Oliver and Mark shared some beads in the ratio of 5 : 8. After both each gave away 77 beads to their brother, the ratio of the number of beads Oliver had to the total number of beads left was 1 : 4. How many beads did the two boys have in the end?

	Oliver	Mark	Difference
Before	5x2 = 10 u	8x2 = 16 u	3x2 = 6 u
Change	- 77	- 77
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of beads that Oliver and Mark each gave to their brother is the same.

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

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

7 u = 77

1 u = 77 ÷ 7 = 11

Number of beads that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 11
= 132

Answer(s): 132