When Gillian was 38 years old, her daughter was 5 times her son's age. Gillian would be twice her daughter's age when her son was 20 years old. How old would Gillian be when her son was 25 years old?

	Gillian	Daughter	Son
Before	38	5 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	20

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

Difference in Gillian's and her daughter's ages at first
38 - 5 u = 2 p - 1 p
38 - 5 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
5 u - 1 u = 1 p - 20
4 u + 20 = 1 p --- (2)

Make p the same.

(1) = (2)
38 - 5 u = 4 u + 20
4 u + 5 u = 38 - 20
9 u = 18

1 u = 18 ÷ 9 = 2

Age difference between Gillian and her son
= 38 - 1 u
= 38 - 2
= 36

Gillian's age when her son was 25 years old
= 36 + 25
= 61

Answer(s): 61