When Penelope was 49 years old, her son was 4 times her daughter's age. Penelope would be twice her son's age when her daughter was 35 years old. How old would Penelope be when her daughter was 6 years old?

	Penelope	Son	Daughter
Before	49	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	35

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

Difference in Penelope's and her son's ages at first
49 - 4 u = 2 p - 1 p
49 - 4 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
4 u - 1 u = 1 p - 35
3 u + 35 = 1 p --- (2)

Make p the same.

(1) = (2)
49 - 4 u = 3 u + 35
3 u + 4 u = 49 - 35
7 u = 14

1 u = 14 ÷ 7 = 2

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

Penelope's age when her daughter was 6 years old
= 47 + 6
= 53

Answer(s): 53