When Lynn was 35 years old, her daughter was 3 times her son's age. Lynn would be twice her daughter's age when her son was 20 years old. How old would Lynn be when her son was 13 years old?

	Lynn	Daughter	Son
Before	35	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	20

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

Difference in Lynn's and her daughter's ages at first
35 - 3 u = 2 p - 1 p
35 - 3 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
3 u - 1 u = 1 p - 20
2 u + 20 = 1 p --- (2)

Make p the same.

(1) = (2)
35 - 3 u = 2 u + 20
2 u + 3 u = 35 - 20
5 u = 15

1 u = 15 ÷ 5 = 3

Age difference between Lynn and her son
= 35 - 1 u
= 35 - 3
= 32

Lynn's age when her son was 13 years old
= 32 + 13
= 45

Answer(s): 45