a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.

Declare variables:

• Let f be the father's age
• Let s be the son's age

We're given two equations:

1. s = f/4
2. f - s = 30. The reason why we subtract s from f is the father is older

Using substitution, we substitute equaiton (1) into equation (2) for s:
f - f/4 = 30

To remove the denominator/fraction, we multiply both sides of the equation by 4:
4f - 4f/4 = 30 *4
4f - f = 120
3f = 120

To solve for f, we divide each side of the equation by 3:
3f/3 = 120/3

Cancel the 3's on the left side and we get:
f = 40