Rachel, Joelle and Jade were playing with beads. Rachel started with 35 beads and in the first game, she won ⁴₅ more beads from Joelle. In the second game, Rachel lost ⁵₇ of her original number of beads to Jade. Joelle lost as many beads as Rachel to Jade. In the final game, Rachel won ¹₅ of her original number of beads from Joelle. All of them ended up with the same number of beads.

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

	Rachel	Joelle	Jade
Before	35
First game	+ 28	- 28
Second game	- 25		+ 25
		- 25	+ 25
Final game	+ 7	- 7
After	1 u	1 u	1 u

(a)
Number of beads that Rachel won from Joelle
= ⁴₅ x 35
= 28

Number of beads that Rachel lost to Jade
= ⁵₇ x 35
= 25

Number of beads that Rachel won from Joelle
= ¹₅ x 35
= 7

Number of beads that Rachel had in the end
= 35 + 28 - 25 + 7
= 45

(b)
Number of beads that Joelle had at first
= 1 u + 7 + 25 + 28
= 45 + 7 + 25 + 28
= 105 

Answer(s): (a) 45 ; (b) 105