When Shannon was 48 years old, her son was 2 times her daughter's age. Shannon would be twice her son's age when her daughter was 27 years old. How old would Shannon be when her daughter was 6 years old?

	Shannon	Son	Daughter
Before	48	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

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

Difference in Shannon's and her son's ages at first
48 - 2 u = 2 p - 1 p
48 - 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 - 27
1 u + 27 = 1 p --- (2)

Make p the same.

(1) = (2)
48 - 2 u = 1 u + 27
1 u + 2 u = 48 - 27
3 u = 21

1 u = 21 ÷ 3 = 7

Age difference between Shannon and her daughter
= 48 - 1 u
= 48 - 7
= 41

Shannon's age when her daughter was 6 years old
= 41 + 6
= 47

Answer(s): 47