Dana, Opal and Gabby were playing with beads. Dana started with 72 beads and in the first game, she won ²₃ more beads from Opal. In the second game, Dana lost ⁵₈ of her original number of beads to Gabby. Opal lost as many beads as Dana to Gabby. In the final game, Dana 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 Dana have in the end?
2. How many beads did Opal have at first?

	Dana	Opal	Gabby
Before	72
First game	+ 48	- 48
Second game	- 45		+ 45
		- 45	+ 45
Final game	+ 18	- 18
After	1 u	1 u	1 u

(a)
Number of beads that Dana won from Opal
= ²₃ x 72
= 48

Number of beads that Dana lost to Gabby
= ⁵₈ x 72
= 45

Number of beads that Dana won from Opal
= ¹₄ x 72
= 18

Number of beads that Dana had in the end
= 72 + 48 - 45 + 18
= 93

(b)
Number of beads that Opal had at first
= 1 u + 18 + 45 + 48
= 93 + 18 + 45 + 48
= 204 

Answer(s): (a) 93 ; (b) 204