Xandra, Gem and Betty were playing with beads. Xandra started with 24 beads and in the first game, she won ³₄ more beads from Gem. In the second game, Xandra lost ¹₈ of her original number of beads to Betty. Gem lost as many beads as Xandra to Betty. In the final game, Xandra won ¹₄ of her original number of beads from Gem. All of them ended up with the same number of beads.

1. How many beads did Xandra have in the end?
2. How many beads did Gem have at first?

	Xandra	Gem	Betty
Before	24
First game	+ 18	- 18
Second game	- 3		+ 3
		- 3	+ 3
Final game	+ 6	- 6
After	1 u	1 u	1 u

(a)
Number of beads that Xandra won from Gem
= ³₄ x 24
= 18

Number of beads that Xandra lost to Betty
= ¹₈ x 24
= 3

Number of beads that Xandra won from Gem
= ¹₄ x 24
= 6

Number of beads that Xandra had in the end
= 24 + 18 - 3 + 6
= 45

(b)
Number of beads that Gem had at first
= 1 u + 6 + 3 + 18
= 45 + 6 + 3 + 18
= 72 

Answer(s): (a) 45 ; (b) 72