Cathy, Diana and Fiona were playing with beads. Cathy started with 72 beads and in the first game, she won ²₃ more beads from Diana. In the second game, Cathy lost ⁵₈ of her original number of beads to Fiona. Diana lost as many beads as Cathy to Fiona. In the final game, Cathy won ¹₃ of her original number of beads from Diana. 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 Diana have at first?

	Cathy	Diana	Fiona
Before	72
First game	+ 48	- 48
Second game	- 45		+ 45
		- 45	+ 45
Final game	+ 24	- 24
After	1 u	1 u	1 u

(a)
Number of beads that Cathy won from Diana
= ²₃ x 72
= 48

Number of beads that Cathy lost to Fiona
= ⁵₈ x 72
= 45

Number of beads that Cathy won from Diana
= ¹₃ x 72
= 24

Number of beads that Cathy had in the end
= 72 + 48 - 45 + 24
= 99

(b)
Number of beads that Diana had at first
= 1 u + 24 + 45 + 48
= 99 + 24 + 45 + 48
= 216 

Answer(s): (a) 99 ; (b) 216