Roshel, Penelope and Nora were playing with beads. Roshel started with 56 beads and in the first game, she won ³₄ more beads from Penelope. In the second game, Roshel lost ⁵₇ of her original number of beads to Nora. Penelope lost as many beads as Roshel to Nora. In the final game, Roshel won ¹₄ of her original number of beads from Penelope. All of them ended up with the same number of beads.

1. How many beads did Roshel have in the end?
2. How many beads did Penelope have at first?

	Roshel	Penelope	Nora
Before	56
First game	+ 42	- 42
Second game	- 40		+ 40
		- 40	+ 40
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Roshel won from Penelope
= ³₄ x 56
= 42

Number of beads that Roshel lost to Nora
= ⁵₇ x 56
= 40

Number of beads that Roshel won from Penelope
= ¹₄ x 56
= 14

Number of beads that Roshel had in the end
= 56 + 42 - 40 + 14
= 72

(b)
Number of beads that Penelope had at first
= 1 u + 14 + 40 + 42
= 72 + 14 + 40 + 42
= 168 

Answer(s): (a) 72 ; (b) 168