Barbara, Kimberly and Vanessa each had some balls and decided to play a game with their balls. In round 1, Barbara lost ¹₂ of her balls to Kimberly. In round 2, Kimberly lost ¹₂ of her total number of balls to Vanessa. In round 3, Vanessa lost ¹₂ of her total number of balls to Barbara. In the end, Barbara, Kimberly and Vanessa had 121, 84 and 58 balls respectively. How many balls did Kimberly have at first?

	Barbara	Kimberly	Vanessa
Before  1	2 b	105
Change 1	- 1 b	+ 1 b
After 1	1 b	168
Before 2	63	2 u
Change 2		- 1 u	+1
After 2		1 u	116
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Barbara, Kimberly and Vanessa in the end	121	84	58

Working backwards.

1 p = 58

At the start of Round 3:
Number of balls that Vanessa had
= 2 p
= 2 x 58 
= 116

At the start of Round 2:
Number of balls that Barbara had
= 121 - 1 p
= 121 - 58
= 63

At the end of Round 3:
Number of balls that Kimberly had = 84

1 u = 84

At the end of Round 1:
Number of balls that Kimberly had
= 2 u
= 2 x 84 
= 168

1 b = 63 

At the end of Round 1:
Number of balls that Barbara had = 63

At the start of Round 1:
Number of balls that Kimberly had
= 168 - 1 b
= 168 - 63
= 105

Answer(s): 105