When Mary was 42 years old, her daughter was 2 times her son's age. Mary would be twice her daughter's age when her son was 33 years old. How old would Mary be when her son was 20 years old?

	Mary	Daughter	Son
Before	42	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	33

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

Difference in Mary'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 - 33
1 u + 33 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 2 u = 1 u + 33
1 u + 2 u = 42 - 33
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Mary and her son
= 42 - 1 u
= 42 - 3
= 39

Mary's age when her son was 20 years old
= 39 + 20
= 59

Answer(s): 59