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

	Charlie	Billy	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 marbles that Charlie and Billy each gave to their cousin is the same.

The difference in the number of marbles at first and in the end between Charlie and Billy remains unchanged.  Make the difference in the number of marbles the same.  LCM of 3 and 2 is 6.

Number of marbles that Charlie gave to their cousin
= 10 u - 3 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

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

Answer(s): 78