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6. A captain, mate and 20 seamen, took a prize worth 3501 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 shat 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 £337 10s. and B £112 10s.-1+3=4 :

450 : : 3 : £337 10s. A's share. 9. Three persons are to share 600t. 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 £66, B £138%, and C. 4400 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 230 dols. of which C 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 824 per yard. Agained

$46, 66:ts. 6m. + and B $85, 33cts. Sn. +

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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 :
mom is ench man's particular producto
To his particular share of the garor los.

they pay

EXAMPI.ES. 1. A, B and C hold a pasture in common, for which

191. per annum. A put in 8 oson for 6 weeks; B 12 oxen for 8 weeks; and C 12 oxon før 12 weeks; what must each pay of the rent? 8 x 6= 48

48 : 3 § 4 A's pte 12x 8 = 96

96 : 6 6 8 B's 12x12144 SAS 988 : 191. : 144 : 9 10 0 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 $146, 25cts.

3. Three persons had received 665 dols. interest: A aad put in 4000 dols. for 12 monthn, 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 110. 128. : A's stock was 1201. 10s. for 4 months, and B's 2001. for 61 nonths; what is each man's part of the gain P Ars. A's part 689 188. 31d.151. B's 1,80 138.814.45

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 dollars; what is each man's share of the gain?

Ans.

S8324, 07 4+ A's share.

28875, 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 o May; what did he then put in to have an equal shuu with A at the year's

end 7 Ho. 8 Mo.

$ As 12 : 1000 :: 8 : 1000 x1la1000 m

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 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 remaing term in the third place. Place the terms of demand, under those of the same kind in the supposition. If the blank prace or term sought, fall under the third terin, 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?

7: S •; 36 Terms of supposition. 20 ; 14 Terms of demand

36

84

504

20

7 XS=21)10080( 480 ods. Ans. 2. If 100l. prinsipal wi.. gain 61. interest in 12 months, what will 4001. gain in 7 months ? Principas Lol. : 18mo. : : 6. Int. 400

Ans. 141.

mo.

mo.

same

3. I 100%. will gain 61. a year ; in what time will 400% pin 141.

2.
100 : 12 : : 6
400 :

: :14 Ans. 7 months 4. If 4002 gain 141. in 7 months : what is the rate per cent per annum ?

Int. 400 : 7 :: 14 190 ; 12

Ans. 26. 5. What Principal at 6l. per cent. per annum, will gain 141 in 7 months ? £. mo.

Int. 100 : 12 : : 6

7:: 14 Ans. £400. 6. An usurer put out 861. to receive interest for the

; and when it had continued 8 months, he received principal and interest, 88l. 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 Que 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

Ans. 600. 9. If the carriage of 5 cwt. 9 grs. 150 miles, cost 24 dollars 58 cents ; what must be paid for the carriage o. 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 :: 20х6х4

24 :

200X8X6 80 days, Ans.

CONJOINED PROPORTION, Is when the coins, weights or measures of severe vores urios are compared in the same question; or it is. many proportions together, and by the relatie mus several antecedents have to their consequents, the proportaon between the first antecedent end 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 Rult 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 100 lb. English make 95 lb. Flemish, and 19 Flemish 25 lb. at Bologna; how many pounds English are equal to 50 lb. at Bologna ?

lb. U. 100 Eag. 95 Flemish. 19 Fle. 25 Bologna ?

50 Bologna Then 95x25=2375 the divisor. 95000 dividend, and 2875)95000(40 Ans.

2. If 40 lb. at New-York make 48 lb. at Antwerp, and 80 lb. at Antwerp make 36 lb. at Leghorn ; how many H. at New-York are equal to 144 lb. at Leghorn ?

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

Ans. 10415

CASE II. When it is required to find how many of the last sort

coin, weight or measure, mentioned in the question, are med toa gran quantity of the first

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