Opal, Cindy and Shiyun were playing with beads. Opal started with 80 beads and in the first game, she won ³₄ more beads from Cindy. In the second game, Opal lost ⁵₈ of her original number of beads to Shiyun. Cindy lost as many beads as Opal to Shiyun. In the final game, Opal won ¹₄ of her original number of beads from Cindy. All of them ended up with the same number of beads.

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

	Opal	Cindy	Shiyun
Before	80
First game	+ 60	- 60
Second game	- 50		+ 50
		- 50	+ 50
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Opal won from Cindy
= ³₄ x 80
= 60

Number of beads that Opal lost to Shiyun
= ⁵₈ x 80
= 50

Number of beads that Opal won from Cindy
= ¹₄ x 80
= 20

Number of beads that Opal had in the end
= 80 + 60 - 50 + 20
= 110

(b)
Number of beads that Cindy had at first
= 1 u + 20 + 50 + 60
= 110 + 20 + 50 + 60
= 240 

Answer(s): (a) 110 ; (b) 240