Bryan and Riordan had 68 beads in total. Bryan had 12 beads less than Riordan at first. After Bryan and Riordan played a game with Hazel, Bryan had ³₅ as many beads as Riordan. If Bryan lost as many beads as Riordan to Hazel, find the number of beads that Riordan lost to Hazel.

	Bryan	Riordan	Difference
Before	1 u	1 u + 12	12
Change	- ?	- ?
After	3 p	5 p	2 p

Total number of beads at first
= 1 u + 1 u + 12 
= 2 u + 12

2 u + 12 = 68
2 u = 68 - 12
2 u = 56

1 u = 56 ÷ 2 = 28

Since Bryan lost the same number of beads as Riordan, the difference in the number of beads between Bryan and Riordan at first and in the end remains the same.

Difference in the number of beads in the end
= 5 p - 3 p
= 2 p

2 p = 12

1 p = 12 ÷ 2 = 6

Number of beads that Bryan lost to Hazel
= 1 u - 3 p
= 28 - 3 x 6
= 28 - 18
= 10

Since Riordan lost the same number of beads as Bryan, the number of beads that each lost to Hazel is the same.

Number of beads that Riordan lost = 10

Answer(s): 10