Lynn, Usha and Sabrina each had some beads and decided to play a game with their beads. In round 1, Lynn lost ¹₂ of her beads to Usha. In round 2, Usha lost ¹₂ of her total number of beads to Sabrina. In round 3, Sabrina lost ¹₂ of her total number of beads to Lynn. In the end, Lynn, Usha and Sabrina had 134, 105 and 75 beads respectively. How many beads did Usha have at first?

	Lynn	Usha	Sabrina
Before  1	2 b	151
Change 1	- 1 b	+ 1 b
After 1	1 b	210
Before 2	59	2 u
Change 2		- 1 u	+1
After 2		1 u	150
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Lynn, Usha and Sabrina in the end	134	105	75

Working backwards.

1 p = 75

At the start of Round 3:
Number of beads that Sabrina had
= 2 p
= 2 x 75 
= 150

At the start of Round 2:
Number of beads that Lynn had
= 134 - 1 p
= 134 - 75
= 59

At the end of Round 3:
Number of beads that Usha had = 105

1 u = 105

At the end of Round 1:
Number of beads that Usha had
= 2 u
= 2 x 105 
= 210

1 b = 59 

At the end of Round 1:
Number of beads that Lynn had = 59

At the start of Round 1:
Number of beads that Usha had
= 210 - 1 b
= 210 - 59
= 151

Answer(s): 151