Gem, Opal and Ivory were playing with beads. Gem started with 70 beads and in the first game, she won ²₅ more beads from Opal. In the second game, Gem lost ³₇ of her original number of beads to Ivory. Opal lost as many beads as Gem to Ivory. In the final game, Gem won ¹₂ of her original number of beads from Opal. All of them ended up with the same number of beads.

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

	Gem	Opal	Ivory
Before	70
First game	+ 28	- 28
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 35	- 35
After	1 u	1 u	1 u

(a)
Number of beads that Gem won from Opal
= ²₅ x 70
= 28

Number of beads that Gem lost to Ivory
= ³₇ x 70
= 30

Number of beads that Gem won from Opal
= ¹₂ x 70
= 35

Number of beads that Gem had in the end
= 70 + 28 - 30 + 35
= 103

(b)
Number of beads that Opal had at first
= 1 u + 35 + 30 + 28
= 103 + 35 + 30 + 28
= 196 

Answer(s): (a) 103 ; (b) 196