When Barbara was 49 years old, her son was 3 times her daughter's age. Barbara would be twice her son's age when her daughter was 29 years old. How old would Barbara be when her daughter was 3 years old?

	Barbara	Son	Daughter
Before	49	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	29

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

Difference in Barbara's and her son's ages at first
49 - 3 u = 2 p - 1 p
49 - 3 u = 1 p --- (1)

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

Difference in her son's and her daughter's ages at first
3 u - 1 u = 1 p - 29
2 u + 29 = 1 p --- (2)

Make p the same.

(1) = (2)
49 - 3 u = 2 u + 29
2 u + 3 u = 49 - 29
5 u = 20

1 u = 20 ÷ 5 = 4

Age difference between Barbara and her daughter
= 49 - 1 u
= 49 - 4
= 45

Barbara's age when her daughter was 3 years old
= 45 + 3
= 48

Answer(s): 48