When Abi was 40 years old, her son was 2 times her daughter's age. Abi would be twice her son's age when her daughter was 22 years old. How old would Abi be when her daughter was 22 years old?

	Abi	Son	Daughter
Before	40	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Abi's and her son's ages at first
40 - 2 u = 2 p - 1 p
40 - 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 - 22
1 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
40 - 2 u = 1 u + 22
1 u + 2 u = 40 - 22
3 u = 18

1 u = 18 ÷ 3 = 6

Age difference between Abi and her daughter
= 40 - 1 u
= 40 - 6
= 34

Abi's age when her daughter was 22 years old
= 34 + 22
= 56

Answer(s): 56