When Risa was 46 years old, her daughter was 2 times her son's age. Risa would be twice her daughter's age when her son was 22 years old. How old would Risa be when her son was 2 years old?

	Risa	Daughter	Son
Before	46	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Risa's and her daughter's ages at first
46 - 2 u = 2 p - 1 p
46 - 2 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
2 u - 1 u = 1 p - 22
1 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 2 u = 1 u + 22
1 u + 2 u = 46 - 22
3 u = 24

1 u = 24 ÷ 3 = 8

Age difference between Risa and her son
= 46 - 1 u
= 46 - 8
= 38

Risa's age when her son was 2 years old
= 38 + 2
= 40

Answer(s): 40