Elyse, Kimberly and Nicole were playing with beads. Elyse started with 40 beads and in the first game, she won ¹₄ more beads from Kimberly. In the second game, Elyse lost ¹₈ of her original number of beads to Nicole. Kimberly lost as many beads as Elyse to Nicole. In the final game, Elyse won ¹₂ of her original number of beads from Kimberly. All of them ended up with the same number of beads.

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

	Elyse	Kimberly	Nicole
Before	40
First game	+ 10	- 10
Second game	- 5		+ 5
		- 5	+ 5
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Elyse won from Kimberly
= ¹₄ x 40
= 10

Number of beads that Elyse lost to Nicole
= ¹₈ x 40
= 5

Number of beads that Elyse won from Kimberly
= ¹₂ x 40
= 20

Number of beads that Elyse had in the end
= 40 + 10 - 5 + 20
= 65

(b)
Number of beads that Kimberly had at first
= 1 u + 20 + 5 + 10
= 65 + 20 + 5 + 10
= 100 

Answer(s): (a) 65 ; (b) 100