Tammy, Abi and Natalie were playing with beads. Tammy started with 64 beads and in the first game, she won ³₄ more beads from Abi. In the second game, Tammy lost ⁵₈ of her original number of beads to Natalie. Abi lost as many beads as Tammy to Natalie. In the final game, Tammy won ¹₂ of her original number of beads from Abi. All of them ended up with the same number of beads.

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

	Tammy	Abi	Natalie
Before	64
First game	+ 48	- 48
Second game	- 40		+ 40
		- 40	+ 40
Final game	+ 32	- 32
After	1 u	1 u	1 u

(a)
Number of beads that Tammy won from Abi
= ³₄ x 64
= 48

Number of beads that Tammy lost to Natalie
= ⁵₈ x 64
= 40

Number of beads that Tammy won from Abi
= ¹₂ x 64
= 32

Number of beads that Tammy had in the end
= 64 + 48 - 40 + 32
= 104

(b)
Number of beads that Abi had at first
= 1 u + 32 + 40 + 48
= 104 + 32 + 40 + 48
= 224 

Answer(s): (a) 104 ; (b) 224