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14. Two merchants companied; A put in £40, and B 288 ducats. They gained £135, of which A took £60.

value of a ducat?

What was the

As £60, A's gain: £40, bis stock :: £135 the whole gain--£ 60, A's gain: £50, B's stock.

Duc. £ Duc. s. d.

Aud, as 288: 50 :: 1 : 3 5 Aus.

15. Four men spent, at a reckoning, 20 shillings, of which they agreed that A should pay, B, 1, C, 1, and D, }. What must each pay in that proportion?

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16. A, B, and C compauied; A put in £40-25; B £80.5; and C 161: they gained £120. What is each man's share?

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40 25+80.5+161: 120 :: 40.25: 17.142475=A's

£

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17. A, B, C, and D gain $200 in trade, of which as often as A has $6, B must have $10, C $14, and D $20: What is the share of each? Ans. A's share $24, B's $40, C's $56, and D's $80.

18. An insolvent estate of $633 60c. is indebted to A, $312 75c. to B, $297, to C, $50 25c. to D, $0 25c. to E, $200, to F, $142 50c. and to G, $21 25c.; what proportion will each creditor receive? $ C. 193 51:41

Ans.

A's share

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12. A ship was driven on shore in a gale, and in lightening and getting her afloat again and in reloading, an expense of $763 was incurred; the ship was valued at $10000, freight at $3200, molasses owned by A, at $5200, sugar owned by B, at $4700, and rum owned by C, at $2500: how much is this loss on every $100, and how much must each party pay of it?

10000+3200+5200+4700+2500

$ $ $ $

$

$

$ $

25600. As 25600: 768::100:3 Ans. on each $100.

Then, As 100 : 3 :: 1000: 300 to be paid by the ship,

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20. A vessel, valued at $13000 was laden with hardware for E valued at $3000, with cordage for F, at $5000, with dry goods for G, at $3200, with goods for H, at $7900, and for I, at $4400; the captain was obliged to prevent sinking in a storm to throw overboard three fifths of the hardware, and two fifths of the cordage, with goods of H valued at $2700; allowing the freight to be $3500, what will be the average of the loss on 100 dolls, and what must be paid to E, F, and H, for their property thrown overboard?

Ans. $16 25cts. on $100, and E, F, and II must receive together $5443 75cts.

Note. If the property of E, F, and H, had been insured, the remainder of their loss must be paid by the insurers. See Policies of Insurance.

DOUBLE FELLOWSHIP,*

Or, Fellowship with Time, is occasioned by the shares of partners being continued unequal times.

RULE.

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

As the whole sum of the 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 £40 per annum. A put in 9 oxen for 5 weeks; B, 12 oxen for 7 weeks, and C & oxen for 16 weeks. What must each pay of the rent?

3x5=45. 12×7=84, and 8x16=128, then 128+84+45=257. As 257: 40 :: 45 As 257: 40:: 84 As 257: 40 :: 128

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* When times are equal, the shares of the gain or loss are evidently as the stocks, as in Single Fellowship; and when the stocks are equal, the shares are as the times; wherefore, when neither are equal, the shares must be as their products.

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2. Four merchants traded in company; A put in $400 for five months, B, $600 for 7 months, C, $960 for 8 months, and D, $1200 for 9 months; but by misfortunes at sea, they lost $750. must each man sustain of the loss.

Answer, {

What

A, $94 93c. 65m. C $227 84c. 8 m. (
B 142 40 5
D 284 81 048

3. A, with a capital of £100 began trade January 1st, 1787, and meeting with success in his business, he took in B as a partner, on the 1st day of March following, with a capital of £150. Three months after that, they admit C as a third partner, who brought into stock £180, and after trading together until the 1st of January, 1788, they found there had been gained since A's commencing business £177 13s. How must this be divided among the partners?

Ans. A, £53 16s. 8d. B, £67 5s. 10d. C, £56 10s. 6d. 4. Two merchants entered into partnership for 18 months; A, at first, put into stock $400, and at the end of 8 months he put in $200 more; B, at first, put in $1100, and at 4 months' end took out $280. Now at the expiration of the time, they found they had gained $1052. What is each man's just share?

