Tommy and Jeremy shared some pens in the ratio of 5 : 7. After both each gave away 9 pens to their brother, the ratio of the number of pens Tommy had to the total number of pens left was 1 : 3. How many pens did the two boys have in the end?

	Tommy	Jeremy	Difference
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	- 9	- 9
After	1x2 = 2 u	2x2 = 4 u	1x2 = 2 u

Number of pens that Tommy and Jeremy each gave to their brother is the same.

The difference in the number of pens at first and in the end between Tommy and Jeremy remains unchanged.  Make the difference in the number of pens the same.  LCM of 2 and 1 is 2.

Number of pens that Tommy gave to their brother
= 5 u - 2 u
= 3 u

3 u = 9

1 u = 9 ÷ 3 = 3

Number of pens that the two boys had in the end
= 2 u + 4 u
= 6 u
= 6 x 3
= 18

Answer(s): 18