Daniel and Brandon shared some beads in the ratio of 3 : 8. After both each gave away 14 beads to their brother, the ratio of the number of beads Daniel had to the total number of beads left was 1 : 6. How many beads did the two boys have in the end?

	Daniel	Brandon	Difference
Before	3x4 = 12 u	8x4 = 32 u	5x4 = 20 u
Change	- 14	- 14
After	1x5 = 5 u	5x5 = 25 u	4x5 = 20 u

Number of beads that Daniel and Brandon each gave to their brother is the same.

The difference in the number of beads at first and in the end between Daniel and Brandon remains unchanged.  Make the difference in the number of beads the same.  LCM of 5 and 4 is 20.

Number of beads that Daniel gave to their brother
= 12 u - 5 u
= 7 u

7 u = 14

1 u = 14 ÷ 7 = 2

Number of beads that the two boys had in the end
= 5 u + 25 u
= 30 u
= 30 x 2
= 60

Answer(s): 60