Eva, Raeann and Emily each had some balls and decided to play a game with their balls. In round 1, Eva lost ¹₂ of her balls to Raeann. In round 2, Raeann lost ¹₂ of her total number of balls to Emily. In round 3, Emily lost ¹₂ of her total number of balls to Eva. In the end, Eva, Raeann and Emily had 133, 87 and 66 balls respectively. How many balls did Raeann have at first?

	Eva	Raeann	Emily
Before  1	2 b	107
Change 1	- 1 b	+ 1 b
After 1	1 b	174
Before 2	67	2 u
Change 2		- 1 u	+1
After 2		1 u	132
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Eva, Raeann and Emily in the end	133	87	66

Working backwards.

1 p = 66

At the start of Round 3:
Number of balls that Emily had
= 2 p
= 2 x 66 
= 132

At the start of Round 2:
Number of balls that Eva had
= 133 - 1 p
= 133 - 66
= 67

At the end of Round 3:
Number of balls that Raeann had = 87

1 u = 87

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

1 b = 67 

At the end of Round 1:
Number of balls that Eva had = 67

At the start of Round 1:
Number of balls that Raeann had
= 174 - 1 b
= 174 - 67
= 107

Answer(s): 107