Joelle, Vanessa and Hilda were playing with beads. Joelle started with 88 beads and in the first game, she won ³₄ more beads from Vanessa. In the second game, Joelle lost ³₈ of her original number of beads to Hilda. Vanessa lost as many beads as Joelle to Hilda. In the final game, Joelle won ¹₂ of her original number of beads from Vanessa. All of them ended up with the same number of beads.

1. How many beads did Joelle have in the end?
2. How many beads did Vanessa have at first?

	Joelle	Vanessa	Hilda
Before	88
First game	+ 66	- 66
Second game	- 33		+ 33
		- 33	+ 33
Final game	+ 44	- 44
After	1 u	1 u	1 u

(a)
Number of beads that Joelle won from Vanessa
= ³₄ x 88
= 66

Number of beads that Joelle lost to Hilda
= ³₈ x 88
= 33

Number of beads that Joelle won from Vanessa
= ¹₂ x 88
= 44

Number of beads that Joelle had in the end
= 88 + 66 - 33 + 44
= 165

(b)
Number of beads that Vanessa had at first
= 1 u + 44 + 33 + 66
= 165 + 44 + 33 + 66
= 308 

Answer(s): (a) 165 ; (b) 308