Natalie, Rachel and Nora were playing with beads. Natalie started with 84 beads and in the first game, she won ³₄ more beads from Rachel. In the second game, Natalie lost ³₇ of her original number of beads to Nora. Rachel lost as many beads as Natalie to Nora. In the final game, Natalie won ¹₃ of her original number of beads from Rachel. All of them ended up with the same number of beads.

1. How many beads did Natalie have in the end?
2. How many beads did Rachel have at first?

	Natalie	Rachel	Nora
Before	84
First game	+ 63	- 63
Second game	- 36		+ 36
		- 36	+ 36
Final game	+ 28	- 28
After	1 u	1 u	1 u

(a)
Number of beads that Natalie won from Rachel
= ³₄ x 84
= 63

Number of beads that Natalie lost to Nora
= ³₇ x 84
= 36

Number of beads that Natalie won from Rachel
= ¹₃ x 84
= 28

Number of beads that Natalie had in the end
= 84 + 63 - 36 + 28
= 139

(b)
Number of beads that Rachel had at first
= 1 u + 28 + 36 + 63
= 139 + 28 + 36 + 63
= 266 

Answer(s): (a) 139 ; (b) 266