Ben and Liam shared some stickers in the ratio of 5 : 8. After both each gave away 21 stickers to their sister, the ratio of the number of stickers Ben had to the total number of stickers left was 1 : 4. How many stickers did the two boys have at first?

	Ben	Liam	Difference
Before	5x2 = 10 u	8x2 = 16 u	3x2 = 6 u
Change	- 21	- 21
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of stickers that Ben and Liam each gave to their sister is the same.

The difference in the number of stickers at first and in the end between Ben and Liam remains unchanged.  Make the difference in the number of stickers the same.  LCM of 3 and 2 is 6.

Number of stickers that Ben gave to their sister
= 10 u - 3 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

Number of stickers that the two boys had at first
= 10 u + 16 u
= 26 u
= 26 x 3
= 78

Answer(s): 78