Question

A man is four times as old as his son. In 3 years, the father will be three times as old as the son. How old is each now?

Answer 1

The man is 27 years old and the son is 9 years old.

We can write the son's age as 'x', and therefore write the man's age as 4x. In 3 years, both their ages will increase by 3, so the son's age is now x + 3, and the man's age is 4x + 3.

We are told that the man is now 3 times older than his son, which means his current age, 4x + 3, is the same as 3 times the son's current age, which is x + 3.

Therefore we can write an equation:

4x + 3 = 3(x + 3)

4x + 3 = 3x + 9

- 3x

x + 3 = 9

- 3

x = 6

We can now substitute this in to find their current ages:

Son's age = x + 3 = 6 + 3 = 9

Man's age = 4x + 3 = 24 + 3 = 27

I hope this helps! Let me know if you have any questions :)