Cathy, Cindy and Wendy were playing with beads. Cathy started with 84 beads and in the first game, she won ¹₄ more beads from Cindy. In the second game, Cathy lost ²₇ of her original number of beads to Wendy. Cindy lost as many beads as Cathy to Wendy. In the final game, Cathy won ¹₂ of her original number of beads from Cindy. All of them ended up with the same number of beads.

1. How many beads did Cathy have in the end?
2. How many beads did Cindy have at first?

	Cathy	Cindy	Wendy
Before	84
First game	+ 21	- 21
Second game	- 24		+ 24
		- 24	+ 24
Final game	+ 42	- 42
After	1 u	1 u	1 u

(a)
Number of beads that Cathy won from Cindy
= ¹₄ x 84
= 21

Number of beads that Cathy lost to Wendy
= ²₇ x 84
= 24

Number of beads that Cathy won from Cindy
= ¹₂ x 84
= 42

Number of beads that Cathy had in the end
= 84 + 21 - 24 + 42
= 123

(b)
Number of beads that Cindy had at first
= 1 u + 42 + 24 + 21
= 123 + 42 + 24 + 21
= 210 

Answer(s): (a) 123 ; (b) 210