Ian and Mark shared some erasers in the ratio of 3 : 8. After both each gave away 84 erasers to their brother, the ratio of the number of erasers Ian had to the total number of erasers left was 1 : 6. How many erasers did the two boys have at first?

	Ian	Mark	Difference
Before	3x4 = 12 u	8x4 = 32 u	5x4 = 20 u
Change	- 84	- 84
After	1x5 = 5 u	5x5 = 25 u	4x5 = 20 u

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

The difference in the number of erasers at first and in the end between Ian and Mark remains unchanged.  Make the difference in the number of erasers the same.  LCM of 5 and 4 is 20.

Number of erasers that Ian gave to their brother
= 12 u - 5 u
= 7 u

7 u = 84

1 u = 84 ÷ 7 = 12

Number of erasers that the two boys had at first
= 12 u + 32 u
= 44 u
= 44 x 12
= 528

Answer(s): 528