When Irene was 46 years old, her son was 2 times her daughter's age. Irene would be twice her son's age when her daughter was 34 years old. How old would Irene be when her daughter was 25 years old?

	Irene	Son	Daughter
Before	46	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	34

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

Difference in Irene's and her son's ages at first
46 - 2 u = 2 p - 1 p
46 - 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 - 34
1 u + 34 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 2 u = 1 u + 34
1 u + 2 u = 46 - 34
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Irene and her daughter
= 46 - 1 u
= 46 - 4
= 42

Irene's age when her daughter was 25 years old
= 42 + 25
= 67

Answer(s): 67