II.

7. Divide $35$ into two parts so that one part shall be greater by $5$ than the other part.

8. Three times a given number is equal to the number increased by $40$. Find the number.

9. Three times a given number diminished by $24$ is equal to the given number. Find the number.

10. One number is $4$ times another, and their difference is $30$. Find the numbers.

11. The sum of two numbers is $36$, and one of them exceeds twice the other by $6$. Find the numbers.

Let $x$ equal the greater number: then $36-x$ will equal the smaller.

12. The sum of two numbers is $40$, and $5$ times the smaller exceeds $2$ times the greater by $25$. Find the numbers.

13. The number $30$ is divided into two parts such that $4$ times the greater part exceeds $5$ times the smaller part by $30$. Find the parts.

14. The sum of two numbers is $27$, and twice the greater number increased by $3$ times the less is $61$. Find the numbers.

15. The sum of two numbers is $32$, and five times the smaller is $3$ times the greater number. Find the numbers.

Exercise 11.

1. A farmer sold a horse and a cow for $$210$. He sold the horse for four times as much as the cow. How much did he get for each?

2. Three times the excess of a certain number over $6$ is equal to the number plus $144$. Find the number.

3. Thirty-one times a certain number is as much above $40$ as nine times the number is below $40$. Find the number.

4. Two numbers differ by $10$, and their sum is equal to seven times their difference. Find the numbers.

5. Find three consecutive numbers, $x$, $x+1$, and $x+2$, whose sum is $78$.

6. Find five consecutive numbers whose sum is $35$.

7. The sum of the ages of A and B is $40$ years, and $10$ years hence A will be twice as old as B. Find their present ages.

8. A father is four times as old as his son, and in $5$ years he will be only three times as old. Find their present ages.

9. One man is $60$ years old, and another man is $50$ years. How many years ago was the first man twice as old as the second?