Rachel, Dana and Ivory were playing with beads. Rachel started with 70 beads and in the first game, she won ²₅ more beads from Dana. In the second game, Rachel lost ²₇ of her original number of beads to Ivory. Dana lost as many beads as Rachel to Ivory. In the final game, Rachel won ¹₂ of her original number of beads from Dana. All of them ended up with the same number of beads.

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

	Rachel	Dana	Ivory
Before	70
First game	+ 28	- 28
Second game	- 20		+ 20
		- 20	+ 20
Final game	+ 35	- 35
After	1 u	1 u	1 u

(a)
Number of beads that Rachel won from Dana
= ²₅ x 70
= 28

Number of beads that Rachel lost to Ivory
= ²₇ x 70
= 20

Number of beads that Rachel won from Dana
= ¹₂ x 70
= 35

Number of beads that Rachel had in the end
= 70 + 28 - 20 + 35
= 113

(b)
Number of beads that Dana had at first
= 1 u + 35 + 20 + 28
= 113 + 35 + 20 + 28
= 196 

Answer(s): (a) 113 ; (b) 196