When Fiona was 42 years old, her son was 2 times her daughter's age. Fiona would be twice her son's age when her daughter was 30 years old. How old would Fiona be when her daughter was 12 years old?

	Fiona	Son	Daughter
Before	42	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	30

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

Difference in Fiona's and her son's ages at first
42 - 2 u = 2 p - 1 p
42 - 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 - 30
1 u + 30 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 2 u = 1 u + 30
1 u + 2 u = 42 - 30
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Fiona and her daughter
= 42 - 1 u
= 42 - 4
= 38

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

Answer(s): 50