Charlie and Vincent had 98 beads in total. Charlie had 48 beads less than Vincent at first. After Charlie and Vincent played a game with Xylia, Charlie had ³₁₁ as many beads as Vincent. If Charlie lost as many beads as Vincent to Xylia, find the number of beads that Vincent lost to Xylia.

	Charlie	Vincent	Difference
Before	1 u	1 u + 48	48
Change	- ?	- ?
After	3 p	11 p	8 p

Total number of beads at first
= 1 u + 1 u + 48 
= 2 u + 48

2 u + 48 = 98
2 u = 98 - 48
2 u = 50

1 u = 50 ÷ 2 = 25

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

Difference in the number of beads in the end
= 11 p - 3 p
= 8 p

8 p = 48

1 p = 48 ÷ 8 = 6

Number of beads that Charlie lost to Xylia
= 1 u - 3 p
= 25 - 3 x 6
= 25 - 18
= 7

Since Vincent lost the same number of beads as Charlie, the number of beads that each lost to Xylia is the same.

Number of beads that Vincent lost = 7

Answer(s): 7