several coun. ries are compared in the same question; or it is joining gody proportions together, and by the relation whic
several antecedents have to their consequents, the propor. tion 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 Three 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 column; then multi. ply the left hand column continually for a dividend, and the right hand for a divisor, and the quotient will be the answer.
1. If 100 lb. English make 95 lb. Flemish, and 19 lb. Flemish 25 lb. at Bologna; how many pounds English aru equal to 50 lb. at Bologna ? 1b.
lb. 100 Eng.95 Flemish. 19 Fle. =25 Bologna. 50 Bologna.
Then 95 x 25=2375 the divisor. 95000 dividend, and 2375)95000(40 Ans.
2. If 40 lb. at New-York make 48 lb. at Antwerp, and 30 lb. at Antwerp make 36 lb. at Leghorn ; how many lb. at New-York are equal to 144 lb. at Leghorn?
Ans. 100°18 3. If 70 braces at Venice be equal to 75 braces at Lego horn, and 7 braces at Leghorn be equal to 4 American yards; how many braces at Venice are equal to 64 American yards ?
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 Erst row for a divisor, and the second for a dividend.
1. If 24 lb. at New-London make 20 lb. at Amsterdam, and 50 lb. at. Amsterdam 60 lb. at Pris; how many at Paris are equal to 40 at New-London? Left. Right. 24
20 X 60 X 40 = 48000 50 60
40 Ans. 40 24 x 50
1200 2. If 50 lb. at New-York make 45 at Amsterdam, and 80 lb. at Amsterdam enake 103 at Dantzic ; how mang lb. at Dantzic are equal to 240 at N. York ? Ans. 2781
3. If 20 braces at Leghorn be equal to 11 vares at Lis bon, and 40 vares at Lisbon to 80 braces at Lucca; how many braces at Lucca are equal to 100 braces at Leghorn ?
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 moneys of foreign nations to that of the United States, you may consult the following
TABLE: Showing the value of the moneys of account, of foreign
nations, estimated in Federal money. cts. Pound Sterling of Great Britain,
4 44 Pound Sterling of Ireland,
4 10 Livre of France,
0 18 Guilder or Florin of the U. Netherlands, 0 39 Mark Banco of Hamburgh, Rix Dollar of Denmark,
* Laws U.S.A.
Rial Plate of Spain,
I. -OF GREAT BRITAIN.
0 0 1 24 1 48 1 94
1. In 45l. 10s. sterling, how many dollars and cents ?
A pound sterling being=444 cents, Therefore-_As 11. : 444 cts. : : 45,5l. : 20202 cts. Ans.
2. In 500 dollars how many pounds sterling? as 444 cts, : 11. : : 50000 cts. : 1121. 12s. 3d. + Ans.
EXAMPLES. 1. In 901. 10s. 6d. Irish money, how many cents?
11. Irish=410 cts. £. cts. £.
cts. * cts Therefore--As 1 : 410 : : 90,525 : 37115!=371, 151
2. In 168 dols. 10 cts. how many pounds Irish? As 410 cts. : 11. : : 16810 cts. : £41 Irish. Anse
12 deniers, or pence, make 1 sol, or shilling.
EXAMPLES 1. In 250 livres, 8 sols, how many dollars and center
I livre of France=18 cts. or 185 mills.
$ 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. As 185 : 1:: 87457 : 472 14 9+ Ans.
IV.-OF THE U. NETHERLANDS. Accounts are kept here in guilders, stivers, groats and phennings.
8 phennings make 1 groat.
I guilder or florine