portional quantities, and multiply each proportional quantity by the quotient.

NOTE. When the sum of the proportional parts is not an exact divisor of the quantity, each couplet must be multiplied by such numbers as will make the sum of the proportional parts a divisor of the entire quantity.

WRITTEN EXERCISES.

2. A grocer wished to mix teas worth 25, 30, 44, and 55 a pound, making a mixture of 68 pounds, worth 35¢ a pound; required the quantity of each kind.

Ans. 8; 36; 20; 4.

3. A merchant mixed sugars worth 5, 7, 11, and 12 a pound, in order to make a mixture of 66 lb. worth 8 a pound; how many pounds of each did it require?

Ans. 24; 18; 6; 18. 4. A man bought 100 apples for $1, some worth of a cent, some, some 14, and some 24 apiece; how many did he purchase of each kind?

Ans. 40, 1st; 10, 2d; 20, 3d; 30, 4th.

5. A lady bought 102 yards of muslin at an average price of 15 ct., some at 8, some at 13, some at 18, and some at 20 ct. a yard; required the number of yards of each kind. Ans. 30; 18; 12; 42.

6. A man has $134 in ten-cent pieces, which he wishes to exchange for pieces worth 3, 5, 25, and 50 cents respectively; how many of each kind will it require?

Ans. 800, 3 ct.; 300, 5 ct.; 100, 25 ct.; 140, 50 ct. 7. A person has some bank-notes whose denominations are respectively $1, $2, $5 and $20, which he wishes to exchange for 62 ten-dollar notes; how many must he exchange of each kind?

Ans. 20 ones; 10 twos; 4 fives; 28 twenties. 8. A person purchased 100 animals for $100; sheep at $3 apiece, calves at $13, and pigs at $; how many animals did he buy of each kind? Sheep, 5, 10, 15.

Ans. Calves, 42, 24, 6.

Pigs, 53, 66, 79.

NOTE. This last problem is from Hackley's Algebra, 3d example, under Indeterminate Analysis. Its solution by Arithmetic is very simple.

PARTNERSHIP.

585. Partnership is the association of two or more persons for the transaction of business.

586. Partners are the persons associated in business, and are of three kinds, General, Limited, and Special.

587. The Capital of a firm is the money or property invested by the partners. The Liabilities are its debts.

588. The Resources or Assets of a firm are its property of any kind, together with the amounts due it. The excess of resources over liabilities is called the Net Capital. 589. Partnership is divided into Simple and Compound Partnership for convenience of treatment.

General Partners risk their whole property in the business; Limited and Special Partners risk only the amount of capital they agree to contribute. Partners whose names do not appear are sometimes called Silent Partners.

SIMPLE PARTNERSHIP.

590. In Simple Partnership the shares of the partners are employed for equal periods of time.

1. A, B, and C, went into partnership; A put in $500, B put in $700, and C, $800; they gained $600; what was each one's share of the gain?

2. A, B, and C form a partnership for shipping peaches; A puts in $680, B $720, C $600; they gain $600; what does each receive? Ans. A, $204; B, $216; C, $180.

3. Three persons enter into partnership, with $6000, of which A contributes, B, and C the remainder; they gain $1800: what sum belongs to each?

Ans. A, $900; B, $600; C, $300.

4. Three men agree to share 60 gal. wine, A taking, B , and C; but upon drawing off these parts they find there is a remainder; how should the wine be divided?

Ans. A, 252 gal.; B, 197 gal.; C, 151 gal.

5. A, B, and C were partners in the coal trade; A furnished $5000, B $7000, and C managed the business; they gained $2400; what was the share of each, if C received as much as both A and B?

Ans. A's, $500; B's, $700; C's, $1200.

6. Three persons engage in cotton speculation; A contributed $6400, B $7200, and C $5400; they lose of their stock by fire, and gained on the remainder of cost; what was the gain of each?

Ans. A's, $2048; B's, $2304; C's, $1728.

