3. Mr. Jenkins has bought $1200 worth of goods on 6 months' credit and $600 worth on 3 months' credit. For what time should he give a note for the whole amount, $1800?

4. $1680 is to be paid in four equal instalments, in 1, 2, 3, and 4 mo. respectively. Equate the time.

5. $500 is due in 8 mo., $900 in 6 mo., $1000 in 3 mo., $1200 in cash [1200 × 0 = 0]. Find the term of credit for a single payment of the whole indebtedness.

6. Equate the time for the payment of $5000, due Feb. 1; of $4000, due June 1; of $3000, due Aug. 1, and of $3000, due Oct. 1.

Suggestion: Count time from Feb. 1.

7. A person owes a certain sum, of which 8 mo., in 9 mo., and the balance in 12 mo. time of payment.

is payable in Equate the

8. Johnson & Co. sold a bill of lumber on the following terms: $1500 cash, $3000 payable in 30 days, and $2000 payable in 90 days. When may the whole debt be cancelled by one payment?

9. If a person lends me $250 for 8 mo., for how long ought I to lend him $480 as an equivalent?

10. I bought on July 5th goods to the amount of $2400. $630 was to be paid at once, $820 in 8 mo., and $950 in 9 mo. What is the equated time for the payment of the whole?

11. A man owes $600, of which is to be paid in 1 yr., and the remainder in 2 yr. Equate the time, and find the present value, money being worth 6%.

12. I bought bills of goods as follows: June 1, $250, on 3 mo. credit; July 5, $300, on 3 mo. credit; Aug. 6, $150, on 3 mo. credit; Oct. 2., $400, on 2 mo. credit. Find the equated time of payment.

13. Mr. B. bought goods as follows: April 15, $150 on 2 mo. credit; May 10, $200 on 3 mo. credit; June 5, $250 on 4 mo. credit. Find the equated date of payment.

14. What is the average time at which the following bills become due: Feb. 1, 1898, $200 on 1 mo. credit; March 10, 1898, $500 on 3 mo. credit; April 12, 1898, $275 on 2 mo. credit; and May 1, 1898, $400 on 4 mo. credit?

15. I owe Mr. Wilson $100, to be paid on the 15th of July; $200 on the 15th of August, and $300 on the 9th of September. What is the mean time of payment?

16. Find the equated time for the payment of $112.30 due July 6, $115.25 due July 30, $232.15 due Sept. 4, and $102.36 due Oct. 1.

17. A merchant bought goods as follows: Mar. 19th, $350 on 4 mo.; Apr. 1st, $430 on 130 da.; May 16th, $540 on 95 da.; June 10th, $730 on 3 mo. ; what is the average time for the payment of the whole?

.;

18. $1200 worth of mdse., bought Nov. 5, and $1000 worth bought on the following Jan. 9, have a credit of 2 mo. When may both be paid at once?

19. A man bought the following bills of goods: Jan. 15, $600 on 2 mo. credit; Feb. 1, $300 on 3 mo. credit; March 25, $550 on 30 da. credit; and April 8, $400 on 60 da. credit. Find the equated time of payment.

20. Find the equated time of payment for the following obligations :

1. $400, due June 15; $375, due July 11; $195, due

Sept. 4.

2. $1394.50, due Dec. 1, 1898; $129.80, due Dec. 10, 1898; $960, due Feb. 1, 1899.

21. A. owes $600, due in 8 mo.

If he pays $160 in 3 mo. and $120 in 6 mo., when should he pay the balance?

8 mo.

- 3 mo. = 5 mo.

8 mo. · 6 mo. = 2 mo.

Therefore A. has to his credit:

22. B. owes $1600, due in 5 mo. ; $2400 due in 7 mo. If at the end of 5 mo. he pays $2800, when should the balance

be paid?

23. A man owes $2000, due in 8 mo. He pays $500 in 2 mo. and $800 in 3 mo. When in equity should he pay the balance?

24. A. owed B. $2000, payable in 4 mo., but at the end of 1 mo. he paid him $500, at the end of 2 mo. $500, and at the end of 3 mo. $500. In how many months is the balance due him?

25. 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?

26. A merchant owes $5400, due in 9 mo. If he pays $2300 in 4 mo., $2000 in 5 mo., and $600 in 7 mo., when should he pay the balance?

27. A modiste bought goods to the amount of $425 on a credit of 20 da. and $380 on a credit of 30 da. At the end

of 15 da. she paid $450, and at the end of 20 da. she paid $150. When can the remainder be equitably paid?

28. What is the average date of payment for the following three notes: March 10, 1898, $240; April 12, 1898, $260; May 14, 1898, $320?

29. I bought goods to the amount of $1200 on the following terms: payable in cash, payable in 2 mo., the When may the whole in equity be paid at

balance in 6 mo.

once?

30. I owe $600, due in 5 mo.; $1000, due in 10 mo., and What is the average term of credit?

$1200, due in 7 mo.

INVOLUTION.

INDUCTIVE STEPS.

1. In the equation 3 x 39, there are how many equal factors? What is the product of those factors?

2. In the equation 5 × 5 × 5 = 125, how many times is 5 taken as a factor? What is 125 called?

3. The product of equal factors is also called the power. 4. Find the product or power of 6 taken twice as a factor. 5. Find the power of six taken 3 times as a factor? 6. When a number is taken twice as a factor, the product is called the second power of the number.

7. When a number is taken 3 times as a factor, the product is called the third power of the number; when taken four times, the fourth power, and so on.

8. Write the second power of 2; of 3; of 4; of 5; of 7; of 8; of 9.

9. Write the third power of 2; of 3; of 4; of 5; of 7; of 8; of 9.

10. What is the product of by 3? Of by by ? 11. What, then, is the second power of ? Third power? 12. What is the second power of ? Third power?

=

13. The equation 2 X 2 X 2 = 8, expressing the third power of 2, is commonly written thus: 23 8. The 3, indicating the number of times 2 is taken as a factor, is called the Exponent.

14. Write an equation showing by an exponent the third power of 4; the fourth power of 5; the fifth power of 6.

15. For the reason that the product of two equal factors equals the area of a square, and the product of three equal factors denotes the volume of

5

5 a cube, the second power of a number is

5

also called the Square, and the third power of a number the Cube.

16. Involution is the process of finding the power of a number.

EXERCISES.

The first power of a number is the number itself.

1. Write the first power of the numbers represented by the digits.

2. Write an equation to denote the square of each of the following numbers: 1, 3, 5, 7, 9, 10, 15, 25.

3. Write an equation to denote the cube of the following numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

4. Find the value of x in each of the following equations:

5. In like manner show the square of 20, 30, 40, 50, 60,

70, 80, 90, 100.

6. Also, the cube of 10, 20, 30, 40, 50, 60, 70, 80.

7. In this manner, (1), write the square of 1, 1, 1,

1; of 4, 3, 4, 5o.