Tommy and Carl shared some beads in the ratio of 4 : 7. After both each gave away 117 beads to their cousin, the ratio of the number of beads Tommy had to the total number of beads left was 1 : 6. How many beads did the two boys have at first?

	Tommy	Carl	Difference
Before	4x4 = 16 u	7x4 = 28 u	3x4 = 12 u
Change	- 117	- 117
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of beads that Tommy and Carl each gave to their cousin is the same.

The difference in the number of beads at first and in the end between Tommy and Carl remains unchanged.  Make the difference in the number of beads the same.  LCM of 3 and 4 is 12.

Number of beads that Tommy gave to their cousin
= 16 u - 3 u
= 13 u

13 u = 117

1 u = 117 ÷ 13 = 9

Number of beads that the two boys had at first
= 16 u + 28 u
= 44 u
= 44 x 9
= 396

Answer(s): 396