Gillian, Hilda and Elyse were playing with beads. Gillian started with 56 beads and in the first game, she won ³₄ more beads from Hilda. In the second game, Gillian lost ²₇ of her original number of beads to Elyse. Hilda lost as many beads as Gillian to Elyse. In the final game, Gillian won ¹₄ of her original number of beads from Hilda. All of them ended up with the same number of beads.

1. How many beads did Gillian have in the end?
2. How many beads did Hilda have at first?

	Gillian	Hilda	Elyse
Before	56
First game	+ 42	- 42
Second game	- 16		+ 16
		- 16	+ 16
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Gillian won from Hilda
= ³₄ x 56
= 42

Number of beads that Gillian lost to Elyse
= ²₇ x 56
= 16

Number of beads that Gillian won from Hilda
= ¹₄ x 56
= 14

Number of beads that Gillian had in the end
= 56 + 42 - 16 + 14
= 96

(b)
Number of beads that Hilda had at first
= 1 u + 14 + 16 + 42
= 96 + 14 + 16 + 42
= 168 

Answer(s): (a) 96 ; (b) 168