Harry and Ethan shared some erasers in the ratio of 3 : 8. After both each gave away 12 erasers to their cousin, the ratio of the number of erasers Harry had to the total number of erasers left was 1 : 5. How many erasers did the two boys have in the end?

	Harry	Ethan	Difference
Before	3x3 = 9 u	8x3 = 24 u	5x3 = 15 u
Change	- 12	- 12
After	1x5 = 5 u	4x5 = 20 u	3x5 = 15 u

Number of erasers that Harry and Ethan each gave to their cousin is the same.

The difference in the number of erasers at first and in the end between Harry and Ethan remains unchanged.  Make the difference in the number of erasers the same.  LCM of 5 and 3 is 15.

Number of erasers that Harry gave to their cousin
= 9 u - 5 u
= 4 u

4 u = 12

1 u = 12 ÷ 4 = 3

Number of erasers that the two boys had in the end
= 5 u + 20 u
= 25 u
= 25 x 3
= 75

Answer(s): 75