ACADEMIC ALGEBRA

ALGEBRAIC SOLUTION

1. PROBLEM 1. A man had 400 acres of corn and oats. If there were 3 times as many acres of corn as of oats, how many acres were there of each?

ARITHMETICAL SOLUTION

= the number of acres of oats.

=

Then, and therefore,

A certain number
3 times that number
4 times that number =

Hence,

and

Let

Then,

and

therefore,

Hence,

and

the number of acres of corn,

the number of acres of both;

4 times that number = 400.

the number = 100, the number of acres of oats,

3 times the number = 300, the number of acres of corn.

=

4x the number of acres of both;
4 x = 400.

x = 100, the number of acres of oats,
3x300, the number of acres of corn.

2. An expression of equality between two numbers or quantities is called an Equation.

5x30 is an equation.

3. A question that can be answered only after a course of reasoning is called a Problem.

4. The process of finding the result sought is called the Solution of the problem.

5. The expression in algebraic language of the conditions of a problem is called the Statement of the problem.

Solve algebraically the following problems:

2. A horse and saddle cost $50. If the horse cost 4 times as much as the saddle, what was the cost of each?

3. A bicycle and suit cost $90. How much did each cost, if the bicycle cost 5 times as much as the suit?

4. Of 240 stamps that Harry and his sister collected, Harry collected 3 times as many as his sister. How many did each collect?

5. If Mr. Brown and his son together had $220, and Mr. Brown had 10 times as much as his son, how much money had each?

6. In a room containing 45 students there were twice as many girls as boys. How many were there of each ?

7. A had 7 times as many sheep as B, and both together had 608. How many sheep had each?

8. A and B began business with a capital of $7500. If A furnished half as much capital as B, how much did each furnish? SUGGESTION. - Let x the number of dollars A furnished.

9. A man bought a cow and a calf for $36, paying 8 times as much for the cow as for the calf. What was the cost of each?

10. James sold his pony and a saddle for $60. If the saddle sold for as much as the pony, what was the selling price of each?

11. A certain number added to twice itself equals 96. What is the number?

12. A farmer raised a certain number of bushels of wheat, 4 times as much corn, and 3 times as much barley. If there were in all 4000 bushels of grain, how many bushels of each kind did he raise?

13. A boy bought a bat, a ball, and a glove for $2.25. If the bat cost twice as much as the ball, and the glove cost 3 times as much as the bat, what was the cost of each?