When Sabrina was 46 years old, her daughter was 2 times her son's age. Sabrina would be twice her daughter's age when her son was 22 years old. How old would Sabrina be when her son was 16 years old?

	Sabrina	Daughter	Son
Before	46	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Sabrina's and her daughter's ages at first
46 - 2 u = 2 p - 1 p
46 - 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 - 22
1 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 2 u = 1 u + 22
1 u + 2 u = 46 - 22
3 u = 24

1 u = 24 ÷ 3 = 8

Age difference between Sabrina and her son
= 46 - 1 u
= 46 - 8
= 38

Sabrina's age when her son was 16 years old
= 38 + 16
= 54

Answer(s): 54