When Xuan was 40 years old, her son was 5 times her daughter's age. Xuan would be twice her son's age when her daughter was 22 years old. How old would Xuan be when her daughter was 13 years old?

	Xuan	Son	Daughter
Before	40	5 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Xuan's and her son's ages at first
40 - 5 u = 2 p - 1 p
40 - 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 - 22
4 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
40 - 5 u = 4 u + 22
4 u + 5 u = 40 - 22
9 u = 18

1 u = 18 ÷ 9 = 2

Age difference between Xuan and her daughter
= 40 - 1 u
= 40 - 2
= 38

Xuan's age when her daughter was 13 years old
= 38 + 13
= 51

Answer(s): 51