When Roshel was 50 years old, her son was 4 times her daughter's age. Roshel would be twice her son's age when her daughter was 29 years old. How old would Roshel be when her daughter was 23 years old?

	Roshel	Son	Daughter
Before	50	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	29

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

Difference in Roshel's and her son's ages at first
50 - 4 u = 2 p - 1 p
50 - 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 - 29
3 u + 29 = 1 p --- (2)

Make p the same.

(1) = (2)
50 - 4 u = 3 u + 29
3 u + 4 u = 50 - 29
7 u = 21

1 u = 21 ÷ 7 = 3

Age difference between Roshel and her daughter
= 50 - 1 u
= 50 - 3
= 47

Roshel's age when her daughter was 23 years old
= 47 + 23
= 70

Answer(s): 70