When Hazel was 46 years old, her daughter was 2 times her son's age. Hazel would be twice her daughter's age when her son was 31 years old. How old would Hazel be when her son was 13 years old?

	Hazel	Daughter	Son
Before	46	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	31

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

Difference in Hazel's and her daughter's ages at first
46 - 2 u = 2 p - 1 p
46 - 2 u = 1 p --- (1)

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

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

Make p the same.

(1) = (2)
46 - 2 u = 1 u + 31
1 u + 2 u = 46 - 31
3 u = 15

1 u = 15 ÷ 3 = 5

Age difference between Hazel and her son
= 46 - 1 u
= 46 - 5
= 41

Hazel's age when her son was 13 years old
= 41 + 13
= 54

Answer(s): 54