When Esther was 45 years old, her son was 4 times her daughter's age. Esther would be twice her son's age when her daughter was 24 years old. How old would Esther be when her daughter was 4 years old?

	Esther	Son	Daughter
Before	45	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	24

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

Difference in Esther's and her son's ages at first
45 - 4 u = 2 p - 1 p
45 - 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 - 24
3 u + 24 = 1 p --- (2)

Make p the same.

(1) = (2)
45 - 4 u = 3 u + 24
3 u + 4 u = 45 - 24
7 u = 21

1 u = 21 ÷ 7 = 3

Age difference between Esther and her daughter
= 45 - 1 u
= 45 - 3
= 42

Esther's age when her daughter was 4 years old
= 42 + 4
= 46

Answer(s): 46