Xandra, Kimberly and Mary were playing with beads. Xandra started with 80 beads and in the first game, she won ¹₂ more beads from Kimberly. In the second game, Xandra lost ³₈ of her original number of beads to Mary. Kimberly lost as many beads as Xandra to Mary. In the final game, Xandra won ¹₄ of her original number of beads from Kimberly. All of them ended up with the same number of beads.

1. How many beads did Xandra have in the end?
2. How many beads did Kimberly have at first?

	Xandra	Kimberly	Mary
Before	80
First game	+ 40	- 40
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Xandra won from Kimberly
= ¹₂ x 80
= 40

Number of beads that Xandra lost to Mary
= ³₈ x 80
= 30

Number of beads that Xandra won from Kimberly
= ¹₄ x 80
= 20

Number of beads that Xandra had in the end
= 80 + 40 - 30 + 20
= 110

(b)
Number of beads that Kimberly had at first
= 1 u + 20 + 30 + 40
= 110 + 20 + 30 + 40
= 200 

Answer(s): (a) 110 ; (b) 200