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EXAMPI ES.

1. A, B and C hold a pasture in common, for which they pay 191. per annum. A putin 8 oxen for 6 weeks; B 12 oxen for 8 weeks; and ( 12 oxen for 12 weeks'; what must each

pay
of the rent:

£ 8 X 6= 48

48 : 3

3 12x 8= 96

96 : 6 6 8 B's 12x12=144 SAS 289 : 191. : : 144 : 9 10 0 C's

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4 A's pt.

Suin 288

Proof 19 0 0 2. Two merchants traded in company; A put in 215 dols. for 6 months, and B 390 dols. for 9 months, but by misfortune they lose 200 dols. ; how must they share the loss : Ans. A's loss $53, 75cts. B's $148, 25cts.

S. Three persons had received 665 dols. interest: A had put in 4000 dols. for 12 months, B 3000 dols. for 15 months, and C 5000 dóls.for 8 inonths; how much is each man's part of the interest?

Ans. A 8240, E 8225 and C 8200 4. Two partners gained by trading 1102. 12s.: A's stock was 1201. 10s. for 4 months, and B's 2001. for 61 months; what is each man's part of the gain ? Ans. As part £29 18s. 31d.1959. B's 1,80 138. 8.10.2013

5. Two merchants enter into partnership for 18 inonths. 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 month'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 ?

ins.

S $324, 07 4+ X's share.

$575, 92 5+B's. do 6. A and B companied ; A put in the first of January, 1000 (lols.; 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 ?

Mo. $
As 12 : 1000 ::8: 1000x12=1500 Ans.

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 terins 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 terin 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 portion is direct; then multiply the first and second terms together for a divisor, and the other three for at 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 56 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 deinanci.

36

84 42

504

20

7X3=21)10080(480 rods Ans. 2. If 1001. principal will gain 61. interest in 12 months, what will 4001. gain in 7 months ? Principal 1001. : 12mo. : : 61. Int. 400

Ans. 141.

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S. If 1001. will gain 6l. a year ; in what time will 4001. gain 141. f.

£ 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. 400 : : : 14 100 : 19

Ans. f.6. 5. What Principal at 6l. per cent. per annum, will gain 141. in 7 months ?

f. mno.

Int. 100 : 12 :: 6 7:: 14

Ans. £,400. 6. An usurer put out $61. to receive interest for the same; and when it had continuedł 8 months, he received principal and interest, 881. 178. 4d.; 1 demand at what rate per cent. per ann. he received interest ? Ans. 5 per ct.

7. If 20 bushels of wheat aré sufficient for a family of 8 persons 5 months, how much will be suflicient 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 tiines
as large in a fifth part of the time?

SO : 20;;1
4: : 4

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, 08cis. 6m. + 10. If S 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 :: 20X6X4

24 :

200X8X6 80 days, Ans.

CONJOINED PROPORTION, Is when the coins, weights or measures of several coun. tries are compared in the same questions wit is jening

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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 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 col umn; then multiply 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 100lb. English make 951b. Flemish, and 1910, Flemish 25lb. at Bologna; how many pounds English are equal to 50lb. at Bologna ? 16.

ib. 100 Eng.=95 Flemish. 19 Fle. =25 Bologna.

50 Bologna.'s Then 95 X25=2375 the divisor. 95000 dividend, and 2575)95000(40 Ans.

2. If 40lb. at New-York, make 48lb. at Antwerp, and Solb. at Antwerp, make s6lb. at Leghorn; how many lb. at New-York are equal to 1441b. at Leghorn ?

Ans. 100lb. 3. If 70 braces at Venice be equal to 75 braces at Loshorn, and 7 braces at Leghorn be equal to 4 American yards; how many braces at Venice are equal to 64 Amc. rican yards ?

Ans. 10445 CASE 11. When it is required to find how many of the last sort of coin, weiglit or measure, mentioned in the question, arc 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.

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1. If 241b. at New-London make 201b. at Amsterdam, and 50lb. at Amsterdain 60lb. at Paris; how many at Paris are equal to 40 at New-London ? Left. Right.

: 20 20 X 60 X 40 = 48000 -50

- 10 Anus. 40 24 X 50

1200 2. If 50lb. at New-York make 45 at Amsterılam, and Bolb. at Amsterdam make 103 at Hantzic; how many lb. at Dantzic are equal to 240 at N. York: Ans. 2781

3. If 20 braces at Lcglorn be equal to 11 vares at Lisbon, and 40 vares at Lisbon to 80 braces at Lucca; how many braces at Lucca are equal to 100 braces at Leghorn

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. Scts. Pound Sterling of Great-Britain,

4 44 Pound Sterling of Ireland,

4 10 Livre of France,

0.183 Guilder or Florin of the U. Netherlands,

OSO Mark Banco of Hamburgh,

0 33} Rix Vollar of Denmark,

10)

*Laws U. S. .1.

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