Gwen, Linda and Marion were playing with beads. Gwen started with 80 beads and in the first game, she won ¹₂ more beads from Linda. In the second game, Gwen lost ¹₈ of her original number of beads to Marion. Linda lost as many beads as Gwen to Marion. In the final game, Gwen won ¹₅ of her original number of beads from Linda. All of them ended up with the same number of beads.

1. How many beads did Gwen have in the end?
2. How many beads did Linda have at first?

	Gwen	Linda	Marion
Before	80
First game	+ 40	- 40
Second game	- 10		+ 10
		- 10	+ 10
Final game	+ 16	- 16
After	1 u	1 u	1 u

(a)
Number of beads that Gwen won from Linda
= ¹₂ x 80
= 40

Number of beads that Gwen lost to Marion
= ¹₈ x 80
= 10

Number of beads that Gwen won from Linda
= ¹₅ x 80
= 16

Number of beads that Gwen had in the end
= 80 + 40 - 10 + 16
= 126

(b)
Number of beads that Linda had at first
= 1 u + 16 + 10 + 40
= 126 + 16 + 10 + 40
= 192 

Answer(s): (a) 126 ; (b) 192