When Hilda was 42 years old, her son was 2 times her daughter's age. Hilda would be twice her son's age when her daughter was 33 years old. How old would Hilda be when her daughter was 19 years old?

	Hilda	Son	Daughter
Before	42	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	33

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

Difference in Hilda'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 - 33
1 u + 33 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 2 u = 1 u + 33
1 u + 2 u = 42 - 33
3 u = 9

1 u = 9 ÷ 3 = 3

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

Hilda's age when her daughter was 19 years old
= 39 + 19
= 58

Answer(s): 58