$500 for 8 months is the same as $4000 for 1 month, and $600 for 10 months is the same as $6000 for 1 month; hence the entire stock is the same as $4000+ $6000, or $10000, for 1 month.

If $10000 gain in a certain time $240, $4000, or of that sum, must gain of $240, or $96, and $6000, or § of the sum, & of $240, or $144.

RULE. Multiply each partner's stock by the time it was invested, and apportion the gain or loss in proportion to the products.

Examples.

2. A, B, and C commenced trade together the first of June, on $6000 put in by A; the first of August B put in $9000, and the first of September C put in $12000. At the end of the year their gains amounted to $4500; what was each partner's share? Ans. A's $1400, B's $1500, and C's $1600.

3. A, B, and C enter into partnership; A put in $500 for 18 months; B $380 for 13 months; C $270 for 9 months. They lost $818.50; what was each man's share?

Ans. A's $450, B's $247, and C's $121.50.

4. Jones and Smith rent a pasture for $275; Jones puts in 80 sheep and Smith 100, but at the end of 6 months they each dispose of half their stock, and allow Hall to put in 50 sheep; what should each pay toward the rent at the end of the year?

Ans. Jones $103.12, Smith $128.90§, and Hall $42.963. 5. A and B entered into partnership for 1 year. A at first put in $500, and at the end of 5 months he put in $150 more; B at first put in $600, and at the end of 9 months took out $200. Their year's profits were $682.50; what was each man's share? Ans. A's $352.50, and B's $330.

Explain the operation. Repeat the Rule.

6. A builds a mill at a cost of $35000; 2 months after its completion B buys stock in it of A to the amount of $11000; and in 3 months more C purchases also of A $4000 worth of stock. They run the mill for 7 months, and gain during that time $9700; what portion of this belongs to each?

Ans. A's share $7205.71+, B's share $2177.55+, and C's share $316.73+.

7. S, T, and Y entered into partnership. S kept his stock in 1 year; T put in as much as S, and for 10 months; Y put in as much as S, and for 4 months. They gained $3400; what was each one's share of the profit?

Ans. S's share $2400, T's share $400, and Y's share $600.

EQUATION OF PAYMENTS.

338. Equation of Payments is the process of finding the average or equitable time for paying several sums due at different times.

339. The Equated Time is the date at which the items due at different times may be justly paid together.

340. The Average Term of Credit is the time that must elapse before the equated time.

CASE I.

341. To find the equated time when the terms of credit begin at the same date.

1. I owe, July 1, to John Wentworth, $600, of which $200 is due in 2 months, $300 due in 4 months, and $100 in 8 months; required the equated time of paying the several items

at once.

REVIEW QUESTIONS. What is a Compound Proportion? (332) The Rule? (333) Partnership? (334) The Rule when the capital of each partner is employed equal times? (335) When for unequal times? (337) – What is Equation of Payments? The Equated Time? The Average Term of Credit?

Hence, the entire credit is equal to a credit on $1 for 2400 mo. ; and a credit on $1 for 2400 mo. is equal to a credit on $600 for of 2400 mo., or 4 mo.; hence, 4 mo. from July 1, or November 1, is the equated time

RULE. Multiply each term of credit by the number denoting its debt, and divide the sum of the products by the number denoting the sum of the debts; the quotient will be the average term of credit.

The average term of credit, added to the date of the debts, will give the equated time.

When any of the items have cents, if 50 or more, reckon them as one dollar, but if less than 50 cents, neglect them. Also, when any result has a fraction of a day, if it is or more, reckon it one day, otherwise neglect it.

Examples.

2. Required the average credit for the payment of $500 payable in 2 months, $1000 in 5 months, and 1500 in 8 months. Ans. 6 months.

3. I owe $1600 payable now, and $800 in 90 days; what is the average term of credit? Ans. 30 days.

4. Required the equated time from March 1st, at which to pay $200, of which $40 is due in 3 months, $60 in 5 months, and the remainder in 10 months. Ans. October 4th. 5. May 16, 1866, Albert Day owes $199.50 payable in 30 days, $150.15 in 60 days, and $300 in 90 days; what is the equated time? Ans. July 20, 1866.

Explain the operation. Repeat the Rule. How do you proceed when any of the items have cents? When any result has a fraction of a day?

Oct. 7, Merchandise, on 90 days, $1000.

Nov. 15, 1866+45 days Dec. 30, 1866, Ans.

95 days, from Nov 15.

$600, are, respectively, 0, 51, and

The average term of these credits, by Case I., is 45 days; hence, 45 days from Nov. 15, 1866, or Dec. 30, 1866, is the equated time.

RULE. Select the earliest date at which any one of the debts became due, and therefrom reckon the terms of credit.

Multiply the terms of credit of each item by the number denoting its item, and divide the sum of the products by the number denoting the sum of the items; the quotient will be the average term of credit.

The average term of credit, added to the selected date, will give the equated time.

Examples.

2. Purchased the following bills of goods: July 1, a bill of $200, on 2 months; July 20th, a bill of $600, on 60 days; Aug. 1, a bill of $1000, on 30 days. What is the equated time of payment? Ans. September 6th.

Explain the operation. Repeat the Rule.

3. I owe Oliver Bates as follows: April 1, for cash, $1400; May 1, for merchandise $500; June 1, for flour, $1100. What is the average date of the items? Ans. April 28th.

4. R. Hicks & Co. have sold a merchant the following bills: Jan. 1, merchandise, $735; Jan. 21, corn, on 30 days, $649.50; Feb. 1, lumber, $100; March 12, merchandise, on 30 days, $200. If they should receive in settlement for the whole, a note, from what date ought it to draw interest?

Ans. February 3d. 343. When the items have the same term of credit, we may First find their average date, and then add the common term of credit, for the equated time.

a

5. Purchased goods, on 4 months, as follows: — - April 1, bill of $1450; May 7, a bill of $1250; June 5th, a bill of $850. Required the equated time of payment.

Ans. August 29th.

6. Sold the following bills of goods, on 6 months: Jan. 15, a bill of $3750; Feb. 10, a bill of $3000; March 6, a bill of $2400; June 8, a bill of $2250. At what time should a note be made payable, that will settle for the whole?

344.

Ans. Sept. 2d.

AVERAGING OF ACCOUNTS.

The Balance of an account is the difference between its debtor and creditor sides.

Accounts are subject to interest after the expiration of the term of credit.

345. The Averaging of an Account is the process of finding the equated time of paying the balance, or the date at which the balance of the account becomes due, or subject to interest.

How may we proceed when the items have a common term of credit? What is the Balance of an Account? When are accounts subject to interest? What is the Averaging of an Account?