Gillian, Tina and Olivia were playing with beads. Gillian started with 84 beads and in the first game, she won ²₃ more beads from Tina. In the second game, Gillian lost ³₇ of her original number of beads to Olivia. Tina lost as many beads as Gillian to Olivia. In the final game, Gillian won ¹₃ of her original number of beads from Tina. 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 Tina have at first?

	Gillian	Tina	Olivia
Before	84
First game	+ 56	- 56
Second game	- 36		+ 36
		- 36	+ 36
Final game	+ 28	- 28
After	1 u	1 u	1 u

(a)
Number of beads that Gillian won from Tina
= ²₃ x 84
= 56

Number of beads that Gillian lost to Olivia
= ³₇ x 84
= 36

Number of beads that Gillian won from Tina
= ¹₃ x 84
= 28

Number of beads that Gillian had in the end
= 84 + 56 - 36 + 28
= 132

(b)
Number of beads that Tina had at first
= 1 u + 28 + 36 + 56
= 132 + 28 + 36 + 56
= 252 

Answer(s): (a) 132 ; (b) 252