When Sabrina was 45 years old, her son was 2 times her daughter's age. Sabrina would be twice her son's age when her daughter was 39 years old. How old would Sabrina be when her daughter was 11 years old?

	Sabrina	Son	Daughter
Before	45	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	39

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

Difference in Sabrina's and her son's ages at first
45 - 2 u = 2 p - 1 p
45 - 2 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
2 u - 1 u = 1 p - 39
1 u + 39 = 1 p --- (2)

Make p the same.

(1) = (2)
45 - 2 u = 1 u + 39
1 u + 2 u = 45 - 39
3 u = 6

1 u = 6 ÷ 3 = 2

Age difference between Sabrina and her daughter
= 45 - 1 u
= 45 - 2
= 43

Sabrina's age when her daughter was 11 years old
= 43 + 11
= 54

Answer(s): 54