When Anna was 41 years old, her son was 2 times her daughter's age. Anna would be twice her son's age when her daughter was 32 years old. How old would Anna be when her daughter was 12 years old?

	Anna	Son	Daughter
Before	41	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	32

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

Difference in Anna's and her son's ages at first
41 - 2 u = 2 p - 1 p
41 - 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 - 32
1 u + 32 = 1 p --- (2)

Make p the same.

(1) = (2)
41 - 2 u = 1 u + 32
1 u + 2 u = 41 - 32
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Anna and her daughter
= 41 - 1 u
= 41 - 3
= 38

Anna's age when her daughter was 12 years old
= 38 + 12
= 50

Answer(s): 50