When Rachel was 43 years old, her daughter was 2 times her son's age. Rachel would be twice her daughter's age when her son was 28 years old. How old would Rachel be when her son was 10 years old?

	Rachel	Daughter	Son
Before	43	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	28

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

Difference in Rachel's and her daughter's ages at first
43 - 2 u = 2 p - 1 p
43 - 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 - 28
1 u + 28 = 1 p --- (2)

Make p the same.

(1) = (2)
43 - 2 u = 1 u + 28
1 u + 2 u = 43 - 28
3 u = 15

1 u = 15 ÷ 3 = 5

Age difference between Rachel and her son
= 43 - 1 u
= 43 - 5
= 38

Rachel's age when her son was 10 years old
= 38 + 10
= 48

Answer(s): 48