Nicole, Dana and Lucy were playing with beads. Nicole started with 40 beads and in the first game, she won ¹₅ more beads from Dana. In the second game, Nicole lost ³₈ of her original number of beads to Lucy. Dana lost as many beads as Nicole to Lucy. In the final game, Nicole 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 Nicole have in the end?
2. How many beads did Dana have at first?

	Nicole	Dana	Lucy
Before	40
First game	+ 8	- 8
Second game	- 15		+ 15
		- 15	+ 15
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Nicole won from Dana
= ¹₅ x 40
= 8

Number of beads that Nicole lost to Lucy
= ³₈ x 40
= 15

Number of beads that Nicole won from Dana
= ¹₂ x 40
= 20

Number of beads that Nicole had in the end
= 40 + 8 - 15 + 20
= 53

(b)
Number of beads that Dana had at first
= 1 u + 20 + 15 + 8
= 53 + 20 + 15 + 8
= 96 

Answer(s): (a) 53 ; (b) 96