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

##### Administrator

**Staff member**

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:

- s = f/4
- 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**