When Natalie was 50 years old, her son was 3 times her daughter's age. Natalie would be twice her son's age when her daughter was 20 years old. How old would Natalie be when her daughter was 12 years old?

	Natalie	Son	Daughter
Before	50	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	20

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

Difference in Natalie's and her son's ages at first
50 - 3 u = 2 p - 1 p
50 - 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 - 20
2 u + 20 = 1 p --- (2)

Make p the same.

(1) = (2)
50 - 3 u = 2 u + 20
2 u + 3 u = 50 - 20
5 u = 30

1 u = 30 ÷ 5 = 6

Age difference between Natalie and her daughter
= 50 - 1 u
= 50 - 6
= 44

Natalie's age when her daughter was 12 years old
= 44 + 12
= 56

Answer(s): 56