Opal, Gillian and Tammy were playing with beads. Opal started with 42 beads and in the first game, she won ²₃ more beads from Gillian. In the second game, Opal lost ²₇ of her original number of beads to Tammy. Gillian lost as many beads as Opal to Tammy. In the final game, Opal won ¹₃ of her original number of beads from Gillian. All of them ended up with the same number of beads.

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

	Opal	Gillian	Tammy
Before	42
First game	+ 28	- 28
Second game	- 12		+ 12
		- 12	+ 12
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Opal won from Gillian
= ²₃ x 42
= 28

Number of beads that Opal lost to Tammy
= ²₇ x 42
= 12

Number of beads that Opal won from Gillian
= ¹₃ x 42
= 14

Number of beads that Opal had in the end
= 42 + 28 - 12 + 14
= 72

(b)
Number of beads that Gillian had at first
= 1 u + 14 + 12 + 28
= 72 + 14 + 12 + 28
= 126 

Answer(s): (a) 72 ; (b) 126