When Tammy was 33 years old, her son was 2 times her daughter's age. Tammy would be twice her son's age when her daughter was 24 years old. How old would Tammy be when her daughter was 22 years old?

	Tammy	Son	Daughter
Before	33	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	24

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

Difference in Tammy's and her son's ages at first
33 - 2 u = 2 p - 1 p
33 - 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 - 24
1 u + 24 = 1 p --- (2)

Make p the same.

(1) = (2)
33 - 2 u = 1 u + 24
1 u + 2 u = 33 - 24
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Tammy and her daughter
= 33 - 1 u
= 33 - 3
= 30

Tammy's age when her daughter was 22 years old
= 30 + 22
= 52

Answer(s): 52