When Xylia was 50 years old, her daughter was 2 times her son's age. Xylia would be twice her daughter's age when her son was 32 years old. How old would Xylia be when her son was 24 years old?

	Xylia	Daughter	Son
Before	50	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	32

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

Difference in Xylia's and her daughter's ages at first
50 - 2 u = 2 p - 1 p
50 - 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 - 32
1 u + 32 = 1 p --- (2)

Make p the same.

(1) = (2)
50 - 2 u = 1 u + 32
1 u + 2 u = 50 - 32
3 u = 18

1 u = 18 ÷ 3 = 6

Age difference between Xylia and her son
= 50 - 1 u
= 50 - 6
= 44

Xylia's age when her son was 24 years old
= 44 + 24
= 68

Answer(s): 68