Ivory, Gillian and Abi were playing with beads. Ivory started with 56 beads and in the first game, she won ¹₄ more beads from Gillian. In the second game, Ivory lost ³₈ of her original number of beads to Abi. Gillian lost as many beads as Ivory to Abi. In the final game, Ivory won ¹₂ of her original number of beads from Gillian. All of them ended up with the same number of beads.

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

	Ivory	Gillian	Abi
Before	56
First game	+ 14	- 14
Second game	- 21		+ 21
		- 21	+ 21
Final game	+ 28	- 28
After	1 u	1 u	1 u

(a)
Number of beads that Ivory won from Gillian
= ¹₄ x 56
= 14

Number of beads that Ivory lost to Abi
= ³₈ x 56
= 21

Number of beads that Ivory won from Gillian
= ¹₂ x 56
= 28

Number of beads that Ivory had in the end
= 56 + 14 - 21 + 28
= 77

(b)
Number of beads that Gillian had at first
= 1 u + 28 + 21 + 14
= 77 + 28 + 21 + 14
= 140 

Answer(s): (a) 77 ; (b) 140