When Zoe was 48 years old, her son was 2 times her daughter's age. Zoe would be twice her son's age when her daughter was 36 years old. How old would Zoe be when her daughter was 9 years old?

	Zoe	Son	Daughter
Before	48	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	36

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

Difference in Zoe's and her son's ages at first
48 - 2 u = 2 p - 1 p
48 - 2 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
2 u - 1 u = 1 p - 36
1 u + 36 = 1 p --- (2)

Make p the same.

(1) = (2)
48 - 2 u = 1 u + 36
1 u + 2 u = 48 - 36
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Zoe and her daughter
= 48 - 1 u
= 48 - 4
= 44

Zoe's age when her daughter was 9 years old
= 44 + 9
= 53

Answer(s): 53