When Victoria was 42 years old, her son was 4 times her daughter's age. Victoria would be twice her son's age when her daughter was 21 years old. How old would Victoria be when her daughter was 20 years old?

	Victoria	Son	Daughter
Before	42	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	21

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

Difference in Victoria's and her son's ages at first
42 - 4 u = 2 p - 1 p
42 - 4 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
4 u - 1 u = 1 p - 21
3 u + 21 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 4 u = 3 u + 21
3 u + 4 u = 42 - 21
7 u = 21

1 u = 21 ÷ 7 = 3

Age difference between Victoria and her daughter
= 42 - 1 u
= 42 - 3
= 39

Victoria's age when her daughter was 20 years old
= 39 + 20
= 59

Answer(s): 59