Opal, Erika and Pamela were playing with beads. Opal started with 84 beads and in the first game, she won ²₃ more beads from Erika. In the second game, Opal lost ⁶₇ of her original number of beads to Pamela. Erika lost as many beads as Opal to Pamela. In the final game, Opal won ¹₄ of her original number of beads from Erika. All of them ended up with the same number of beads.

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

	Opal	Erika	Pamela
Before	84
First game	+ 56	- 56
Second game	- 72		+ 72
		- 72	+ 72
Final game	+ 21	- 21
After	1 u	1 u	1 u

(a)
Number of beads that Opal won from Erika
= ²₃ x 84
= 56

Number of beads that Opal lost to Pamela
= ⁶₇ x 84
= 72

Number of beads that Opal won from Erika
= ¹₄ x 84
= 21

Number of beads that Opal had in the end
= 84 + 56 - 72 + 21
= 89

(b)
Number of beads that Erika had at first
= 1 u + 21 + 72 + 56
= 89 + 21 + 72 + 56
= 238 

Answer(s): (a) 89 ; (b) 238