When Xylia was 49 years old, her son was 3 times her daughter's age. Xylia would be twice her son's age when her daughter was 34 years old. How old would Xylia be when her daughter was 15 years old?

	Xylia	Son	Daughter
Before	49	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	34

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

Difference in Xylia's and her son's ages at first
49 - 3 u = 2 p - 1 p
49 - 3 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
3 u - 1 u = 1 p - 34
2 u + 34 = 1 p --- (2)

Make p the same.

(1) = (2)
49 - 3 u = 2 u + 34
2 u + 3 u = 49 - 34
5 u = 15

1 u = 15 ÷ 5 = 3

Age difference between Xylia and her daughter
= 49 - 1 u
= 49 - 3
= 46

Xylia's age when her daughter was 15 years old
= 46 + 15
= 61

Answer(s): 61