Xylia, Zoe and Wendy were playing with beads. Xylia started with 24 beads and in the first game, she won ³₄ more beads from Zoe. In the second game, Xylia lost ¹₈ of her original number of beads to Wendy. Zoe lost as many beads as Xylia to Wendy. In the final game, Xylia won ¹₃ of her original number of beads from Zoe. All of them ended up with the same number of beads.

1. How many beads did Xylia have in the end?
2. How many beads did Zoe have at first?

	Xylia	Zoe	Wendy
Before	24
First game	+ 18	- 18
Second game	- 3		+ 3
		- 3	+ 3
Final game	+ 8	- 8
After	1 u	1 u	1 u

(a)
Number of beads that Xylia won from Zoe
= ³₄ x 24
= 18

Number of beads that Xylia lost to Wendy
= ¹₈ x 24
= 3

Number of beads that Xylia won from Zoe
= ¹₃ x 24
= 8

Number of beads that Xylia had in the end
= 24 + 18 - 3 + 8
= 47

(b)
Number of beads that Zoe had at first
= 1 u + 8 + 3 + 18
= 47 + 8 + 3 + 18
= 76 

Answer(s): (a) 47 ; (b) 76