Penelope, Kimberly and Jane were playing with beads. Penelope started with 24 beads and in the first game, she won ²₃ more beads from Kimberly. In the second game, Penelope lost ³₈ of her original number of beads to Jane. Kimberly lost as many beads as Penelope to Jane. In the final game, Penelope won ¹₂ of her original number of beads from Kimberly. All of them ended up with the same number of beads.

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

	Penelope	Kimberly	Jane
Before	24
First game	+ 16	- 16
Second game	- 9		+ 9
		- 9	+ 9
Final game	+ 12	- 12
After	1 u	1 u	1 u

(a)
Number of beads that Penelope won from Kimberly
= ²₃ x 24
= 16

Number of beads that Penelope lost to Jane
= ³₈ x 24
= 9

Number of beads that Penelope won from Kimberly
= ¹₂ x 24
= 12

Number of beads that Penelope had in the end
= 24 + 16 - 9 + 12
= 43

(b)
Number of beads that Kimberly had at first
= 1 u + 12 + 9 + 16
= 43 + 12 + 9 + 16
= 80 

Answer(s): (a) 43 ; (b) 80