Shannon, Joelle and Sarah were playing with beads. Shannon started with 84 beads and in the first game, she won ¹₄ more beads from Joelle. In the second game, Shannon lost ⁶₇ of her original number of beads to Sarah. Joelle lost as many beads as Shannon to Sarah. In the final game, Shannon won ¹₃ of her original number of beads from Joelle. All of them ended up with the same number of beads.

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

	Shannon	Joelle	Sarah
Before	84
First game	+ 21	- 21
Second game	- 72		+ 72
		- 72	+ 72
Final game	+ 28	- 28
After	1 u	1 u	1 u

(a)
Number of beads that Shannon won from Joelle
= ¹₄ x 84
= 21

Number of beads that Shannon lost to Sarah
= ⁶₇ x 84
= 72

Number of beads that Shannon won from Joelle
= ¹₃ x 84
= 28

Number of beads that Shannon had in the end
= 84 + 21 - 72 + 28
= 61

(b)
Number of beads that Joelle had at first
= 1 u + 28 + 72 + 21
= 61 + 28 + 72 + 21
= 182 

Answer(s): (a) 61 ; (b) 182