When Kimberly was 46 years old, her daughter was 2 times her son's age. Kimberly would be twice her daughter's age when her son was 22 years old. How old would Kimberly be when her son was 13 years old?

	Kimberly	Daughter	Son
Before	46	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Kimberly's and her daughter's ages at first
46 - 2 u = 2 p - 1 p
46 - 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 - 22
1 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 2 u = 1 u + 22
1 u + 2 u = 46 - 22
3 u = 24

1 u = 24 ÷ 3 = 8

Age difference between Kimberly and her son
= 46 - 1 u
= 46 - 8
= 38

Kimberly's age when her son was 13 years old
= 38 + 13
= 51

Answer(s): 51