Xandra, Natalie and Nora were playing with beads. Xandra started with 48 beads and in the first game, she won ¹₃ more beads from Natalie. In the second game, Xandra lost ¹₈ of her original number of beads to Nora. Natalie lost as many beads as Xandra to Nora. In the final game, Xandra won ¹₂ of her original number of beads from Natalie. 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 Natalie have at first?

	Xandra	Natalie	Nora
Before	48
First game	+ 16	- 16
Second game	- 6		+ 6
		- 6	+ 6
Final game	+ 24	- 24
After	1 u	1 u	1 u

(a)
Number of beads that Xandra won from Natalie
= ¹₃ x 48
= 16

Number of beads that Xandra lost to Nora
= ¹₈ x 48
= 6

Number of beads that Xandra won from Natalie
= ¹₂ x 48
= 24

Number of beads that Xandra had in the end
= 48 + 16 - 6 + 24
= 82

(b)
Number of beads that Natalie had at first
= 1 u + 24 + 6 + 16
= 82 + 24 + 6 + 16
= 128 

Answer(s): (a) 82 ; (b) 128