Kylie, Esther and Xandra were playing with beads. Kylie started with 72 beads and in the first game, she won ³₄ more beads from Esther. In the second game, Kylie lost ⁵₈ of her original number of beads to Xandra. Esther lost as many beads as Kylie to Xandra. In the final game, Kylie won ¹₄ of her original number of beads from Esther. All of them ended up with the same number of beads.

1. How many beads did Kylie have in the end?
2. How many beads did Esther have at first?

	Kylie	Esther	Xandra
Before	72
First game	+ 54	- 54
Second game	- 45		+ 45
		- 45	+ 45
Final game	+ 18	- 18
After	1 u	1 u	1 u

(a)
Number of beads that Kylie won from Esther
= ³₄ x 72
= 54

Number of beads that Kylie lost to Xandra
= ⁵₈ x 72
= 45

Number of beads that Kylie won from Esther
= ¹₄ x 72
= 18

Number of beads that Kylie had in the end
= 72 + 54 - 45 + 18
= 99

(b)
Number of beads that Esther had at first
= 1 u + 18 + 45 + 54
= 99 + 18 + 45 + 54
= 216 

Answer(s): (a) 99 ; (b) 216