7. 'Squire Jones left by his will $5000 to his wife, $3500 to his son, and $4500 to his daughter; but upon settling his estate it was found to amount to only $10400; how much Idid each receive?

Ans. Wife, $4000; son, $2800; daughter, $3600. 8. A, B, and C go into the lumber trade with a joint capital of $9500; at the end of a year it is found that A's gain is $1650, B's $1500, and C's $1600; required each one's stock. Ans. A's, $3300; B's, $3000; C's, $3200.

9. A shipping firm gained one year $4200; A's stock was $6500, B's stock $5300, and C's gain $1250; required C's "tock and A's and B's gain.

Ans. A's, $1625; B's, $1325; C's stock, $5000. 10. A, B, and C form a partnership for carrying on a nursery; A contributes $800, B $600, and C 10 acres of land on which to establish the nursery; their first year's profits are $1500, of which C receives $660; what are A's and B's gain, and the value of C's land per acre?

Ans. A's, $480; B's, $360; $110 per acre.

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COMPOUND PARTNERSHIP

591. In Compound Partnership the capitals of the partners are employed for different periods of time.

CASE I.

592. When the profits and losses are divided in proportion to capital and time.

1. Two persons enter into partnership and gain $328; A put in $800 for 5 mo., and B $700 for 6 mo.; what was each man's share of the gain?

Rule. Multiply each partner's capital by the time it was employed, and divide the gain or loss in proportion to these products.

WRITTEN EXERCISES.

2. A, B, and C engaged in partnership; A had $500 in trade for 9 mo., B $800 for 8 mo., and C $1200 for 7 mo.; they gain $488.70; what was each one's share of the gain? Ans. A's, $113.94; B's, $162.06; C's, $212.70. 3. Four gentlemen rented a pasture-field for $62.40; the first put in 3 horses for 7 weeks, the second 4 horses for 8 weeks, the third 2 horses for 13 weeks, and the fourth 5 horses for 5 weeks; what should each pay y?

Ans. $12.60; $19.20; $15.60; $15. 4. A, B, C, and D agree to clear a tract of woodland for $120; A worked 9 days of 10 hours each, B 15 days of 6 hours each, O 10 days of 9 hours each, and D 3 weeks 5 hours a day; what does each receive? Ans. $30.

5. Mr. Allen commenced business with $10000 capital; at

the end of 3 months he took in Mr. Green, with $7000 capital, and at the end of 6 months Mr. Handy with $3000 capital; at the end of the year they had gained $4020; required the share of each. Ans. $2400; $1260; $360.

6. Two persons, A and B, were in partnership 2 years; A at first put in $2500 and B $3000; at the end of 9 mo. A took out $800 and B put in $500; they lost in 2 yr. $3825; what was each one's share of the loss?

Ans. A's, $1440; B's, $2385.

7. Three drovers, A, B, and C, hire a pasture for $51.70 for 5 mo.; A put in 60 cows, B 80 cows, and C 90 cows; at the end of 3 mo. A sells of his, B 4 of his, and C of his; how much rent ought each to pay?

Ans. A, $13.00; B, $18.00; C, $20.70. 8. A and B went into the hardware business, A's capital being to B's as 5 to 7; at the end of 6 months A withdraws of his capital, and B of his, and during the year they lose $1430; what was each man's share of the loss? Ans. A's, $585; B's, $845. 9. Brown's capital was in trade 6 mo., Black's 8 mo., and White's 10 mo. Brown's gain was $750, Black's $1200, White's $800, and the whole capital, $19880; how much did each own? Ans. $7000; $8400; $4480.

REMARK. Find each one's gain for 1 mo., and divide the whole capital In that proportion.

CASE II.

593. When the proportion of profits or losses is fixed, and interest is allowed for the difference between each partner's proportion of capital and the amount he actually contributes.

1. A and B form a partnership; A contributes $1700, and is to have of the profits; B contributes $700, and is to have profits; each partner is to receive or pay interest at the rate of 6% per annum for any excess or deficit in his proportionate share of capital. At the end of a year the profits are $900. How much has each gained?

F