When Gwen was 46 years old, her son was 3 times her daughter's age. Gwen would be twice her son's age when her daughter was 31 years old. How old would Gwen be when her daughter was 20 years old?

	Gwen	Son	Daughter
Before	46	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	31

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

Difference in Gwen's and her son's ages at first
46 - 3 u = 2 p - 1 p
46 - 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 - 31
2 u + 31 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 3 u = 2 u + 31
2 u + 3 u = 46 - 31
5 u = 15

1 u = 15 ÷ 5 = 3

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

Gwen's age when her daughter was 20 years old
= 43 + 20
= 63

Answer(s): 63