Barbara, Opal and Usha were playing with beads. Barbara started with 84 beads and in the first game, she won ¹₃ more beads from Opal. In the second game, Barbara lost ⁶₇ of her original number of beads to Usha. Opal lost as many beads as Barbara to Usha. In the final game, Barbara won ¹₄ of her original number of beads from Opal. All of them ended up with the same number of beads.

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

	Barbara	Opal	Usha
Before	84
First game	+ 28	- 28
Second game	- 72		+ 72
		- 72	+ 72
Final game	+ 21	- 21
After	1 u	1 u	1 u

(a)
Number of beads that Barbara won from Opal
= ¹₃ x 84
= 28

Number of beads that Barbara lost to Usha
= ⁶₇ x 84
= 72

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

Number of beads that Barbara had in the end
= 84 + 28 - 72 + 21
= 61

(b)
Number of beads that Opal had at first
= 1 u + 21 + 72 + 28
= 61 + 21 + 72 + 28
= 182 

Answer(s): (a) 61 ; (b) 182