Gem, Dana and Tiffany were playing with beads. Gem started with 80 beads and in the first game, she won ¹₅ more beads from Dana. In the second game, Gem lost ³₈ of her original number of beads to Tiffany. Dana lost as many beads as Gem to Tiffany. In the final game, Gem 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 Gem have in the end?
2. How many beads did Dana have at first?

	Gem	Dana	Tiffany
Before	80
First game	+ 16	- 16
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Gem won from Dana
= ¹₅ x 80
= 16

Number of beads that Gem lost to Tiffany
= ³₈ x 80
= 30

Number of beads that Gem won from Dana
= ¹₄ x 80
= 20

Number of beads that Gem had in the end
= 80 + 16 - 30 + 20
= 86

(b)
Number of beads that Dana had at first
= 1 u + 20 + 30 + 16
= 86 + 20 + 30 + 16
= 152 

Answer(s): (a) 86 ; (b) 152