When Hazel was 41 years old, her son was 2 times her daughter's age. Hazel would be twice her son's age when her daughter was 29 years old. How old would Hazel be when her daughter was 6 years old?

	Hazel	Son	Daughter
Before	41	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	29

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

Difference in Hazel's and her son's ages at first
41 - 2 u = 2 p - 1 p
41 - 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 - 29
1 u + 29 = 1 p --- (2)

Make p the same.

(1) = (2)
41 - 2 u = 1 u + 29
1 u + 2 u = 41 - 29
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Hazel and her daughter
= 41 - 1 u
= 41 - 4
= 37

Hazel's age when her daughter was 6 years old
= 37 + 6
= 43

Answer(s): 43