Luke and Eric had 55 beads in total. Eric had 9 beads more than Luke at first. After Luke and Eric played a game with Gwen, Luke had ¹₄ as many beads as Eric. If Luke lost as many beads as Eric to Gwen, find the number of beads that Luke lost to Gwen.

	Luke	Eric	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 = 55
2 u = 55 - 9
2 u = 46

1 u = 46 ÷ 2 = 23

Since Luke lost the same number of beads as Eric, the difference in the number of beads between Luke and Eric 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 Luke lost to Gwen
= 1 u - 1 p
= 23 - 1 x 3
= 23 - 3
= 20

Answer(s): 20