When Olivia was 40 years old, her daughter was 5 times her son's age. Olivia would be twice her daughter's age when her son was 22 years old. How old would Olivia be when her son was 6 years old?

	Olivia	Daughter	Son
Before	40	5 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Olivia's and her daughter's ages at first
40 - 5 u = 2 p - 1 p
40 - 5 u = 1 p --- (1)

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

Difference in her daughter's and her son's ages at first
5 u - 1 u = 1 p - 22
4 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
40 - 5 u = 4 u + 22
4 u + 5 u = 40 - 22
9 u = 18

1 u = 18 ÷ 9 = 2

Age difference between Olivia and her son
= 40 - 1 u
= 40 - 2
= 38

Olivia's age when her son was 6 years old
= 38 + 6
= 44

Answer(s): 44