When Vanessa was 47 years old, her daughter was 5 times her son's age. Vanessa would be twice her daughter's age when her son was 20 years old. How old would Vanessa be when her son was 2 years old?

	Vanessa	Daughter	Son
Before	47	5 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	20

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

Difference in Vanessa's and her daughter's ages at first
47 - 5 u = 2 p - 1 p
47 - 5 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
5 u - 1 u = 1 p - 20
4 u + 20 = 1 p --- (2)

Make p the same.

(1) = (2)
47 - 5 u = 4 u + 20
4 u + 5 u = 47 - 20
9 u = 27

1 u = 27 ÷ 9 = 3

Age difference between Vanessa and her son
= 47 - 1 u
= 47 - 3
= 44

Vanessa's age when her son was 2 years old
= 44 + 2
= 46

Answer(s): 46