for 30 years?

9. What is the amount of $50, at 7 % compound interest, Ans. $380.61+. Here, find the amount for 20 years, and then the amount of that sum for 10 years, by aid of the table.

REVIEW EXERCISES.

1. If on settlement with a merchant I give my note for $5400 payable in 6 months, with 6 % interest, how much must be paid when the note becomes due? Ans. $5562. 2. A certain sum lent at 6 % produced $250, between July 5, 1865, and December 6, 1866; what was the sum?

Ans. $2935.42+. 3. My money at interest doubles itself, I find, in just 144 years; what is the rate per cent.? Ans. 7%.

4. On the 15th of July, 1866, I paid $65, the interest due on a note of $250, at 6%; from what date did the interest commence? Ans. March 15, 1862.

5. How much more is the bank than the true discount on $800, for 3 years, 4 months, and 18 days? Ans. $27.80+.

6. Having a gold watch to sell, one man offers $220 payable in two years, and another offers me $200 cash in hand; which is the better offer, and how much?

Ans. $200 cash in hand, by $3.58+.

7. I have received a note dated April 10, 1866, for $500, payable six months after date; required when it becomes due, the time to run if discounted Aug. 11, and the proceeds at 6 %. Ans. Due Oct. 1013; time to run, 63 days; proceeds, $494 75

8.* How much more is the compound than the total interest, payable annually, of $1300, at 6 %, for 4 years? Ans. $1.13+

REVIEW QUESTIONS. What is the Present Worth of any sum? (302) The Discount? (302) The Rule for finding the present worth? (303) What is a Promissory Note? (306) The Face of a Note? (306) Days of Grace? (306) Bank Discount? (307) Rule for finding bank discount?

(308)

RATIO AND PROPORTION.

320. Ratio is the measure of the relation of two like quantities.

It is determined by dividing the first quantity by the second. Thus,

The ratio of 6 to 3 is 2, or of $8 to $2 is 4.

321. The Terms of a ratio are the two quantities compared.

The ANTECEDENT is the first term of the ratio.

The CONSEQUENT is the second term of the ratio.

322. The relation of antecedent to consequent may be indicated by writing, or the sign of division, between two numbers. Thus,

6 3, or 63, indicate the ratio of 6 to 3.

The sign is an abbreviated form of, and has a like meaning.

:

Some few American authors determine ratio by dividing the consequent by the antecedent, after the old method of La Croix, which has become quite obsolete in the country where it originated.

323. A Simple Ratio is a single ratio of two terms. Thus,

8

: 2 expresses a simple ratio.

324. A Compound Ratio is the product of two er mere simple ratios. Thus,

(65) × (2 3), or X, expresses a compound ratio. 325. From the definition of ratio, follow the

PRINCIPLES.

1. Ratio can only exist between quantities of the same name and kind.

2. The ratio is equal to the quotient of the antecedent di vided by the consequent.

What is Ratio? Terms of a ratio? The Antecedent? The Consequert ? How may the relation of antecedent to consequent be indicated? What is a Simple Ratio? A Compound Ratio? Give the first Principle. The secord.

3. The antecedent is equal to the product of the consequent

and ratio.

4. The consequent is equal to the quotient of the antecedent divided by the ratio.

Also, since ratio may be expressed by a fraction:

5. The ratio is not changed, if both the antecedent and consequent are multiplied or divided by the same number.

Write the ratio of

Exercises.

1. 3 to 5. Ans. 3:5. | 4. 3X2 to 4 X 3. Ans. (3 × 2): (4×3).

13. Reduce the ratio 6: 30 to its smallest terms.

Ans. .

15. Reduce to a simple ratio × 2

14. Reduce to a simple ratio 8 X 3: 6 × 2.

16. Find the ratio of 6 h. 20 m. to 2 h. 17. If the antecedent is 15.6 and the ratio 6, what is the consequent?

Ans. 2.6.

18. If the consequent is and the ratio, what is the antecedent?

Ans. 15.

Ans. 2.

Ans. 3

PROPORTION.

326. A Proportion is an equality of ratios. Thus,

8: 216 4 is a proportion.

The equality is generally indicated by writing :: between the ratios. Thus,

8 2 16 4 indicates a proportion,

Give the third Principle. The fourth. The fifth. What is Proportion? How is the equality generally indicated?

and may be read, the ratio of 8

2 is equal to the ratio of

16 to 4, or 8 is to 2 as 16 is to 4.

327. The Terms of a proportion are those of its ratios. The EXTREMES are the first and fourth terms.

The MEANS are the second and third terms.

A PROPORTIONAL is any one of the terms.

A MEAN PROPORTIONAL is a term repeated between the other two. Thus,

In 12 6 6 3, 6 is a mean proportional.

PRINCIPLES.

328. 1. In every proportion the product of the means is equal to the product of the extremes.

For, in the proportion 6: 3 :: 4 : 2, since the ratios are equal (Art. 326), we have § = . Now, these equal fractions reduced to equivalent fractions having a common denominator, give 8x2 dropping the common denominator, 6 × 2 = 4 × 3. Hence,

6×2

4X3

2× 89

and by

2. Either extreme is equal to the product of the means divided by the other extreme.

3. Either mean is equal to the product of the extremes divided by the other mean.

4. The fourth term is equal to the quotient of the third term divided by the ratio of the first to the second.

Exercises.

Find the missing term in

Ans.

1. 27: 3 :: 54: (). Ans. 6. |5. f : :: 15 : ( ). Ans. 12. 2. 12 yd. 4 yd. :: $9 : ( ). 6. () Ans. $3. 7. $1.50

3. 20 rd. 25 rd. :: (): $10.

4. 51: ( ) :: 16: 32.

: 2 $7.50:: (): 3 bu. Ans. bu.

Ans. $8. 8. 2 gal. 2 qt.:() :: $4: $80.

Here, in example 8, the 2 gal. 2 qt. must be reduced to an equivalent single denomination before proceeding to find the missing term.

What are the terms of a proportion? The Extremes? The Means? A Proportional? A Mean Proportional? The Principles ?

SIMPLE PROPORTION.

329. In Simple Proportion the terms of two equal simple ratios are compared.

It applies to the solution of questions, in which three given quantities are so related that a fourth may be determined from them, by equality of ratios.

Of the three given quantities, two of them must be of the same name, and constitute a ratio, and the third must be of like name with the required quantity, so as to constitute with it a second ratio.

330. To solve questions by simple proportion.

1. If 8 yards of cloth cost $66, what will 32 yards cost?

Since the product of the means divided by either extreme must give the other extreme (Art. 328), the required extreme is equal to ($66 X32) 8, or $264.

Or, if 8 yards of cloth cost $66, 32 yards, which are 4 times 8 yards, must cost 4 times $66, or $264.

RULE.

Arrange the given terms so that, from the nature of the question, the ratios shall be equal.

Find, then, the required term by dividing the product of the second and third terms by the first; or, by dividing the third term by the ratio of the first term to the second.

All questions in proportion may also be solved by Analysis. It is recommended to the learner to solve the examples that follow by both methods.

What are compared in Simple Proportion? To what questions does Sim ole Proportion apply? Explain the operation. Repeat the Rule.