Question

A father's age now is three times the age that his son was four years ago. In 12 years, the father will be twice as old as his son. Find their ages.

Answer 1

Now, the father is 60, and the son is 24.

Explanation:

Now:

Father's age = f

Son's age = s

4 years ago:

Father's age = f - 4

Son's age = s - 4

In 12 years:

Father's age = f + 12

Son's age = s + 12

Now:

f = 3(s - 4)

In 12 years:

f + 12 = 2(s + 12)

We have 2 equations that we can solve in a system of equations.

f = 3(s - 4)

f + 12 = 2(s + 12)

f = 3s - 12

f + 12 = 2s + 24

f = 3s - 12

f = 2s + 12

Since above both equations are in terms of f, set the right sides equal and solve for s.

3s - 12 = 2s + 12

s = 24

f = 3(s - 4)

f = 3(24 - 4)

f = 3(20)

f = 60

Now, the father is 60, and the son is 24.