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4. A, B, and C pay $1, $2, and $3, respectively, towards the purchase of some oranges; the oranges are sold for $12; what should each receive for his share of the proceeds ?

5. If 25 cents are divided between two boys so that one of them receives 3 cents as often as the other receives 2, how many cents will each boy receive?

6. A works 3 hours, B 4 hours, and C 5 hours, for which they receive $7.20 in all; if they are paid at the same rate, what is each man's share?

WRITTEN EXERCISES. 1. A ship is valued at $16000; A owns , B1, C1, and the captain has the remaining share. The ship being injured in a storm, the repairs cost $2560; what is each one's share of the expense?

ANALYSIS.—The value of the ship is $16000, and the loss $2560; $2560 -- 16000, or $ 2.56%= the loss on each dollar of capital invested; A owns of $16000=$3000, B owns of $16000= $4000, C owns of $16000=$8000, and the captain owns to of $16000= $1000. A's loss will be $ 25.696 3000=$480; B's loss, $ 2.560 x 4000= $640; C's loss, $ 2.560 X 8000= $1280; the captain's loss, $ 2560 x 1000 = $160.

RULE. Make the whole gain or loss the numerator, and the whole capital the denominator of a fraction; multiply this fraction by each partner's capital, for his share of the gain or loss.

2. A, B, and C agree to form a company for the purchase and sale of flour. A puts in $1200, B, $1800, and C, $3000. At the expiration of three years they find that they are $5000 in debt; what is each man's share of the indebtedness ?

3. Two men purchase a piece of land for $1800. They sell it so as to gain $500; what is each man's share of the gain, if the first man paid twice as much as the second ?

4. A property worth $20000 is to be divided in the proportion of 1, 1, and }; what is the value of each share?

5. Four persons, A, B, C, and D, engage to perform a piece of work; A does twice as much as B, C does 3 times as much as B, and D does as much as B and C both. They receive $60; how much is each person's share?

6. A bankrupt, whose estate is worth $3000, owes $15000. What should A receive, his claim against the estate being $5000 ?

COMPOUND PARTNERSHIP.

ORAL EXERCISES. 1. Two men agree to build a wall for $20. The first man works 5 hours a day for 4 days, and the second man works 10 hours a day for 6 days; how should the money be divided between them?

ANALYSIS.—The first man works 5 X 4= 20 hours; the second works 10 X 6=60 hours. The total number of hours' work is 60+ 20=80. If 80 hours' work is worth $20, each man is entitled to as many 80ths of $20 as he has worked hours. The first man works 20 hours, and earns , or of $20=$5; and the second man works 60 hours, and earns 60, or of $20=$15.

2. John and James agree to do a piece of work for $5. John works 2 hours a day for 5 days, and James works 4 hours a day for 10 days; how much should each receive?

3. Two men agree to carry 100 pounds of groceries 5 miles, for $1. One of them carries 50 pounds 4 miles, the other carries his 50 pounds the entire distance, and the remaining 50 pounds 1 mile. How should they divide $1 between them?

WRITTEN EXERCISES. 1. A and B formed a partnership; A invests $2000 for 6 months, and B $1000 for 4 months; they gain $1600; how much is each man's share of the gain?

A's capital = $2000 x 6 = $12000 for 1 month.
B's capital = $1000 x 4= $4000 for 1 month.
$12000 + $4000 = $16000, capital for 1 month.
$160= the amount gained by $1 of capital.
$ 16.000 X 12000 = $1200, A's share of the gain.
$ 160000 X 4000 = $400, B's share of the gain.

ANALYSIS.—If A's capital was employed but 1 month, it would require 6 times $2000, or $12000, to gain the amount earned by $2000 in 6 months. If B's capital was employed but 1 month, it would require 4 times $1000, or $4000, to gain the amount earned by $1000 in 4 months. It would therefore require $16000 to gain as much in 1 month as $2000 in 6 months and $1000 in 4 months. If it requires $16000 of capital to gain $1600, $1 of capital will gain to voy of $1600 =$16600%. А’s $12000 will gain $16600.% 12000 = $1200; and B's $4000 will gain $ 16.00 X 4000 = $400.

RULE. Multiply each partner's capital by the time it is employed. Make the sum of all these products the denominator of a fraction, and the total gain or loss the numerator. Multiply this fraction by the product of each partner's capital by the time it is employed, and the result will be each partner's share of the gain or loss.

2. Messrs. Brown and Jones formed a partnership for 2 years. Brown paid in $5000 at once, and Jones invested $6000 at the beginning of the second year. At the end of 18 months, Brown withdrew $1500. Their loss in the business was $2500; how should it be divided between them?

3. A, B, and C formed a partnership. A invested $1000 for 6 mo., B $2000 for 9 mo., and C $900 for 12 mo. They gained $1000; how should it be divided among them?

4. The entire capital of a company is $6000. The gain in one year is $4800. John Thompson has invested of the capital during 6 mo., Amos Little 1 the capital for 8 mo., and James Loomis the remainder for 12 mo.; what is each man’s share of the gain?

5. Three men rented a farm for pasture, at a cost of $500. A has 50 head of cattle pastured for 4 mo., B has 200 head for 3 mo., and C has 300 head for 34 mo.; what should each man pay for his share of the rent?

6. January 1, 1876, John Jones commenced business with a capital of $2500. April 1, Lewis Smith became a partner with $3000 capital. July 1, Isaac Perkins entered the firm with $6000. January 1, 1877, the firm divided $3000; what did each partner receive?

7. Peter Carter enters a partnership six months after it is formed, and is required to invest sufficient capital to entitle him to i of the profits. William Johnson has $2000 invested for 9 mo., and Samuel Davis has $6000 in the business during the entire year. They divide $4400; how much did Carter invest?

8. Three men agree to form a partnership for 18 months. A invests of the capital for 9 mo., and increases his proportion to 1 the capital during the next 9 mo.; B invests 4 of the capital for 6 mo., and then increases his share to { for the remaining time; C invests of the capital during the first 6 mo., then withdraws of his share for 3 mo., and for the last 9 mo. he has but of the entire capital. How should they divide a profit of $2060?

EQUATION OF PAYMENTS. Equation of Payments is the process of finding the time when the payment of several sums of money due at different periods may be made at once, without loss of interest to debtor or creditor.

The Equated Time is the date at which the sum of the debts may be paid without loss to either party.

The Term of Credit is the time between the contracting of a debt, and the date when it becomes due.

The Average Term of Credit is the time between the contracting of the first debt, and the equated time for the payment of them all.

CASE I. To find the equated time when the terms of credit

begin at the same date.

ORAL EXERCISES. 1. If the interest of $1 for 1 day is ab of a cent, what is the interest of $60 for 1 day at the same rate?

2. At 6%, what will be the interest of $1 for 60 days?

3. What is the interest of $10 for 12 days? Of $1 for 120 days?

4. What is the interest of $60 for 60 days? Of $1 for 3600 days?

5. If the interest of $1 for 1 month is į cent, what is the interest of $40 for 3 months? Of $1 for 120 months ?

6. What is the interest of $100 for 5 months? Of $1 for 500 months ?

1. If I borrow $150 for 3 months, for how long should T lend $50 to balance the account?

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