Caden and Pierre had 100 beads in total. Pierre had 50 beads more than Caden at first. After Caden and Pierre played a game with Wendy, Caden had ²₇ as many beads as Pierre. If Caden lost as many beads as Pierre to Wendy, find the number of beads that Caden lost to Wendy.

	Caden	Pierre	Difference
Before	1 u	1 u + 50	50
Change	- ?	- ?
After	2 p	7 p	5 p

Total number of beads at first
= 1 u + 1 u + 50 
= 2 u + 50

2 u + 50 = 100
2 u = 100 - 50
2 u = 50

1 u = 50 ÷ 2 = 25

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

Difference in the number of beads in the end
= 7 p - 2 p
= 5 p

5 p = 50

1 p = 50 ÷ 5 = 10

Number of beads that Caden lost to Wendy
= 1 u - 2 p
= 25 - 2 x 10
= 25 - 20
= 5

Answer(s): 5