When Vanessa was 43 years old, her daughter was 4 times her son's age. Vanessa would be twice her daughter's age when her son was 29 years old. How old would Vanessa be when her son was 10 years old?

	Vanessa	Daughter	Son
Before	43	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	29

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

Difference in Vanessa's and her daughter's ages at first
43 - 4 u = 2 p - 1 p
43 - 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 - 29
3 u + 29 = 1 p --- (2)

Make p the same.

(1) = (2)
43 - 4 u = 3 u + 29
3 u + 4 u = 43 - 29
7 u = 14

1 u = 14 ÷ 7 = 2

Age difference between Vanessa and her son
= 43 - 1 u
= 43 - 2
= 41

Vanessa's age when her son was 10 years old
= 41 + 10
= 51

Answer(s): 51