11. Mr. James invested $27,390 in an 8% stock which he bought at 114, brokerage %. What was his yearly income from this stock?

12. Later he sold his stock at 118. What did he receive for it? How much did he gain by the transaction? What would have been his loss if he had sold it for 111?

13. How much greater was Mr. James' rate of income from this stock than the rate of income of the one to whom he sold it?

14. Which would you rather buy, 5 % stock at 75, or 7 % stock at 105? Why?

15. Find the proceeds of a 60-day note for $925, bearing interest at 6%, discounted 24 days after it was made.

16. Mr. Brown bought a farm for $3,400. He paid $1,300 cash. For the balance he gave a mortgage with interest at 5%. This mortgage was not paid until the end of 5 years. What was the entire amount, including interest, that he had to pay for the farm?

SUMMARY OF CHAPTER V

BANKING.

Banks.

Clearing Houses.

Savings Banks.

Trust Companies.
Loans.

Mortgages.

Bank Discount.

Exchange.

BUSINESS PRACTICE.

Stocks.

Bonds.

Insurance.

CHAPTER VI

HOW TO SOLVE A PROBLEM-ELEMENTS OF ALGEBRA

THE THREE METHODS

271. The ratio of 12 to 6 = the ratio of 8 to what number?

Read the problem carefully, to see

(1) What is given?

There is given a ratio, 12:6, which is 2, and one term, 8, the dividend of an equal ratio.

(2) What is to be found?

There must be found the second term, or the divisor, of the equal ratio.

(3) What is their relation?

The ratio is the quotient of one term divided by the other. 8, the first term, is the dividend. 2 is the ratio or quotient. The relation is that of dividend to quotient.

(4) What principle must you employ to find the unknown term from the known?

The principle is this:

Dividend quotient = divisor.

824 the divisor or second term of the incomplete

ratio.

That is, 12:68:4.

How can you prove the correctness of your answer? Divisor x quotient = dividend. 4 x 2 = 8.

Give other proofs.

Name the steps in the solution of a problem.

Select ten problems in your book and name these steps for each one.

Naming the steps in the solution of a problem is called stating the problem. It is important to state all problems before beginning to solve them.

Several methods of solving problems are used in arithmetic. One is analysis, sometimes called unitary analysis. Another makes use of ratio, and a third employs the equation. Frequently the equation includes one or both of the other methods.

272.

SOLVING BY ANALYSIS

1. If 2 apples cost 4 cents, what will 6 apples cost? 2 apples cost 4 cents.

2. What are three eggs worth at 24 cents a dozen?

If 12 eggs cost 24 cents, 1 egg will cost

2 cents. 3 eggs will cost 3 x 2 cents = 6 cents.

of 24 cents =

3. of Daisy's money is $15. How much money has

she?

of the money is $15.

of the money is of $15-$5.

of the money is 4 x $5 $20.

=

273.

SOLVING BY RATIO

1. If 2 apples cost 5 cents, what will 6 apples cost? The ratio of 6 apples to 2 apples is 3.

Therefore, 6 apples cost 3 x 5 cents 15 cents.

2. What are 3 eggs worth at 24 cents a dozen?

WRITTEN EXERCISES

274. Solve the following by any method:

1. If ğ of an acre of land was sold for $1,200, what is the value of 21 acres at that price?

2. If of Mr. Lanning's crop of wheat is worth $840, what is the value of the crop?

3. If 121 yards of silk cost $20, how much will 100 yards cost? How many yards can be bought for $80? For $95? For $105?

4. A jobber bought 100 books for $16. cost of 75 books at that rate?

5. A farmer had 1,000 bushels of potatoes. bushels for $810. What is the value of his rate?

What was the

He sold 750

crop at that

6. Mr. Rankin deposited $2,400 in the bank, which was of his money. How much had he?

7. A farmer sold 371⁄2 pounds of butter for $7.50. What are 100 pounds worth at that rate?

8. If 621% of a number is 15, what is the number?

9. of a number is 80. What is the number?

10. 87% of my bank account is $3,500.

of it?

What is 121%

11. 62% of Mr. Randolph's wheat is 2,500 bushels. He sold 37%. How many bushels did he sell?

12. If ğ of a barrel of apples are worth $2, what are of a barrel worth?

13. A real estate agent sold a house for $4,200 and made 40% on it. What did it cost?

14. He sold another for the same price and lost 40%. What did it cost?

15. What was the gain or loss on both sales?

SOLVING BY EQUATIONS—THE USE OF LETTERS

275. A still better method for the solution of different problems is by the use of the equation, using a letter or letters, as x, or y, to represent the quantity to be found.

Numbers are often represented by letters of the alphabet instead of by the ordinary numerals. Numbers represented by letters are called literal quantities.

Thus we may speak of a apples, b boys, î hats.

We can use the letters in calculation as if they were figures. They may represent any numbers that we choose and then may be added, subtracted, multiplied, or divided, as we please.

Suppose you say that a = 6, then 6 boys may be written a boys.

2 x 6 boys may be written 2 x a boys.

Suppose you decide that you will use b for 2. Then 2 × 6 boys may be written a × b boys, etc.

2 boys + 6 boys will be a boys +b boys.

In writing numbers by the use of letters, use the, same signs that you do with numerals. In representing multiplication, however, the sign may be omitted. ab = a × b; 2 × a; 2 bc 2 xbx c. All other signs must always be used to indicate the operations to be performed.

2 a

=

In the expression, 2 abc, 2 is called the coefficient of abc. When a literal quantity is represented as multiplied by an Arabic numeral, or figure, the figure is called the coefficient of the literal quantity.

276. Letting a = 2, b = 3, c = 4, and d = 5, find the values of: