Dana, Joelle and Kimberly were playing with beads. Dana started with 40 beads and in the first game, she won ¹₂ more beads from Joelle. In the second game, Dana lost ⁵₈ of her original number of beads to Kimberly. Joelle lost as many beads as Dana to Kimberly. In the final game, Dana won ¹₅ of her original number of beads from Joelle. All of them ended up with the same number of beads.

1. How many beads did Dana have in the end?
2. How many beads did Joelle have at first?

	Dana	Joelle	Kimberly
Before	40
First game	+ 20	- 20
Second game	- 25		+ 25
		- 25	+ 25
Final game	+ 8	- 8
After	1 u	1 u	1 u

(a)
Number of beads that Dana won from Joelle
= ¹₂ x 40
= 20

Number of beads that Dana lost to Kimberly
= ⁵₈ x 40
= 25

Number of beads that Dana won from Joelle
= ¹₅ x 40
= 8

Number of beads that Dana had in the end
= 40 + 20 - 25 + 8
= 43

(b)
Number of beads that Joelle had at first
= 1 u + 8 + 25 + 20
= 43 + 8 + 25 + 20
= 96 

Answer(s): (a) 43 ; (b) 96