Ans. A, $385 90c. B, $666 10c. 5. A and B companied; A put in the 1st of January, £150; but B could not put in any until the 1st of May: What did he then put" in, to have an equal share with A at the year's end?

Ans. £225.

6. E, F, and G companied; E put in, the first of March, £30, F, the first of May, put in 80 yards of broadcloth; and on the 1st of June, G put in $120. On the 1st of January following, they reckoned their gains, of which E and F took £228. F and G £215 10s. and G and E £187 10s. What was the whole gain, and the gain of each? What did they value a yard of cloth at? and, what was G's dollar worth?

2281.2151. 10s.+1871. 10s. 6311: and 63112=315!. 10s. the whole gain; then, 315l. 10s.-228-871. 10s. G's gain. 3151. 10s. ----2151. 108.1001. E's gain, and 3151. 10s -1871. 103.=1281. F's gain. To find the value of one yard of cloth, say, As 1001. E's gain 301. his stock :: 1281. F's gain: 381. 8s.; then, inversely, As 10 months: 331, 83. :: 8 months: 481. the value of the whole cloth.

:

As 80yds.: 491. :: 1yd.: 12s. answer. Now, to find the value of a dollar. As 1001. E's gain : 301. his stock :: 871. 10s. G's gain : 261. 5s. ; then, inversely, As 10 months: 261. 5s. :: 7 months: 371. 10s. 120 dollars. Lastly: As 120 dollars: 371. 10s. :: 1 dollar : 63. 3d. Answer.

7. E, F and G companied; E put in $400 for 75 of a year; F $300 for 5 of a year, and G $500 for 25 of a year; with which they gained $720: Required the share of each.

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8. A put in for 3 of a year, B for a year, and C the rest for one year; their joint stock was 1, and their gain 1; what is each share?

Ans. A's is 14
B's. 127

C's

Proof. =1

9. A and B entered into partnership for 16 months. A put in $1200 at first, and 9 months afterwards $200 more; B put in at first $1500, and at the end of 6 months took out $500; their gain was $772 20c.? what is the share of each?

Ans. A's share $401 70c. B's share $370 50c.

PRACTICE,

IS a contraction of the rule of Three Direct, when the first term happens to be a unit, or one; and has its name from its daily use among merchants and tradesmen, being an easy and concise method of working most questions which occur in trade and business.

The method of proof is by the Rule of Three, Compound Multiplication, or by varying the order of them.

A variety of rules, adapted to particular cases, is usually given under Practice. Most of the sums, however, fall under two heads, and may be wrought by two General Rules, adapted to these cases. On account of their great practical importance, these two rules should be thoroughly understood.

GENERAL RULE I.

When the price of 1 yard, 1b, &c. is given to find the value of any Tumber of yards, &c.

1. Suppose the price of the given quantity to be 11. 1D. 1s. &c. then will the quantity itself be the answer, at the supposed price. 2. Divide the given price into aliquot parts, either of the sup posed price or of one another, and find the quotients of the several aliquot parts; and their sum will be the true answer. W

EXAMPLE.

What is the value of 468 yards, at 2s. 91d. per yard?

£468 s. d.

Answer at £1 s. d.

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In this example it is plain, that the quantity 468 is the answer at £1; consequently as 2s. 6d. is of a pound, part of that quantity, or £58 10s. is the price at 2s. 6d. ; in like manner, as 3d. is the part of 2s. 6d. so part of £58 10s. or £5 178. is the answer at 3d. and as id. is of 3d. so of £5 17s. or 9s. 9d. is the answer at 1d. Now, as the sum of all these parts is equal to the whole price (28. 94d.) so the sum of the answers belonging to each price will be the answer at the full price required, and the same will be true in any example whatever.

Before the questions, hereafter given, can be wrought, the fullowing Tables must be perfectly gotten by heart.

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