Emily, Tammy and Jen were playing with beads. Emily started with 96 beads and in the first game, she won ²₃ more beads from Tammy. In the second game, Emily lost ¹₈ of her original number of beads to Jen. Tammy lost as many beads as Emily to Jen. In the final game, Emily won ¹₃ of her original number of beads from Tammy. All of them ended up with the same number of beads.

1. How many beads did Emily have in the end?
2. How many beads did Tammy have at first?

	Emily	Tammy	Jen
Before	96
First game	+ 64	- 64
Second game	- 12		+ 12
		- 12	+ 12
Final game	+ 32	- 32
After	1 u	1 u	1 u

(a)
Number of beads that Emily won from Tammy
= ²₃ x 96
= 64

Number of beads that Emily lost to Jen
= ¹₈ x 96
= 12

Number of beads that Emily won from Tammy
= ¹₃ x 96
= 32

Number of beads that Emily had in the end
= 96 + 64 - 12 + 32
= 180

(b)
Number of beads that Tammy had at first
= 1 u + 32 + 12 + 64
= 180 + 32 + 12 + 64
= 288 

Answer(s): (a) 180 ; (b) 288