When Cathy was 41 years old, her daughter was 2 times her son's age. Cathy would be twice her daughter's age when her son was 20 years old. How old would Cathy be when her son was 9 years old?

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

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

Difference in Cathy'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 Cathy and her son
= 41 - 1 u
= 41 - 7
= 34

Cathy's age when her son was 9 years old
= 34 + 9
= 43

Answer(s): 43