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? Sum 288
Proof 1900 2. Two merchants traded in company; A put in 215 dols. for 6 months, and B 390 dols. for 9 months, but by misforime they lose 200 dols. ; how must they share the foss?
Ans. A's loss $53, 75 cts. B's $146, 25 cts. *. 3. Three persons had received 665 dols. interest: A had put in 4000 dollars for 12 months, B 3000 dollars for 15 months, and C 5000 dollars for 8 months; how much is cach man's part of the interest ?
Ans. A $240, B $225, and C $200. 4. Two partners gained by trading 1101. 12s. : A's stock was 1201. 10s. for 4 months, and B's 2001. for 6 months ; what is each man's part of the gain? e Ans. A's part £29 18s.3 0.134 B's £80 138.81d. 14 1:5. Two merchants enter into partnership for 18 months. A at first put into stock 500 dollars, and at the end of 8 months he put in 100 dollars more; B at first put in 800 dollars, and at 4 months' 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? Peter
$324,07 4+ A's sharc.
$375, 92 5+ B's do. 6. A and B companied; A put in the first of January, 1000 dollars; 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 di the year's end ?
Mo. $ No.
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.
Rulr.-In stating the question, place the terms of the supposi. tion so that the principal cause of loss, gain, or action, possess the first placo ; that which signifies time, distance of place, &c. in the second place; and the remaining term in the third pice, 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 tha first and second tcris together for a divisor, and the other thren 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 ; hor many rods can 20 men build in 14 days ?
ng : 3 :: 36 Terms of supposition. 20 : 14 Terms of d'anand.
20 7x3=21)10080(480 rods. Anv.
2. If 1001. principal will gain 61. inter ist in 12 months what will 4001. gain in 7 months ? . Principal 1001. : 12 mo. :.0 interest. 400 : 7
3. If 1001. will gain 6l. a year; in what time will 4001. gain 141.
£. mo. £ 100 : 12 : : 6
400 : ::14 Ans. 7 months. 4. If 4001. gain 141. in 7 months : what is the rate per cent. per annum ? £. nio. Int.
400 : 7 :: 14
Ans. £6. 3. What principal at 6l. per cent. per annum, will give 141. in 7 months ? £. mo. 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. lf 20 bushels of wheat are sufficient for a family of 8 persons 5 months, how much will be sufficient for 4 percons 12 inopths ?
Ans. 24 bushels. 8. If 30 men perform a picce of work in 20 days; how inany men will accomplish another piece of work 4 times us large in a fifth part of the time?
80 : 20 ::]
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. $14,08 cts. 6m.'t 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 mer build one 200 feet long, 8 feet high, and 6 feet thick ?
8: 12 : : 20 x 6x4 24 : 200 x8 x6 80 days. Ans.
CONJOINED PROPORTION, IS when the coins, weights or measures of several coun. ries are compared in the same question; or it is joinin pany 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.—T his 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, wcight 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 mul is ply the left hand column continually for a dividend, and the right hand for a divisor, and the quotient will be the answer.
EXAMPLES 1. If 100 lb. English make 95 lb. Flemish, and 19 lb. Flemish 25. Ib. at Bologna ; how many pounds English are equal to 50 lb. at Bologna?
Ib. 1b. 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 Autwerp, 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 lb 3. If 70 braces at Venice be equal to 75 braces at Leg. horn, and 7 braces at Leghorn be equal to 4 Arnerican yards; how many braces at Venice are equal to 64 American yards ? '
CASE II. When it is required to fmd how many of the last sort of coin, weight or measure, mentioned in the nuestion, are equal to 7 given quantity of the first.
... Rult. Place the numbers alternately, oeginning at the lef hand, and let the last number stand on the right hand; then multiply the Qist row for a divisor, and the second for a dividend
: 1. If 24 lb. at New-London make 20 lb. at Amsterdam, Vand 50 lb, at. Amsterdam 60 lb. at Paris; how many at Paris are equal to 40 at New-London ? Liji. Right.
- 20 20 x 60 x 40 = 48000 50 - CO
40 Ans. 1024 x 50 =
1200 2. If 55 ib. at New-York make 45 at Amsterdam, and 80 lb. at Ansterdam make 103 at Dantzic ; how many lb. at Dantzic are equal to 240 at N. York?' Ans. 27876
3. If 20 braces at Leghorn be equal to 11 vares at Lishon, and 40 varez 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 110 be received in one country, for ai.y 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 bil nited States, you may consult the following
TABLE: Sh owing the value of the moneys of account, of foreign
i nations, estimated in Federal money.* $ cts. *** Pound Sterling of Great Britain,
4 44 113 Pound Sterling of Ireland,
4 10 in Livre of France,
@ 18! Guilder or Florin of the U. Netherlands,
089 Mark Banco of Hamburgh,
0 331 10 . Rix Dollar of Denmark,