Tammy, Usha and Anna each had some balls and decided to play a game with their balls. In round 1, Tammy lost ¹₂ of her balls to Usha. In round 2, Usha lost ¹₂ of her total number of balls to Anna. In round 3, Anna lost ¹₂ of her total number of balls to Tammy. In the end, Tammy, Usha and Anna had 115, 96 and 72 balls respectively. How many balls did Usha have at first?

	Tammy	Usha	Anna
Before  1	2 b	149
Change 1	- 1 b	+ 1 b
After 1	1 b	192
Before 2	43	2 u
Change 2		- 1 u	+1
After 2		1 u	144
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Tammy, Usha and Anna in the end	115	96	72

Working backwards.

1 p = 72

At the start of Round 3:
Number of balls that Anna had
= 2 p
= 2 x 72 
= 144

At the start of Round 2:
Number of balls that Tammy had
= 115 - 1 p
= 115 - 72
= 43

At the end of Round 3:
Number of balls that Usha had = 96

1 u = 96

At the end of Round 1:
Number of balls that Usha had
= 2 u
= 2 x 96 
= 192

1 b = 43 

At the end of Round 1:
Number of balls that Tammy had = 43

At the start of Round 1:
Number of balls that Usha had
= 192 - 1 b
= 192 - 43
= 149

Answer(s): 149