When Barbara was 37 years old, her daughter was 4 times her son's age. Barbara would be twice her daughter's age when her son was 23 years old. How old would Barbara be when her son was 22 years old?

	Barbara	Daughter	Son
Before	37	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	23

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

Difference in Barbara's and her daughter's ages at first
37 - 4 u = 2 p - 1 p
37 - 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 - 23
3 u + 23 = 1 p --- (2)

Make p the same.

(1) = (2)
37 - 4 u = 3 u + 23
3 u + 4 u = 37 - 23
7 u = 14

1 u = 14 ÷ 7 = 2

Age difference between Barbara and her son
= 37 - 1 u
= 37 - 2
= 35

Barbara's age when her son was 22 years old
= 35 + 22
= 57

Answer(s): 57