Simon and Jack shared some beads in the ratio of 5 : 8. After both each gave away 14 beads to their brother, the ratio of the number of beads Simon had to the total number of beads left was 1 : 4. How many beads did the two boys have at first?

	Simon	Jack	Difference
Before	5x2 = 10 u	8x2 = 16 u	3x2 = 6 u
Change	- 14	- 14
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of beads that Simon and Jack each gave to their brother is the same.

The difference in the number of beads at first and in the end between Simon and Jack remains unchanged.  Make the difference in the number of beads the same.  LCM of 3 and 2 is 6.

Number of beads that Simon gave to their brother
= 10 u - 3 u
= 7 u

7 u = 14

1 u = 14 ÷ 7 = 2

Number of beads that the two boys had at first
= 10 u + 16 u
= 26 u
= 26 x 2
= 52

Answer(s): 52