Dylan and Glen had 53 beads in total. Dylan had 9 beads less than Glen at first. After Dylan and Glen played a game with Cathy, Dylan had ¹₄ as many beads as Glen. If Dylan lost as many beads as Glen to Cathy, find the number of beads that Glen lost to Cathy.

	Dylan	Glen	Difference
Before	1 u	1 u + 9	9
Change	- ?	- ?
After	1 p	4 p	3 p

Total number of beads at first
= 1 u + 1 u + 9 
= 2 u + 9

2 u + 9 = 53
2 u = 53 - 9
2 u = 44

1 u = 44 ÷ 2 = 22

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

Difference in the number of beads in the end
= 4 p - 1 p
= 3 p

3 p = 9

1 p = 9 ÷ 3 = 3

Number of beads that Dylan lost to Cathy
= 1 u - 1 p
= 22 - 1 x 3
= 22 - 3
= 19

Since Glen lost the same number of beads as Dylan, the number of beads that each lost to Cathy is the same.

Number of beads that Glen lost = 19

Answer(s): 19