When Penelope was 38 years old, her daughter was 4 times her son's age. Penelope would be twice her daughter's age when her son was 24 years old. How old would Penelope be when her son was 25 years old?

	Penelope	Daughter	Son
Before	38	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	24

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

Difference in Penelope's and her daughter's ages at first
38 - 4 u = 2 p - 1 p
38 - 4 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
4 u - 1 u = 1 p - 24
3 u + 24 = 1 p --- (2)

Make p the same.

(1) = (2)
38 - 4 u = 3 u + 24
3 u + 4 u = 38 - 24
7 u = 14

1 u = 14 ÷ 7 = 2

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

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

Answer(s): 61