When Nora was 31 years old, her son was 3 times her daughter's age. Nora would be twice her son's age when her daughter was 21 years old. How old would Nora be when her daughter was 2 years old?

	Nora	Son	Daughter
Before	31	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	21

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

Difference in Nora's and her son's ages at first
31 - 3 u = 2 p - 1 p
31 - 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 - 21
2 u + 21 = 1 p --- (2)

Make p the same.

(1) = (2)
31 - 3 u = 2 u + 21
2 u + 3 u = 31 - 21
5 u = 10

1 u = 10 ÷ 5 = 2

Age difference between Nora and her daughter
= 31 - 1 u
= 31 - 2
= 29

Nora's age when her daughter was 2 years old
= 29 + 2
= 31

Answer(s): 31