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6. B sells goods to C on credit of 60 days as follows: Jan. 14, 1894, a bill of $2000; Feb. 10, 1894, a bill of $1500; Mar. 25, 1894, a bill of $3000; find the equated time and date of payment.

7. B borrowed $1200 for 6 mo.: at the end of 2 mo. he paid $400, and at the end of 4 mo. he paid $600; when should the balance be paid?

8. What is the average time of paying $120 due in 5 mo, $150 due in 6 mo., and $160 due in 4 mo.?

9. What is the date of paying $60 due May 18, $130 due June 24, and $180 due Aug. 1?

10. I gave B $12000 for 10 mo., of which he paid in 4 mo., and of the remainder in 6 mo.; how long may the balance remain unpaid?

11. A merchant owes $2200 due in 9 mo.; if he pays $800 in 3 mo., $600 in 5 mo., and $400 in 7 mo., how long in justice may the balance remain unpaid?

12. I sold goods to Mr. Martin as follows:

Oct. 14, 1893, a bill of $600 on 3 mo. credit;

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13. A owes $800 due in 5 mo., $1200 due in 7 mo.; if at the end of 5 mo. he pays $1400, when should the balance be paid?

14. Three 90-day notes bear date as follows: Apr. 10, 1894, $480; May 12, 1894, $520; June 14, 1894, $640. What is the average date of payment, counting three days of grace?

15. A sells B goods as follows: $200 in 90 days, $300 in 60 days, $400 in 30 days, $500 in 10 days, and $600 cash; what is the average term of credit?

16. A merchant owes $3300 due in 8 months; if he pays $1200 in 3 mo., $1000 in 4 mo., and $500 in 6 mo., when should he pay the balance?

AVERAGING OF ACCOUNTS.

211. Averaging of Accounts is the process of finding the time when the balance of an account may be paid with justice to both debtor and creditor.

WRITTEN EXERCISES.

1. When is the balance of the following account due?

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The payment for the flour sold Apr. 20th on 2 mo. credit is due June 20th, and that sold May 28th on 1 mo. credit is due June 28th. The 15-day draft of May 24th is due 18 days after May 24th, or June 11th.

It will be seen that Mar. 15th is the earliest date at which any one of the items is due. Using this as the focal date, we find the sum of the products on the debit side to be equivalent to $1 for 50900 days, and the sum of the products on the credit side to be equivalent to $1 for 42260 days. Subtracting 42260 from 50900, there is a balance on the debit side equivalent to the use of $1 for 8640 days.

In order to make the products on the debit side equal to the products on the credit side, it is evident that the balance of $100 must be paid after the focal date, Mar. 15th. Now, for the credit of $100 to be equivalent to $1 for 8640 days, it must have a credit of 86 days.

Hence the account can be settled by paying $100 86 days after Mar. 15th, or on June 9th.

2. When is the balance of the following account due?

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1850 + 50

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37 da. 37 da. back from Sept. 20th is Aug. 14th, Ans.

Solving this problem as Ex. 1, we find that the balances are on opposite sides of the account.

Now, in order to make the products of both sides equal the credit of the balance, $50, for 37 days must be subtracted from the sum of the products on the credit side. This indicates that it should have been paid 37 days before the focal date, Sept. 20th, or on Aug. 14th.

It is evident from these examples that if the two balances are on the same side of the account, the equated time is after the focal date; if they are on opposite sides of the account, the equated time is before the focal date.

3. Find the equated time for paying the balance of the following account:

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4. Find the equated time for paying the balance of the

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5. Find the equated time for paying the balance of the following account:

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6. Find the equated time for paying the balance of the following account:

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NOTE 1.-Any other date than the earliest might be selected as the focal date. If we reckon from the last date at which any item becomes due, as a focal date, and the balances are on the same side of the account, the equated time is before the focal date; if they are on opposite sides, the equated time is after the focal date.

NOTE 2.-An account may be averaged by finding the interest at any per cent. on each item, and dividing the balance of interest by the interest on the balance of the account for one day; the quotient will be the number of days to be added to or subtracted from the focal date.

SECTION X.

INVOLUTION AND EVOLUTION.

INVOLUTION.

212. Involution is the process of raising a number to any required power.

213. The Power of a number is the product obtained by using the number several times as a factor.

The Power is indicated by a small figure, called an Exponent, placed at the right of and a little above the number. Thus,

4 = 41,

4°X 4 = 42 =

the first power of 4. 16, the second power of 4,

or the square of 4.

4 X 4 X 4 = 464, the third power of 4, or

=

the cube of 4.

4X4 X 4X4 4 256, the fourth power of 4, etc.

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ORAL EXERCISES.

1. Square 2, 3, 4, 5, 6, 7, 8, 9, 10.
2. Cube 2, 3, 4, 5, 6, 7, 8, 9, 10.
3. Square 20, 25, 30, 40, 50, 60, 70.
4. Cube 20, 30, 40, 50, 60, 70, 80.
5. Find the value of 42, 43, 4, 52, 53, 89.
83.
6. Square .2, .3, .4, .6, .8, .9, .03, .05.
7. Cube .2, .3, .4, .5, .6, .7, .8, .9.

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