Kimberly, Dana and Betty were playing with beads. Kimberly started with 84 beads and in the first game, she won ¹₃ more beads from Dana. In the second game, Kimberly lost ²₇ of her original number of beads to Betty. Dana lost as many beads as Kimberly to Betty. In the final game, Kimberly won ¹₄ of her original number of beads from Dana. 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 Dana have at first?

	Kimberly	Dana	Betty
Before	84
First game	+ 28	- 28
Second game	- 24		+ 24
		- 24	+ 24
Final game	+ 21	- 21
After	1 u	1 u	1 u

(a)
Number of beads that Kimberly won from Dana
= ¹₃ x 84
= 28

Number of beads that Kimberly lost to Betty
= ²₇ x 84
= 24

Number of beads that Kimberly won from Dana
= ¹₄ x 84
= 21

Number of beads that Kimberly had in the end
= 84 + 28 - 24 + 21
= 109

(b)
Number of beads that Dana had at first
= 1 u + 21 + 24 + 28
= 109 + 21 + 24 + 28
= 182 

Answer(s): (a) 109 ; (b) 182