Shiyun, Gwen and Roshel were playing with beads. Shiyun started with 42 beads and in the first game, she won ²₃ more beads from Gwen. In the second game, Shiyun lost ⁶₇ of her original number of beads to Roshel. Gwen lost as many beads as Shiyun to Roshel. In the final game, Shiyun won ¹₂ of her original number of beads from Gwen. All of them ended up with the same number of beads.

1. How many beads did Shiyun have in the end?
2. How many beads did Gwen have at first?

	Shiyun	Gwen	Roshel
Before	42
First game	+ 28	- 28
Second game	- 36		+ 36
		- 36	+ 36
Final game	+ 21	- 21
After	1 u	1 u	1 u

(a)
Number of beads that Shiyun won from Gwen
= ²₃ x 42
= 28

Number of beads that Shiyun lost to Roshel
= ⁶₇ x 42
= 36

Number of beads that Shiyun won from Gwen
= ¹₂ x 42
= 21

Number of beads that Shiyun had in the end
= 42 + 28 - 36 + 21
= 55

(b)
Number of beads that Gwen had at first
= 1 u + 21 + 36 + 28
= 55 + 21 + 36 + 28
= 140 

Answer(s): (a) 55 ; (b) 140