Esther, Yen and Fanny were playing with beads. Esther started with 72 beads and in the first game, she won ²₃ more beads from Yen. In the second game, Esther lost ¹₈ of her original number of beads to Fanny. Yen lost as many beads as Esther to Fanny. In the final game, Esther won ¹₂ of her original number of beads from Yen. All of them ended up with the same number of beads.

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

	Esther	Yen	Fanny
Before	72
First game	+ 48	- 48
Second game	- 9		+ 9
		- 9	+ 9
Final game	+ 36	- 36
After	1 u	1 u	1 u

(a)
Number of beads that Esther won from Yen
= ²₃ x 72
= 48

Number of beads that Esther lost to Fanny
= ¹₈ x 72
= 9

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

Number of beads that Esther had in the end
= 72 + 48 - 9 + 36
= 147

(b)
Number of beads that Yen had at first
= 1 u + 36 + 9 + 48
= 147 + 36 + 9 + 48
= 240 

Answer(s): (a) 147 ; (b) 240