Fiona, Victoria and Hazel were playing with beads. Fiona started with 40 beads and in the first game, she won ³₄ more beads from Victoria. In the second game, Fiona lost ¹₈ of her original number of beads to Hazel. Victoria lost as many beads as Fiona to Hazel. In the final game, Fiona won ¹₂ of her original number of beads from Victoria. All of them ended up with the same number of beads.

1. How many beads did Fiona have in the end?
2. How many beads did Victoria have at first?

	Fiona	Victoria	Hazel
Before	40
First game	+ 30	- 30
Second game	- 5		+ 5
		- 5	+ 5
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Fiona won from Victoria
= ³₄ x 40
= 30

Number of beads that Fiona lost to Hazel
= ¹₈ x 40
= 5

Number of beads that Fiona won from Victoria
= ¹₂ x 40
= 20

Number of beads that Fiona had in the end
= 40 + 30 - 5 + 20
= 85

(b)
Number of beads that Victoria had at first
= 1 u + 20 + 5 + 30
= 85 + 20 + 5 + 30
= 140 

Answer(s): (a) 85 ; (b) 140