When Olivia was 42 years old, her son was 4 times her daughter's age. Olivia would be twice her son's age when her daughter was 21 years old. How old would Olivia be when her daughter was 3 years old?

	Olivia	Son	Daughter
Before	42	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	21

The difference in the ages between Olivia and her son remains unchanged.

Difference in Olivia's and her son's ages at first
42 - 4 u = 2 p - 1 p
42 - 4 u = 1 p --- (1)

The difference in the ages between her son and her daughter remains unchanged.

Difference in her son's and her daughter's ages at first
4 u - 1 u = 1 p - 21
3 u + 21 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 4 u = 3 u + 21
3 u + 4 u = 42 - 21
7 u = 21

1 u = 21 ÷ 7 = 3

Age difference between Olivia and her daughter
= 42 - 1 u
= 42 - 3
= 39

Olivia's age when her daughter was 3 years old
= 39 + 3
= 42

Answer(s): 42