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Proof.-Add all the particular shares of the gain ar loss together, and if it be right, the sum will be equal to the whole gain or loss.

EXAMPLES 1. Two partners, A and B, join their stock and buy a quantity of merchandize, to the amount of 820 dollars ; in the purchase of which A laid out 350 dollars, and B 470 dollars; the commodity being sold, they find their clear gain amounts to 250 dollars. What is each per. son's share of the gain!

A put in 550
B - 470

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· Proof 249,9999+=8250 2. Three merchants make a joint stock of 12001. Os which A put in 2401. B 3601. and C 6001.; and by trading they gain 325l. what is each one's part of the gain ?

Ans. A's part £65, B's 697 10s. C's £ 162 10s. 3. Three partners, A, B, and C, shipped 108 mules for the West-Indies; of which A owned 48, B 36, and C 24. But in stress of weather, the mariners were obliged to throw 45 of them overboard ; I demand how much of the loss each owner nust sustain ?

Ans. A 20, B 15, C 10. 4. Four men traded with a stock of 800 dollars, by which they gained som duls. A's stock was 140 dols. B's 260 dols. C's 300 dols. I demand D's stock and what each man gained by trading?

Ans. D's stock was $100, and A gained $53, 72cts 574 B 899, 77fcts. C 8115, 12 futs. and D 838, 37fcts.

5. A bankrupt is indebted to A 2111. to B 300l and to C 3911. and his whole estate amounts only to 6751. 105. which he gives up to those creditors; how much must each have in proportion to his debt ?

ens. id must have 158 06. 31d. B 284 186 chaud C £292 169. 8td.

6. A captain, mate and 20 seamen, took a prize worth 9501 dols. of which the captain takes 11 shares, and the mate 5 shares; the remainder of the prize is equally or vided among the sailors ; how much did each man receive ?

$ cts. Ans. The captain received 1069, 75 The mate

486, 25 Each sailor

97, 25 '7. Divide the number of 360 into 3 parts, which shal be to each other as 2, 3 and 4. Ans. 80, 120 and 160.

8. Two merchants have gained 450l. of which A is to have 3 times as much as B; how much is each to have ?

Ans. A £357 10s. and B £112 10s.-1+3=4 :

450 ; : 3 : £337 10s. A's share. 9. Three persons are to share 6001. A is to have a certain sum, B as much again as A, and C three times as much as B I demand cach man's part ?

Ans. A 466, B £138%, and C. £400 10. A and B traded together and gained 100 dols. A put in 640 dols. B put in so much that he must receive 60 dols. of the gain ; I demand B’s stock? Ans. $960

11. A, B and C traded in company: A put in 140 dols. B 250 dols. and C put in 120 yds. of cloth, at cash price ; they gained 250 dols. of which took 100 dols. for his share of the gain : how did C value his cloth per yard in common stock, and what was A and B’s part of the gain Ans. C put in the cloth at 82. per yard. A gained

$46, 66;ts. 6m. + and B 885, 33cts. Snr. +

COMPOUND FELLOWSHIP, OR Fellowship with time, is occasioned by several shares of partners being continued in trade an unequal term of time

- RULE. Multiply each man's stock or share by tno me it was continued in trade: then.

As the sum of the severa, products,
Is to the whole gain or loss ;
on is ench man's partícu ar prudacte
To his particular share of the gainor lo sa.

EXAMPLES. 1. A, B and C hold a pasture in common, for wheel they pay 191, per annum.“ A put in 8 oson for 6 weeks ; B 12 oxen for 8 weeks ; and C 12 oxon for 12 weeks ; what must each pay of the rent?

8x 6= 487

( 48 : 3 g 4 A's pt. 12x 8- 96

1 96 : 6 6 8 B's 12x12144 SAS 988 : 191, : 144 : 9 10 O C's Sum 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 853, 75cts. B's $148, 25cts.'

3. Three persons had received 665 dols. interost: A nad 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 11012s. : A's stock was 1201. 10s. for 4 months, and B's 2001. for 61 months; whiat is each man's part of the gain P Ans. A's part 689 188. 31d.7*4. B's £ 80 13s. 810.41

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 mure; 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 dol. lars; what is each man's share of the gain?

Ans. $ 8324, 07 4 + A's share.

18. $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 @ May; what did he then put in to have an equal shu with A at the year's end 7

No. S Mo.
A, 1.2 : 1000 :: 8 : 1000 x12m 1000 sm

DOUBLE RULE OF THREE THIS Rule 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 à supposition, the two last a demand.

RULE.. In stating the question, place the terms of the supposi. tion so that the principal cause of loss, gain or action possess the first place; that whịch 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 piace or term sought, fall under the third term, the pro proportion is Jirect; 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 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 ?

T: S : 36 Terms of supposition. 20 ; 14 Terms of demand

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7x321)10080(480 ods. Ans. 2. If 100l. principal wi.. gain 61. interest in 12 months, what will 4001. gain in 7 months ? Principas LO0l. : 19mo. : : 6. Int. 400 : 7

Ane. 141.

3. If 1001. will gain 61. a year ; in what time will 4002 pin 141.

2. mo. . . 100 : 12 : : 6

400 : : :14 Ans. 7 montha. 4. If 4001. gain 141. in 7 months : what is the rate per sent per annum ? . .. mo. Int.

400 : 7 ::14
100; 12.

Ans. 26.. 3. What Principal at 6l. per cent. per annum, will gain 147 in 7 months ? £. mo. Int.

100 : 12 : : 6

.. mer . 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. 178. 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 a 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 ?

30 : 20 : :1
4:: 4

Ans. 600. 9. If the carriage of 5 cwt. 3 grs. 150 miles, cost 24 dollars 58 cents ; what must be paid for the carriage on 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 6 feet thick ?

8: 12 : : 20x6x4

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CONJOINED PROPORTION, Is when the coins, weights or measures of severe vous vios are compared in the same question; or it is there many proportions together, and by the remtia hizi

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