When Xuan was 46 years old, her daughter was 4 times her son's age. Xuan would be twice her daughter's age when her son was 25 years old. How old would Xuan be when her son was 9 years old?

	Xuan	Daughter	Son
Before	46	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	25

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

Difference in Xuan's and her daughter's ages at first
46 - 4 u = 2 p - 1 p
46 - 4 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
4 u - 1 u = 1 p - 25
3 u + 25 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 4 u = 3 u + 25
3 u + 4 u = 46 - 25
7 u = 21

1 u = 21 ÷ 7 = 3

Age difference between Xuan and her son
= 46 - 1 u
= 46 - 3
= 43

Xuan's age when her son was 9 years old
= 43 + 9
= 52

Answer(s): 52