Henry and Ryan had 64 beads in total. Henry had 4 beads less than Ryan at first. After Henry and Ryan played a game with Dana, Henry had ¹₃ as many beads as Ryan. If Henry lost as many beads as Ryan to Dana, find the number of beads that Ryan lost to Dana.

	Henry	Ryan	Difference
Before	1 u	1 u + 4	4
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of beads at first
= 1 u + 1 u + 4 
= 2 u + 4

2 u + 4 = 64
2 u = 64 - 4
2 u = 60

1 u = 60 ÷ 2 = 30

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

Difference in the number of beads in the end
= 3 p - 1 p
= 2 p

2 p = 4

1 p = 4 ÷ 2 = 2

Number of beads that Henry lost to Dana
= 1 u - 1 p
= 30 - 1 x 2
= 30 - 2
= 28

Since Ryan lost the same number of beads as Henry, the number of beads that each lost to Dana is the same.

Number of beads that Ryan lost = 28

Answer(s): 28