Gem, Kimberly and Nicole were playing with beads. Gem started with 70 beads and in the first game, she won ³₅ more beads from Kimberly. In the second game, Gem lost ³₇ of her original number of beads to Nicole. Kimberly lost as many beads as Gem to Nicole. In the final game, Gem 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 Gem have in the end?
2. How many beads did Kimberly have at first?

	Gem	Kimberly	Nicole
Before	70
First game	+ 42	- 42
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Gem won from Kimberly
= ³₅ x 70
= 42

Number of beads that Gem lost to Nicole
= ³₇ x 70
= 30

Number of beads that Gem won from Kimberly
= ¹₅ x 70
= 14

Number of beads that Gem had in the end
= 70 + 42 - 30 + 14
= 96

(b)
Number of beads that Kimberly had at first
= 1 u + 14 + 30 + 42
= 96 + 14 + 30 + 42
= 182 

Answer(s): (a) 96 ; (b) 182