Michael and Liam shared some stickers in the ratio of 3 : 8. After both each gave away 21 stickers to their cousin, the ratio of the number of stickers Michael had to the total number of stickers left was 1 : 6. How many stickers did the two boys have at first?

	Michael	Liam	Difference
Before	3x4 = 12 u	8x4 = 32 u	5x4 = 20 u
Change	- 21	- 21
After	1x5 = 5 u	5x5 = 25 u	4x5 = 20 u

Number of stickers that Michael and Liam each gave to their cousin is the same.

The difference in the number of stickers at first and in the end between Michael and Liam remains unchanged.  Make the difference in the number of stickers the same.  LCM of 5 and 4 is 20.

Number of stickers that Michael gave to their cousin
= 12 u - 5 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

Number of stickers that the two boys had at first
= 12 u + 32 u
= 44 u
= 44 x 3
= 132

Answer(s): 132