Natalie, Esther and Sarah were playing with beads. Natalie started with 96 beads and in the first game, she won ¹₃ more beads from Esther. In the second game, Natalie lost ¹₈ of her original number of beads to Sarah. Esther lost as many beads as Natalie to Sarah. In the final game, Natalie 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 Natalie have in the end?
2. How many beads did Esther have at first?

	Natalie	Esther	Sarah
Before	96
First game	+ 32	- 32
Second game	- 12		+ 12
		- 12	+ 12
Final game	+ 24	- 24
After	1 u	1 u	1 u

(a)
Number of beads that Natalie won from Esther
= ¹₃ x 96
= 32

Number of beads that Natalie lost to Sarah
= ¹₈ x 96
= 12

Number of beads that Natalie won from Esther
= ¹₄ x 96
= 24

Number of beads that Natalie had in the end
= 96 + 32 - 12 + 24
= 140

(b)
Number of beads that Esther had at first
= 1 u + 24 + 12 + 32
= 140 + 24 + 12 + 32
= 208 

Answer(s): (a) 140 ; (b) 208