Opal, Gwen and Lucy each had some beads and decided to play a game with their beads. In round 1, Opal lost ¹₂ of her beads to Gwen. In round 2, Gwen lost ¹₂ of her total number of beads to Lucy. In round 3, Lucy lost ¹₂ of her total number of beads to Opal. In the end, Opal, Gwen and Lucy had 135, 80 and 70 beads respectively. How many beads did Gwen have at first?

	Opal	Gwen	Lucy
Before  1	2 b	95
Change 1	- 1 b	+ 1 b
After 1	1 b	160
Before 2	65	2 u
Change 2		- 1 u	+1
After 2		1 u	140
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Opal, Gwen and Lucy in the end	135	80	70

Working backwards.

1 p = 70

At the start of Round 3:
Number of beads that Lucy had
= 2 p
= 2 x 70 
= 140

At the start of Round 2:
Number of beads that Opal had
= 135 - 1 p
= 135 - 70
= 65

At the end of Round 3:
Number of beads that Gwen had = 80

1 u = 80

At the end of Round 1:
Number of beads that Gwen had
= 2 u
= 2 x 80 
= 160

1 b = 65 

At the end of Round 1:
Number of beads that Opal had = 65

At the start of Round 1:
Number of beads that Gwen had
= 160 - 1 b
= 160 - 65
= 95

Answer(s): 95