When Tiffany was 36 years old, her daughter was 4 times her son's age. Tiffany would be twice her daughter's age when her son was 22 years old. How old would Tiffany be when her son was 13 years old?

	Tiffany	Daughter	Son
Before	36	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Tiffany's and her daughter's ages at first
36 - 4 u = 2 p - 1 p
36 - 4 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
4 u - 1 u = 1 p - 22
3 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
36 - 4 u = 3 u + 22
3 u + 4 u = 36 - 22
7 u = 14

1 u = 14 ÷ 7 = 2

Age difference between Tiffany and her son
= 36 - 1 u
= 36 - 2
= 34

Tiffany's age when her son was 13 years old
= 34 + 13
= 47

Answer(s): 47