When Gabby was 32 years old, her daughter was 2 times her son's age. Gabby would be twice her daughter's age when her son was 20 years old. How old would Gabby be when her son was 3 years old?

	Gabby	Daughter	Son
Before	32	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	20

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

Difference in Gabby's and her daughter's ages at first
32 - 2 u = 2 p - 1 p
32 - 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)
32 - 2 u = 1 u + 20
1 u + 2 u = 32 - 20
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Gabby and her son
= 32 - 1 u
= 32 - 4
= 28

Gabby's age when her son was 3 years old
= 28 + 3
= 31

Answer(s): 31