When Gwen was 41 years old, her son was 5 times her daughter's age. Gwen would be twice her son's age when her daughter was 23 years old. How old would Gwen be when her daughter was 6 years old?

	Gwen	Son	Daughter
Before	41	5 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	23

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

Difference in Gwen's and her son's ages at first
41 - 5 u = 2 p - 1 p
41 - 5 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
5 u - 1 u = 1 p - 23
4 u + 23 = 1 p --- (2)

Make p the same.

(1) = (2)
41 - 5 u = 4 u + 23
4 u + 5 u = 41 - 23
9 u = 18

1 u = 18 ÷ 9 = 2

Age difference between Gwen and her daughter
= 41 - 1 u
= 41 - 2
= 39

Gwen's age when her daughter was 6 years old
= 39 + 6
= 45

Answer(s): 45