When Olivia was 46 years old, her son was 4 times her daughter's age. Olivia would be twice her son's age when her daughter was 25 years old. How old would Olivia be when her daughter was 13 years old?

	Olivia	Son	Daughter
Before	46	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	25

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

Difference in Olivia's and her son's ages at first
46 - 4 u = 2 p - 1 p
46 - 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 - 25
3 u + 25 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 4 u = 3 u + 25
3 u + 4 u = 46 - 25
7 u = 21

1 u = 21 ÷ 7 = 3

Age difference between Olivia and her daughter
= 46 - 1 u
= 46 - 3
= 43

Olivia's age when her daughter was 13 years old
= 43 + 13
= 56

Answer(s): 56