Zoe, Irene and Sabrina each had some beads and decided to play a game with their beads. In round 1, Zoe lost ¹₂ of her beads to Irene. In round 2, Irene lost ¹₂ of her total number of beads to Sabrina. In round 3, Sabrina lost ¹₂ of her total number of beads to Zoe. In the end, Zoe, Irene and Sabrina had 111, 87 and 69 beads respectively. How many beads did Irene have at first?

	Zoe	Irene	Sabrina
Before  1	2 b	132
Change 1	- 1 b	+ 1 b
After 1	1 b	174
Before 2	42	2 u
Change 2		- 1 u	+1
After 2		1 u	138
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Zoe, Irene and Sabrina in the end	111	87	69

Working backwards.

1 p = 69

At the start of Round 3:
Number of beads that Sabrina had
= 2 p
= 2 x 69 
= 138

At the start of Round 2:
Number of beads that Zoe had
= 111 - 1 p
= 111 - 69
= 42

At the end of Round 3:
Number of beads that Irene had = 87

1 u = 87

At the end of Round 1:
Number of beads that Irene had
= 2 u
= 2 x 87 
= 174

1 b = 42 

At the end of Round 1:
Number of beads that Zoe had = 42

At the start of Round 1:
Number of beads that Irene had
= 174 - 1 b
= 174 - 42
= 132

Answer(s): 132