When Linda was 42 years old, her daughter was 2 times her son's age. Linda would be twice her daughter's age when her son was 27 years old. How old would Linda be when her son was 10 years old?

	Linda	Daughter	Son
Before	42	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

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

Difference in Linda's and her daughter's ages at first
42 - 2 u = 2 p - 1 p
42 - 2 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
2 u - 1 u = 1 p - 27
1 u + 27 = 1 p --- (2)

Make p the same.

(1) = (2)
42 - 2 u = 1 u + 27
1 u + 2 u = 42 - 27
3 u = 15

1 u = 15 ÷ 3 = 5

Age difference between Linda and her son
= 42 - 1 u
= 42 - 5
= 37

Linda's age when her son was 10 years old
= 37 + 10
= 47

Answer(s): 47