Fiona, Cindy and Diana were playing with beads. Fiona started with 48 beads and in the first game, she won ¹₃ more beads from Cindy. In the second game, Fiona lost ⁵₈ of her original number of beads to Diana. Cindy lost as many beads as Fiona to Diana. In the final game, Fiona won ¹₄ of her original number of beads from Cindy. All of them ended up with the same number of beads.

1. How many beads did Fiona have in the end?
2. How many beads did Cindy have at first?

	Fiona	Cindy	Diana
Before	48
First game	+ 16	- 16
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 12	- 12
After	1 u	1 u	1 u

(a)
Number of beads that Fiona won from Cindy
= ¹₃ x 48
= 16

Number of beads that Fiona lost to Diana
= ⁵₈ x 48
= 30

Number of beads that Fiona won from Cindy
= ¹₄ x 48
= 12

Number of beads that Fiona had in the end
= 48 + 16 - 30 + 12
= 46

(b)
Number of beads that Cindy had at first
= 1 u + 12 + 30 + 16
= 46 + 12 + 30 + 16
= 104 

Answer(s): (a) 46 ; (b) 104