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97, 25

as B.

6. A captain, mate and 20 seamen, took a prize worth 3501 dols. of which the captain takes 11 shares, and the nate 5 shares ; the remainder of the prize is equally divided among the sailors ; how much did each man receive ?

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

486, 25 Each sailor 7. Divide the number of 360 into 3 parts, which shall e 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 three times as much as B ; how much is each to have?

Ans. A £337 10s. and B £112 108.-1+3=4 :

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

ins. A £66), B £133%, 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 230 dols. of which C took 100 dols. for his share of the gain : how did C value his cloth per yard in ammon stock, and what was A and B's part of the gain? Ans. C put in the cloth at $2} per yard. A gained

$46, 67 cts. 6m. +and B $83, 33ets. 3m. +

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

RULE. Multiply each man's stock or share by the time it was continued in trade : then,

As the sum of the several products,
Is to the whole gain or loss :
So is each man's particular product,
To his particular share of the gain or loss.

EXAMPLES.

1. A, B and C hold a pasture in common, for which they pay 19l. per annum. A put in 8 oxen for 6 weeks", B 12 oxen for 8 weeks; and C 12 oxen for 12 weeks ; what must each pay of the rent?

£. d. 8x 6= 48

48 : 3 3 12x 83 96

96 : 6 6

8 B's 12x12=144 > As 288 : 191. :: 144 : 910 0 C's

S.

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 $146, 25cts.

3. 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 dols. for 8 months ; how much is each 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 6.1 months ; what is each man's part of the gain ? Ans. A's part £29 18s. 31d.1th. B's £80 13s. 812.12

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

Ans. { $375, 92 57B'S
$324, 07 4+ A's share.

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 of May ; what did he then put in to have an equal share with A u the year's end ? Mo. $ Mo.

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

8

DOUBLE RULE OF THREE.

vic HE Double Rule of Three teaches to resolve at once uch 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 -ast two a demand.

RULE. In stating the question, place the terms of the supposiion 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 n the third place. Place the terms of demand, under hose of the same kind in the supposition. If the blank lace or term sought, fall under the third term, the proportion is direct ; then multiply the first and second cerms together for a divisor, and the other three for a dividend : but if the blank sall 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 divi dend, and the quotient will be the answer.

EXAMPLES. 1. If n men can build 36 rods of wall in 3 days ; how Enany rods can 20 men build in 14 days ?

7: 3 :: 36 Terms of supposition, 20 : 14

Terms of demand. 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 : 7

Ans. 141.

gain 141.

mo.

mo.

100 :

mo.

: 14

3. If 1001. will gain 61. a year ; in what time will 4001.

£.

£ 100 : 12 :: 6 400 :

::14 Ans. 7 months. 4. If 4001. gain 141. in 7 months : what is the rate per cent. per annum ?

Int. 400 : 7 :: 14 12

Ans. £0. 5. What Principal at 61. per cent. per annum, will gain 141. in 7 months ? £.

Int.
100 : 12 :: 6
7:

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 cent. per ann. he received interest? Ans. 5 per ct.

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 busheis. 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 qrs. 150 miles, cost24 aollars 58 cents ; what must be paid for the carriage of 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

24 :

200X8X6 80 days, Ans

CONJOINED PROPORTION, Is when the coins, weights or measures of severa countries are compared in the same question; or it is joini ig many proportions together, and by the relation which

N*

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.

Nore.--This rule may generally be abridged by can celling 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 multiply the left hand column continually for a dividend, and the right hand for a divisor, and the quotient will be the answer.

EXAMPLES.

ib.

1. If 100 lb. English make 95 lb. Flemish, and 19 lb. Flenish 25 lb. at Bologna ; how many pounds English are equal to 50 lb. at Bologna ?

16.
jou Eng.=95 Flemisha
'19 Fle. =25 Bologna •

50 Bologna Then 95 X25=2375 the divisor 95000 dividend, and 2375)95000(40 Ins.

2. If 40 lb. at New-York make 48 lb. at Antwerp, ana 30 lb. a. Antwerp make 36 lb. at Leghorn ; how many lb. at New York are equal to 144 lb. at Leghorn ?

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

Ans. 104;5.

CASE IE. 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.

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