When Erika was 42 years old, her son was 4 times her daughter's age. Erika would be twice her son's age when her daughter was 21 years old. How old would Erika be when her daughter was 12 years old?

	Erika	Son	Daughter
Before	42	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	21

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

Difference in Erika's and her son's ages at first
42 - 4 u = 2 p - 1 p
42 - 4 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
4 u - 1 u = 1 p - 21
3 u + 21 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 4 u = 3 u + 21
3 u + 4 u = 42 - 21
7 u = 21

1 u = 21 ÷ 7 = 3

Age difference between Erika and her daughter
= 42 - 1 u
= 42 - 3
= 39

Erika's age when her daughter was 12 years old
= 39 + 12
= 51

Answer(s): 51