When Gem was 48 years old, her son was 3 times her daughter's age. Gem would be twice her son's age when her daughter was 38 years old. How old would Gem be when her daughter was 2 years old?

	Gem	Son	Daughter
Before	48	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	38

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

Difference in Gem's and her son's ages at first
48 - 3 u = 2 p - 1 p
48 - 3 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
3 u - 1 u = 1 p - 38
2 u + 38 = 1 p --- (2)

Make p the same.

(1) = (2)
48 - 3 u = 2 u + 38
2 u + 3 u = 48 - 38
5 u = 10

1 u = 10 ÷ 5 = 2

Age difference between Gem and her daughter
= 48 - 1 u
= 48 - 2
= 46

Gem's age when her daughter was 2 years old
= 46 + 2
= 48

Answer(s): 48