Opal, Lynn and Penelope were playing with beads. Opal started with 70 beads and in the first game, she won ¹₂ more beads from Lynn. In the second game, Opal lost ⁴₇ of her original number of beads to Penelope. Lynn lost as many beads as Opal to Penelope. In the final game, Opal won ¹₅ of her original number of beads from Lynn. 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 Lynn have at first?

	Opal	Lynn	Penelope
Before	70
First game	+ 35	- 35
Second game	- 40		+ 40
		- 40	+ 40
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Opal won from Lynn
= ¹₂ x 70
= 35

Number of beads that Opal lost to Penelope
= ⁴₇ x 70
= 40

Number of beads that Opal won from Lynn
= ¹₅ x 70
= 14

Number of beads that Opal had in the end
= 70 + 35 - 40 + 14
= 79

(b)
Number of beads that Lynn had at first
= 1 u + 14 + 40 + 35
= 79 + 14 + 40 + 35
= 168 

Answer(s): (a) 79 ; (b) 168