Luis and Bobby shared some erasers in the ratio of 5 : 8. After both each gave away 77 erasers to their cousin, the ratio of the number of erasers Luis had to the total number of erasers left was 1 : 4. How many erasers did the two boys have at first?

	Luis	Bobby	Difference
Before	5x2 = 10 u	8x2 = 16 u	3x2 = 6 u
Change	- 77	- 77
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of erasers that Luis and Bobby each gave to their cousin is the same.

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

Number of erasers that Luis gave to their cousin
= 10 u - 3 u
= 7 u

7 u = 77

1 u = 77 ÷ 7 = 11

Number of erasers that the two boys had at first
= 10 u + 16 u
= 26 u
= 26 x 11
= 286

Answer(s): 286