Neave and Will shared some beads in the ratio of 3 : 7. After both each gave away 35 beads to their brother, the ratio of the number of beads Neave had to the total number of beads left was 1 : 5. How many beads did the two boys have in the end?

	Neave	Will	Difference
Before	3x3 = 9 u	7x3 = 21 u	4x3 = 12 u
Change	- 35	- 35
After	1x4 = 4 u	4x4 = 16 u	3x4 = 12 u

Number of beads that Neave and Will each gave to their brother is the same.

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

Number of beads that Neave gave to their brother
= 9 u - 4 u
= 5 u

5 u = 35

1 u = 35 ÷ 5 = 7

Number of beads that the two boys had in the end
= 4 u + 16 u
= 20 u
= 20 x 7
= 140

Answer(s): 140