Usha, Opal and Fanny were playing with beads. Usha started with 96 beads and in the first game, she won ³₄ more beads from Opal. In the second game, Usha lost ³₈ of her original number of beads to Fanny. Opal lost as many beads as Usha to Fanny. In the final game, Usha won ¹₃ of her original number of beads from Opal. All of them ended up with the same number of beads.

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

	Usha	Opal	Fanny
Before	96
First game	+ 72	- 72
Second game	- 36		+ 36
		- 36	+ 36
Final game	+ 32	- 32
After	1 u	1 u	1 u

(a)
Number of beads that Usha won from Opal
= ³₄ x 96
= 72

Number of beads that Usha lost to Fanny
= ³₈ x 96
= 36

Number of beads that Usha won from Opal
= ¹₃ x 96
= 32

Number of beads that Usha had in the end
= 96 + 72 - 36 + 32
= 164

(b)
Number of beads that Opal had at first
= 1 u + 32 + 36 + 72
= 164 + 32 + 36 + 72
= 304 

Answer(s): (a) 164 ; (b) 304