Emma, Esther and Gem were playing with beads. Emma started with 72 beads and in the first game, she won ³₄ more beads from Esther. In the second game, Emma lost ¹₈ of her original number of beads to Gem. Esther lost as many beads as Emma to Gem. In the final game, Emma won ¹₂ of her original number of beads from Esther. All of them ended up with the same number of beads.

1. How many beads did Emma have in the end?
2. How many beads did Esther have at first?

	Emma	Esther	Gem
Before	72
First game	+ 54	- 54
Second game	- 9		+ 9
		- 9	+ 9
Final game	+ 36	- 36
After	1 u	1 u	1 u

(a)
Number of beads that Emma won from Esther
= ³₄ x 72
= 54

Number of beads that Emma lost to Gem
= ¹₈ x 72
= 9

Number of beads that Emma won from Esther
= ¹₂ x 72
= 36

Number of beads that Emma had in the end
= 72 + 54 - 9 + 36
= 153

(b)
Number of beads that Esther had at first
= 1 u + 36 + 9 + 54
= 153 + 36 + 9 + 54
= 252 

Answer(s): (a) 153 ; (b) 252