When Jean was 41 years old, her daughter was 2 times her son's age. Jean would be twice her daughter's age when her son was 20 years old. How old would Jean be when her son was 17 years old?

	Jean	Daughter	Son
Before	41	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	20

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

Difference in Jean's and her daughter's ages at first
41 - 2 u = 2 p - 1 p
41 - 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)
41 - 2 u = 1 u + 20
1 u + 2 u = 41 - 20
3 u = 21

1 u = 21 ÷ 3 = 7

Age difference between Jean and her son
= 41 - 1 u
= 41 - 7
= 34

Jean's age when her son was 17 years old
= 34 + 17
= 51

Answer(s): 51