When Xandra was 37 years old, her daughter was 2 times her son's age. Xandra would be twice her daughter's age when her son was 22 years old. How old would Xandra be when her son was 9 years old?

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

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

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

Make p the same.

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

1 u = 15 ÷ 3 = 5

Age difference between Xandra and her son
= 37 - 1 u
= 37 - 5
= 32

Xandra's age when her son was 9 years old
= 32 + 9
= 41

Answer(s): 41