When Winnie was 37 years old, her son was 3 times her daughter's age. Winnie would be twice her son's age when her daughter was 22 years old. How old would Winnie be when her daughter was 22 years old?

	Winnie	Son	Daughter
Before	37	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Winnie's and her son's ages at first
37 - 3 u = 2 p - 1 p
37 - 3 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
3 u - 1 u = 1 p - 22
2 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
37 - 3 u = 2 u + 22
2 u + 3 u = 37 - 22
5 u = 15

1 u = 15 ÷ 5 = 3

Age difference between Winnie and her daughter
= 37 - 1 u
= 37 - 3
= 34

Winnie's age when her daughter was 22 years old
= 34 + 22
= 56

Answer(s): 56