When Gillian was 49 years old, her son was 5 times her daughter's age. Gillian would be twice her son's age when her daughter was 31 years old. How old would Gillian be when her daughter was 20 years old?

	Gillian	Son	Daughter
Before	49	5 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	31

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

Difference in Gillian's and her son's ages at first
49 - 5 u = 2 p - 1 p
49 - 5 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
5 u - 1 u = 1 p - 31
4 u + 31 = 1 p --- (2)

Make p the same.

(1) = (2)
49 - 5 u = 4 u + 31
4 u + 5 u = 49 - 31
9 u = 18

1 u = 18 ÷ 9 = 2

Age difference between Gillian and her daughter
= 49 - 1 u
= 49 - 2
= 47

Gillian's age when her daughter was 20 years old
= 47 + 20
= 67

Answer(s): 67