Cathy, Gabby and Vanessa were playing with beads. Cathy started with 48 beads and in the first game, she won ¹₂ more beads from Gabby. In the second game, Cathy lost ¹₈ of her original number of beads to Vanessa. Gabby lost as many beads as Cathy to Vanessa. In the final game, Cathy won ¹₄ of her original number of beads from Gabby. All of them ended up with the same number of beads.

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

	Cathy	Gabby	Vanessa
Before	48
First game	+ 24	- 24
Second game	- 6		+ 6
		- 6	+ 6
Final game	+ 12	- 12
After	1 u	1 u	1 u

(a)
Number of beads that Cathy won from Gabby
= ¹₂ x 48
= 24

Number of beads that Cathy lost to Vanessa
= ¹₈ x 48
= 6

Number of beads that Cathy won from Gabby
= ¹₄ x 48
= 12

Number of beads that Cathy had in the end
= 48 + 24 - 6 + 12
= 78

(b)
Number of beads that Gabby had at first
= 1 u + 12 + 6 + 24
= 78 + 12 + 6 + 24
= 120 

Answer(s): (a) 78 ; (b) 120