When Sarah was 47 years old, her son was 3 times her daughter's age. Sarah would be twice her son's age when her daughter was 32 years old. How old would Sarah be when her daughter was 21 years old?

	Sarah	Son	Daughter
Before	47	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	32

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

Difference in Sarah's and her son's ages at first
47 - 3 u = 2 p - 1 p
47 - 3 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
3 u - 1 u = 1 p - 32
2 u + 32 = 1 p --- (2)

Make p the same.

(1) = (2)
47 - 3 u = 2 u + 32
2 u + 3 u = 47 - 32
5 u = 15

1 u = 15 ÷ 5 = 3

Age difference between Sarah and her daughter
= 47 - 1 u
= 47 - 3
= 44

Sarah's age when her daughter was 21 years old
= 44 + 21
= 65

Answer(s): 65