Carl and Ian shared some erasers in the ratio of 5 : 7. After both each gave away 78 erasers to their brother, the ratio of the number of erasers Carl had to the total number of erasers left was 1 : 5. How many erasers did the two boys have at first?

	Carl	Ian	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 78	- 78
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of erasers that Carl and Ian each gave to their brother is the same.

The difference in the number of erasers at first and in the end between Carl and Ian remains unchanged.  Make the difference in the number of erasers the same.  LCM of 2 and 3 is 6.

Number of erasers that Carl gave to their brother
= 15 u - 2 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of erasers that the two boys had at first
= 15 u + 21 u
= 36 u
= 36 x 6
= 216

Answer(s): 216