Hazel, Kimberly and Esther were playing with beads. Hazel started with 40 beads and in the first game, she won ¹₂ more beads from Kimberly. In the second game, Hazel lost ³₈ of her original number of beads to Esther. Kimberly lost as many beads as Hazel to Esther. In the final game, Hazel won ¹₅ of her original number of beads from Kimberly. All of them ended up with the same number of beads.

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

	Hazel	Kimberly	Esther
Before	40
First game	+ 20	- 20
Second game	- 15		+ 15
		- 15	+ 15
Final game	+ 8	- 8
After	1 u	1 u	1 u

(a)
Number of beads that Hazel won from Kimberly
= ¹₂ x 40
= 20

Number of beads that Hazel lost to Esther
= ³₈ x 40
= 15

Number of beads that Hazel won from Kimberly
= ¹₅ x 40
= 8

Number of beads that Hazel had in the end
= 40 + 20 - 15 + 8
= 53

(b)
Number of beads that Kimberly had at first
= 1 u + 8 + 15 + 20
= 53 + 8 + 15 + 20
= 96 

Answer(s): (a) 53 ; (b) 96