When Cathy was 40 years old, her son was 4 times her daughter's age. Cathy would be twice her son's age when her daughter was 26 years old. How old would Cathy be when her daughter was 9 years old?

	Cathy	Son	Daughter
Before	40	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	26

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

Difference in Cathy's and her son's ages at first
40 - 4 u = 2 p - 1 p
40 - 4 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
4 u - 1 u = 1 p - 26
3 u + 26 = 1 p --- (2)

Make p the same.

(1) = (2)
40 - 4 u = 3 u + 26
3 u + 4 u = 40 - 26
7 u = 14

1 u = 14 ÷ 7 = 2

Age difference between Cathy and her daughter
= 40 - 1 u
= 40 - 2
= 38

Cathy's age when her daughter was 9 years old
= 38 + 9
= 47

Answer(s): 47