When Kathy was 45 years old, her son was 2 times her daughter's age. Kathy would be twice her son's age when her daughter was 21 years old. How old would Kathy be when her daughter was 17 years old?

	Kathy	Son	Daughter
Before	45	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	21

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

Difference in Kathy's and her son's ages at first
45 - 2 u = 2 p - 1 p
45 - 2 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
2 u - 1 u = 1 p - 21
1 u + 21 = 1 p --- (2)

Make p the same.

(1) = (2)
45 - 2 u = 1 u + 21
1 u + 2 u = 45 - 21
3 u = 24

1 u = 24 ÷ 3 = 8

Age difference between Kathy and her daughter
= 45 - 1 u
= 45 - 8
= 37

Kathy's age when her daughter was 17 years old
= 37 + 17
= 54

Answer(s): 54