ALGEBRAIC SOLUTIONS If 1. PROBLEM 1. A man had 400 acres of corn and oats. there were 3 times as many acres of corn as of oats, how many acres were there of each? Then, and therefore, Hence, and Let and Then, therefore, and Hence, ARITHMETICAL SOLUTION A certain number the number of acres of oats. 3 times that number = the number of acres of corn, 4 times that number 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. ALGEBRAIC SOLUTION x= the number of acres of oats. 3x: the number of acres of corn, = 4x the number of acres of both; x = 100, the number of acres of oats, 2. An expression of equality between two numbers or quantities is called 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? |