When Erika was 41 years old, her daughter was 2 times her son's age. Erika would be twice her daughter's age when her son was 32 years old. How old would Erika be when her son was 22 years old?

	Erika	Daughter	Son
Before	41	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	32

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

Difference in Erika's and her daughter's ages at first
41 - 2 u = 2 p - 1 p
41 - 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 - 32
1 u + 32 = 1 p --- (2)

Make p the same.

(1) = (2)
41 - 2 u = 1 u + 32
1 u + 2 u = 41 - 32
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Erika and her son
= 41 - 1 u
= 41 - 3
= 38

Erika's age when her son was 22 years old
= 38 + 22
= 60

Answer(s): 60