When Gabby was 42 years old, her daughter was 2 times her son's age. Gabby would be twice her daughter's age when her son was 33 years old. How old would Gabby be when her son was 17 years old?

	Gabby	Daughter	Son
Before	42	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	33

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

Difference in Gabby's and her daughter's ages at first
42 - 2 u = 2 p - 1 p
42 - 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 - 33
1 u + 33 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 2 u = 1 u + 33
1 u + 2 u = 42 - 33
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Gabby and her son
= 42 - 1 u
= 42 - 3
= 39

Gabby's age when her son was 17 years old
= 39 + 17
= 56

Answer(s): 56