Jen, Shiyun and Zoe were playing with beads. Jen started with 40 beads and in the first game, she won ¹₅ more beads from Shiyun. In the second game, Jen lost ³₈ of her original number of beads to Zoe. Shiyun lost as many beads as Jen to Zoe. In the final game, Jen won ¹₄ of her original number of beads from Shiyun. All of them ended up with the same number of beads.

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

	Jen	Shiyun	Zoe
Before	40
First game	+ 8	- 8
Second game	- 15		+ 15
		- 15	+ 15
Final game	+ 10	- 10
After	1 u	1 u	1 u

(a)
Number of beads that Jen won from Shiyun
= ¹₅ x 40
= 8

Number of beads that Jen lost to Zoe
= ³₈ x 40
= 15

Number of beads that Jen won from Shiyun
= ¹₄ x 40
= 10

Number of beads that Jen had in the end
= 40 + 8 - 15 + 10
= 43

(b)
Number of beads that Shiyun had at first
= 1 u + 10 + 15 + 8
= 43 + 10 + 15 + 8
= 76 

Answer(s): (a) 43 ; (b) 76