Kimberly, Sarah and Gabby were playing with beads. Kimberly started with 48 beads and in the first game, she won ¹₂ more beads from Sarah. In the second game, Kimberly lost ⁵₈ of her original number of beads to Gabby. Sarah lost as many beads as Kimberly to Gabby. In the final game, Kimberly won ¹₃ of her original number of beads from Sarah. All of them ended up with the same number of beads.

1. How many beads did Kimberly have in the end?
2. How many beads did Sarah have at first?

	Kimberly	Sarah	Gabby
Before	48
First game	+ 24	- 24
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 16	- 16
After	1 u	1 u	1 u

(a)
Number of beads that Kimberly won from Sarah
= ¹₂ x 48
= 24

Number of beads that Kimberly lost to Gabby
= ⁵₈ x 48
= 30

Number of beads that Kimberly won from Sarah
= ¹₃ x 48
= 16

Number of beads that Kimberly had in the end
= 48 + 24 - 30 + 16
= 58

(b)
Number of beads that Sarah had at first
= 1 u + 16 + 30 + 24
= 58 + 16 + 30 + 24
= 128 

Answer(s): (a) 58 ; (b) 128