Kimberly, Jaslyn and Risa each had some beads and decided to play a game with their beads. In round 1, Kimberly lost ¹₂ of her beads to Jaslyn. In round 2, Jaslyn lost ¹₂ of her total number of beads to Risa. In round 3, Risa lost ¹₂ of her total number of beads to Kimberly. In the end, Kimberly, Jaslyn and Risa had 129, 103 and 55 beads respectively. How many beads did Jaslyn have at first?

	Kimberly	Jaslyn	Risa
Before  1	2 b	132
Change 1	- 1 b	+ 1 b
After 1	1 b	206
Before 2	74	2 u
Change 2		- 1 u	+1
After 2		1 u	110
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Kimberly, Jaslyn and Risa in the end	129	103	55

Working backwards.

1 p = 55

At the start of Round 3:
Number of beads that Risa had
= 2 p
= 2 x 55 
= 110

At the start of Round 2:
Number of beads that Kimberly had
= 129 - 1 p
= 129 - 55
= 74

At the end of Round 3:
Number of beads that Jaslyn had = 103

1 u = 103

At the end of Round 1:
Number of beads that Jaslyn had
= 2 u
= 2 x 103 
= 206

1 b = 74 

At the end of Round 1:
Number of beads that Kimberly had = 74

At the start of Round 1:
Number of beads that Jaslyn had
= 206 - 1 b
= 206 - 74
= 132

Answer(s): 132