Fred and Dylan shared some erasers in the ratio of 3 : 8. After both each gave away 20 erasers to their sister, the ratio of the number of erasers Fred had to the total number of erasers left was 1 : 5. How many erasers did the two boys have at first?

	Fred	Dylan	Difference
Before	3x3 = 9 u	8x3 = 24 u	5x3 = 15 u
Change	- 20	- 20
After	1x5 = 5 u	4x5 = 20 u	3x5 = 15 u

Number of erasers that Fred and Dylan each gave to their sister is the same.

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

Number of erasers that Fred gave to their sister
= 9 u - 5 u
= 4 u

4 u = 20

1 u = 20 ÷ 4 = 5

Number of erasers that the two boys had at first
= 9 u + 24 u
= 33 u
= 33 x 5
= 165

Answer(s): 165