Hilda, Roshel and Shannon were playing with beads. Hilda started with 84 beads and in the first game, she won ¹₃ more beads from Roshel. In the second game, Hilda lost ⁵₇ of her original number of beads to Shannon. Roshel lost as many beads as Hilda to Shannon. In the final game, Hilda won ¹₄ of her original number of beads from Roshel. All of them ended up with the same number of beads.

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

	Hilda	Roshel	Shannon
Before	84
First game	+ 28	- 28
Second game	- 60		+ 60
		- 60	+ 60
Final game	+ 21	- 21
After	1 u	1 u	1 u

(a)
Number of beads that Hilda won from Roshel
= ¹₃ x 84
= 28

Number of beads that Hilda lost to Shannon
= ⁵₇ x 84
= 60

Number of beads that Hilda won from Roshel
= ¹₄ x 84
= 21

Number of beads that Hilda had in the end
= 84 + 28 - 60 + 21
= 73

(b)
Number of beads that Roshel had at first
= 1 u + 21 + 60 + 28
= 73 + 21 + 60 + 28
= 182 

Answer(s): (a) 73 ; (b) 182