Shannon, Shiyun and Jaslyn were playing with beads. Shannon started with 21 beads and in the first game, she won ²₃ more beads from Shiyun. In the second game, Shannon lost ³₇ of her original number of beads to Jaslyn. Shiyun lost as many beads as Shannon to Jaslyn. In the final game, Shannon won ¹₃ of her original number of beads from Shiyun. All of them ended up with the same number of beads.

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

	Shannon	Shiyun	Jaslyn
Before	21
First game	+ 14	- 14
Second game	- 9		+ 9
		- 9	+ 9
Final game	+ 7	- 7
After	1 u	1 u	1 u

(a)
Number of beads that Shannon won from Shiyun
= ²₃ x 21
= 14

Number of beads that Shannon lost to Jaslyn
= ³₇ x 21
= 9

Number of beads that Shannon won from Shiyun
= ¹₃ x 21
= 7

Number of beads that Shannon had in the end
= 21 + 14 - 9 + 7
= 33

(b)
Number of beads that Shiyun had at first
= 1 u + 7 + 9 + 14
= 33 + 7 + 9 + 14
= 63 

Answer(s): (a) 33 ; (b) 63