When Fanny was 48 years old, her son was 2 times her daughter's age. Fanny would be twice her son's age when her daughter was 39 years old. How old would Fanny be when her daughter was 8 years old?

	Fanny	Son	Daughter
Before	48	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	39

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

Difference in Fanny'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 - 39
1 u + 39 = 1 p --- (2)

Make p the same.

(1) = (2)
48 - 2 u = 1 u + 39
1 u + 2 u = 48 - 39
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Fanny and her daughter
= 48 - 1 u
= 48 - 3
= 45

Fanny's age when her daughter was 8 years old
= 45 + 8
= 53

Answer(s): 53