Wendy, Penelope and Jade each had some beads and decided to play a game with their beads. In round 1, Wendy lost ¹₂ of her beads to Penelope. In round 2, Penelope lost ¹₂ of her total number of beads to Jade. In round 3, Jade lost ¹₂ of her total number of beads to Wendy. In the end, Wendy, Penelope and Jade had 137, 81 and 60 beads respectively. How many beads did Penelope have at first?

	Wendy	Penelope	Jade
Before  1	2 b	85
Change 1	- 1 b	+ 1 b
After 1	1 b	162
Before 2	77	2 u
Change 2		- 1 u	+1
After 2		1 u	120
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Wendy, Penelope and Jade in the end	137	81	60

Working backwards.

1 p = 60

At the start of Round 3:
Number of beads that Jade had
= 2 p
= 2 x 60 
= 120

At the start of Round 2:
Number of beads that Wendy had
= 137 - 1 p
= 137 - 60
= 77

At the end of Round 3:
Number of beads that Penelope had = 81

1 u = 81

At the end of Round 1:
Number of beads that Penelope had
= 2 u
= 2 x 81 
= 162

1 b = 77 

At the end of Round 1:
Number of beads that Wendy had = 77

At the start of Round 1:
Number of beads that Penelope had
= 162 - 1 b
= 162 - 77
= 85

Answer(s): 85