Joelle, Usha and Kathy were playing with beads. Joelle started with 84 beads and in the first game, she won ¹₂ more beads from Usha. In the second game, Joelle lost ⁶₇ of her original number of beads to Kathy. Usha lost as many beads as Joelle to Kathy. In the final game, Joelle won ¹₃ of her original number of beads from Usha. All of them ended up with the same number of beads.

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

	Joelle	Usha	Kathy
Before	84
First game	+ 42	- 42
Second game	- 72		+ 72
		- 72	+ 72
Final game	+ 28	- 28
After	1 u	1 u	1 u

(a)
Number of beads that Joelle won from Usha
= ¹₂ x 84
= 42

Number of beads that Joelle lost to Kathy
= ⁶₇ x 84
= 72

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

Number of beads that Joelle had in the end
= 84 + 42 - 72 + 28
= 82

(b)
Number of beads that Usha had at first
= 1 u + 28 + 72 + 42
= 82 + 28 + 72 + 42
= 224 

Answer(s): (a) 82 ; (b) 224