When Dana was 32 years old, her daughter was 2 times her son's age. Dana would be twice her daughter's age when her son was 20 years old. How old would Dana be when her son was 10 years old?

	Dana	Daughter	Son
Before	32	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	20

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

Difference in Dana's and her daughter's ages at first
32 - 2 u = 2 p - 1 p
32 - 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 - 20
1 u + 20 = 1 p --- (2)

Make p the same.

(1) = (2)
32 - 2 u = 1 u + 20
1 u + 2 u = 32 - 20
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Dana and her son
= 32 - 1 u
= 32 - 4
= 28

Dana's age when her son was 10 years old
= 28 + 10
= 38

Answer(s): 38