Rachel, Shannon and Fanny were playing with beads. Rachel started with 40 beads and in the first game, she won ³₅ more beads from Shannon. In the second game, Rachel lost ⁵₈ of her original number of beads to Fanny. Shannon lost as many beads as Rachel to Fanny. In the final game, Rachel won ¹₅ of her original number of beads from Shannon. 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 Shannon have at first?

	Rachel	Shannon	Fanny
Before	40
First game	+ 24	- 24
Second game	- 25		+ 25
		- 25	+ 25
Final game	+ 8	- 8
After	1 u	1 u	1 u

(a)
Number of beads that Rachel won from Shannon
= ³₅ x 40
= 24

Number of beads that Rachel lost to Fanny
= ⁵₈ x 40
= 25

Number of beads that Rachel won from Shannon
= ¹₅ x 40
= 8

Number of beads that Rachel had in the end
= 40 + 24 - 25 + 8
= 47

(b)
Number of beads that Shannon had at first
= 1 u + 8 + 25 + 24
= 47 + 8 + 25 + 24
= 104 

Answer(s): (a) 47 ; (b) 104