Shiyun, Jane and Sabrina each had some beads and decided to play a game with their beads. In round 1, Shiyun lost ¹₂ of her beads to Jane. In round 2, Jane lost ¹₂ of her total number of beads to Sabrina. In round 3, Sabrina lost ¹₂ of her total number of beads to Shiyun. In the end, Shiyun, Jane and Sabrina had 140, 88 and 71 beads respectively. How many beads did Jane have at first?

	Shiyun	Jane	Sabrina
Before  1	2 b	107
Change 1	- 1 b	+ 1 b
After 1	1 b	176
Before 2	69	2 u
Change 2		- 1 u	+1
After 2		1 u	142
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Shiyun, Jane and Sabrina in the end	140	88	71

Working backwards.

1 p = 71

At the start of Round 3:
Number of beads that Sabrina had
= 2 p
= 2 x 71 
= 142

At the start of Round 2:
Number of beads that Shiyun had
= 140 - 1 p
= 140 - 71
= 69

At the end of Round 3:
Number of beads that Jane had = 88

1 u = 88

At the end of Round 1:
Number of beads that Jane had
= 2 u
= 2 x 88 
= 176

1 b = 69 

At the end of Round 1:
Number of beads that Shiyun had = 69

At the start of Round 1:
Number of beads that Jane had
= 176 - 1 b
= 176 - 69
= 107

Answer(s): 107