When Mary was 37 years old, her son was 3 times her daughter's age. Mary would be twice her son's age when her daughter was 27 years old. How old would Mary be when her daughter was 23 years old?

	Mary	Son	Daughter
Before	37	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

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

Difference in Mary's and her son's ages at first
37 - 3 u = 2 p - 1 p
37 - 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 - 27
2 u + 27 = 1 p --- (2)

Make p the same.

(1) = (2)
37 - 3 u = 2 u + 27
2 u + 3 u = 37 - 27
5 u = 10

1 u = 10 ÷ 5 = 2

Age difference between Mary and her daughter
= 37 - 1 u
= 37 - 2
= 35

Mary's age when her daughter was 23 years old
= 35 + 23
= 58

Answer(s): 58