Opal, Gabby and Joelle were playing with beads. Opal started with 96 beads and in the first game, she won ¹₄ more beads from Gabby. In the second game, Opal lost ¹₈ of her original number of beads to Joelle. Gabby lost as many beads as Opal to Joelle. In the final game, Opal won ¹₃ of her original number of beads from Gabby. 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 Gabby have at first?

	Opal	Gabby	Joelle
Before	96
First game	+ 24	- 24
Second game	- 12		+ 12
		- 12	+ 12
Final game	+ 32	- 32
After	1 u	1 u	1 u

(a)
Number of beads that Opal won from Gabby
= ¹₄ x 96
= 24

Number of beads that Opal lost to Joelle
= ¹₈ x 96
= 12

Number of beads that Opal won from Gabby
= ¹₃ x 96
= 32

Number of beads that Opal had in the end
= 96 + 24 - 12 + 32
= 140

(b)
Number of beads that Gabby had at first
= 1 u + 32 + 12 + 24
= 140 + 32 + 12 + 24
= 208 

Answer(s): (a) 140 ; (b) 208