When Kylie was 38 years old, her daughter was 4 times her son's age. Kylie would be twice her daughter's age when her son was 24 years old. How old would Kylie be when her son was 13 years old?

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

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

Difference in Kylie'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 Kylie and her son
= 38 - 1 u
= 38 - 2
= 36

Kylie's age when her son was 13 years old
= 36 + 13
= 49

Answer(s): 49