When Barbara was 42 years old, her daughter was 2 times her son's age. Barbara would be twice her daughter's age when her son was 27 years old. How old would Barbara be when her son was 8 years old?

	Barbara	Daughter	Son
Before	42	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

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

Difference in Barbara'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 - 27
1 u + 27 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 2 u = 1 u + 27
1 u + 2 u = 42 - 27
3 u = 15

1 u = 15 ÷ 3 = 5

Age difference between Barbara and her son
= 42 - 1 u
= 42 - 5
= 37

Barbara's age when her son was 8 years old
= 37 + 8
= 45

Answer(s): 45