Zoe, Gabby and Esther were playing with beads. Zoe started with 72 beads and in the first game, she won ¹₃ more beads from Gabby. In the second game, Zoe lost ¹₈ of her original number of beads to Esther. Gabby lost as many beads as Zoe to Esther. In the final game, Zoe won ¹₂ of her original number of beads from Gabby. All of them ended up with the same number of beads.

1. How many beads did Zoe have in the end?
2. How many beads did Gabby have at first?

	Zoe	Gabby	Esther
Before	72
First game	+ 24	- 24
Second game	- 9		+ 9
		- 9	+ 9
Final game	+ 36	- 36
After	1 u	1 u	1 u

(a)
Number of beads that Zoe won from Gabby
= ¹₃ x 72
= 24

Number of beads that Zoe lost to Esther
= ¹₈ x 72
= 9

Number of beads that Zoe won from Gabby
= ¹₂ x 72
= 36

Number of beads that Zoe had in the end
= 72 + 24 - 9 + 36
= 123

(b)
Number of beads that Gabby had at first
= 1 u + 36 + 9 + 24
= 123 + 36 + 9 + 24
= 192 

Answer(s): (a) 123 ; (b) 192