5. A and B engaged in business: A put in 5 times as much capital as B; if they gained $1434, what was each one's share of the gain?

6. E failed in business, owing A $214, B $316, and C $470; what was the share of each creditor, if the resources of E amounted to $350.25?

7. M, N, and P engaged in the hardware business with a joint capital of $7280: M put in twice as much as N, and P put in $1040; if they gained $1820, what was each one's share of the gain?

8. A, B, and C engaged in business, A putting in as much capital as B, and B as much as C; if they gained $3610, what was each one's gain?

9. A man dying willed $5000 to each of two daughters, $4000 to each of three sons, and $8000 to his widow on settling the estate it was found to be $25,000; how should it be divided?

10. A, B, and C engaged in business with a joint capital of $25,000: at the end of the year A's share of the gain was $1620, B's $2214, and C's $2416; required the capital of each.

11. Three farmers raised 500 bushels of wheat on a tract of land cultivated by them conjointly: they agreed that A should take, B, and C of it; but after this division there is a remainder; how should it be divided?

12. A, B, and C formed a partnership to operate a dairy: A contributed $500, B $700, and C 24 cows; the first year they gained $1728, of which C received $768; what were A's and B's gain and the average value of C's cows?

13. M, N, and O buy a property for $12,000: M contributes $4500, N $3000, and O the remainder; the rents received from this property amount to $100 per month, and the taxes and. other expenses to $180 per annum; what is each man's yearly share of the proceeds?

208. Compound Partnership.

In Compound Partnership each partner's capital is invested for unequal periods of time, and the profits or losses are divided in proportion to the capital and the length of time it is invested.

WRITTEN EXERCISES.

1. A, B, and C form a partnership: A puts in $300 for 5 months, B $500 for 6 months, and C $700 for 7 months; they gain $1974; what is each partner's share of the gain?

2. M and N formed a partnership: M put in $2300 for 8 months and N $3200 for 7 months; if they gained $1264.80, what was each one's share of the gain?

3. R and S formed a partnership: R put in $1100 for 9 months, S $1300 for 11 months; they lost $726; what was each man's share of the loss?

4. A, B, and C entered into partnership: A invested $325 for 10 months, B $450 for 13 months, and C $300 for 14 months; they gained $798; what was each man's gain?

5. R, S, and T hire a pasture for $115.20: R puts in 10 cows for 3 months, S 12 cows for 3 months, and T 16 cows for 4 months; what should each man pay?

6. A commenced business with $800 capital: at the end of 4 months he took in B, with $1000 capital, and at the end of

8 months he took in C, with $1200 capital; at the end of the year they had gained $2912; required the gain of each.

7. M and N formed a partnership for one year: M put in $1600 at the beginning of the year and $900 at the end of 7 months; N put in $1200 at the beginning of the year and $1200 at the end of 8 months; they gained $4719; required the gain of each.

8. A and B engaged in business for one year: A put in $2000 and B $3500; at the end of 8 months A put in $500 and B drew out $900; they gained $8372; what was each man's share of the gain?

9. A, B, and C agreed to do a piece of work for $65.50: A labored 8 days of 10 hours each, B 7 days of 9 hours each, and C 14 days of 8 hours each; how much should each receive?

10. M, N, and P entered into partnership for one year: M put in $1500, and at the end of 7 months added $900; N put in $2000, and at the end of 9 months took out $500; P put in $1800, at the end of 5 months put in $600, and at the end of 9 months took out $1100; they gained $4650.60; what was each man's share of the gain?

11. A, B, and C entered into partnership for one year: at the beginning of the year A put in $2000, B $2200, and C $2460; at the end of 5 months A added $800, C $600, and B took out $400; at the end of 8 months A took out $500, C $1240, and B added $1200; they gained $8476; what was each man's share of the gain?

EQUATION OF PAYMENTS.

209. Equation of Payments is the process of finding at what time several sums due at different times may all be paid together, with justice to both debtor and creditor.

The time thus found is the Equated Time.

210. The Focal Date is the date from which we begin to reckon in averaging an account.

WRITTEN EXERCISES.

1. A owes B $70 due in 4 months, and $80 due in 6 months; what is the average term of credit?

A credit on $70 for 4 mo. is equivalent to a credit on $1 for 280 mo. A credit on $80 for 6 mo. is equivalent to a credit on $1 for 480 mo. Adding, A is entitled to a credit on $1 for 760 mo.; hence he is entitled to a credit on $150 for as many months as 150 is contained times in 760, which is 5 months, or 5 mo. 2 da.

2. I purchased the following bill of goods:

May 5, a bill of $500 on 3 mo. credit,

When can I settle these bills in one payment without loss to

either party?

of 56 days after Aug. 5, which is Sept. 30.

3. A owes $300 due in 8 months; if he pays $80 in 3 months and $60 in 6 months, when should he pay the balance?

after it becomes due to equal $1 for 520 mo., which is 1 of 520 mo., or 3 mo.

4. M owes $400 due in 5 mo., $500 due in 6 mo., and $600 due in 7 mo.; what is the average term of credit?

5. Mr. Bowman bought goods as follows: Mar. 15, $300 on 2 mo. credit; Apr. 10, $400 on 3 mo. credit; May 5, $500 on 4 mo. credit; what is the equated date of payment?