When Fiona was 50 years old, her daughter was 5 times her son's age. Fiona would be twice her daughter's age when her son was 32 years old. How old would Fiona be when her son was 7 years old?

	Fiona	Daughter	Son
Before	50	5 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	32

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

Difference in Fiona's and her daughter's ages at first
50 - 5 u = 2 p - 1 p
50 - 5 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
5 u - 1 u = 1 p - 32
4 u + 32 = 1 p --- (2)

Make p the same.

(1) = (2)
50 - 5 u = 4 u + 32
4 u + 5 u = 50 - 32
9 u = 18

1 u = 18 ÷ 9 = 2

Age difference between Fiona and her son
= 50 - 1 u
= 50 - 2
= 48

Fiona's age when her son was 7 years old
= 48 + 7
= 55

Answer(s): 55