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350 : 500 :: 220 :

500

35,0)11000,0(314-28

105

50

35

150

140

100

70

300

280

20

$185.713=A's share.

314.28 B's share

$500.00 the proof.

2. A and B have gained by trading $182.

A put into stock $300 and B $400; what is each person's share of the profit? Ans. A $78 and B $104.

whole gain; if my part of the whole stock be, my share of the whole gain or loss ought to be also. And generally, if I put in of the stock, I ought to have part of the whole gain or loss; that is, the same ratio, that the whole stock has to the

whole gain or loss, must each person's particular stock have to his particular gain or loss.

3. Divide $120 between three persons, so that their shares shall be to each other as 1, 2, and 3 respectively.

Ans. $20, $40, and $60.

4. Three persons make a joint stock. A put in $185.66, B $98.50, and C $76.85; they trade and gain $222; what is each person's share of the gain?

83

Ans. A $104.17101, B $60.57-243,& C$47•2539771.

5. Three merchants, A, B, and C, freight a ship with 340 tuns of wine; A loaded 110 tuns, B 97, and C the rest. In a storm the seamen were obliged to throw 85 tuns overboard; how much must each sustain of the loss?

Ans. A 271, B 241, and C 334.

6. A ship worth $860 being entirely lost, of which belonged to A, to B, and the rest to C; what loss will each sustain, supposing $500 of her to be insured?

Ans. A $45, B $90, and C $225.

7. A bankrupt is indebted to A 8277-33, to B $305.17, to C $152, and to D $105. His estate is worth only $677. 50; how must it be divided?

Ans. A $223.813588, B $246.286

C $122.66933, and D $84-738888.

395

8. A and B, venturing equal sums of money, clear by joint trade $154. By agreement A was to have 8 per cent. because he spent his time in the execution of the project, and B was to have only 5 per cent.; what was A allowed for his trouble? Ans. $35.531.

DOUBLE FELLOWSHIP.

Double Fellowship is when different or equal stocks are employed for different times.

RULE.*

Multiply each man's stock into the time of its continuance, then say,

As the total sum of all 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 and B hold a piece of ground in common, for which they are to pay $36. A put in 23 oxen for 27 days, and B 21 oxen for 35 days; what part of the rent ought each man to pay?

* Mr. MALCOM, Mr. WARD, and several other authors have given an analytical investigation of this rule; but the most general and elegant method perhaps is that, which Dr. HUTTON has given in his Arithmetic, namely,

When the 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. Three graziers hired a piece of land for $60.50. A put in 5 sheep for 4 months, B put in 8 for 5 months, and C put in 9 for 6 months; how much must each pay of the rent? Ans. A $11.25, B $20, and C $29.25.

3. Two merchants enter into partnership for 18 months; A put into stock at first $200, and at the end of 8 months he put in $100 more; B put in at first $550, and at the end of 4 months took out $140. Now at the expiration of the time they find they have gained $526; what is each man's just share? Ans. A's $192.95-70 B's 333-041191.

4. A, with a capital of $1000 began trade January 1, 1776, and meeting with success in business he took in B as a partner, with a capital of $1500 on the first of March following. Three months after that they admit C as a third partner, who brought into stock $2800, and after trading together till the first of the next year, they find the gain, since A commenced business, to be $1776.50. How must this be divided among the partners?

Ans. A's $457.4638.

B's 571-83.
C's 747-1938

ALLIGATION.

ALLIGATION teaches how to mix several simples of different qualities, so that the composition may be of a middle quality; and is commonly distinguished into two principal cases, called Alligation medial and Alligation alternate.

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