When Penelope was 50 years old, her son was 2 times her daughter's age. Penelope would be twice her son's age when her daughter was 29 years old. How old would Penelope be when her daughter was 14 years old?

	Penelope	Son	Daughter
Before	50	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	29

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

Difference in Penelope's and her son's ages at first
50 - 2 u = 2 p - 1 p
50 - 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 - 29
1 u + 29 = 1 p --- (2)

Make p the same.

(1) = (2)
50 - 2 u = 1 u + 29
1 u + 2 u = 50 - 29
3 u = 21

1 u = 21 ÷ 3 = 7

Age difference between Penelope and her daughter
= 50 - 1 u
= 50 - 7
= 43

Penelope's age when her daughter was 14 years old
= 43 + 14
= 57

Answer(s): 57