Tammy, Usha and Wendy 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 Wendy. In round 3, Wendy lost ¹₂ of her total number of balls to Tammy. In the end, Tammy, Usha and Wendy had 129, 93 and 61 balls respectively. How many balls did Usha have at first?

	Tammy	Usha	Wendy
Before  1	2 b	118
Change 1	- 1 b	+ 1 b
After 1	1 b	186
Before 2	68	2 u
Change 2		- 1 u	+1
After 2		1 u	122
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Tammy, Usha and Wendy in the end	129	93	61

Working backwards.

1 p = 61

At the start of Round 3:
Number of balls that Wendy had
= 2 p
= 2 x 61 
= 122

At the start of Round 2:
Number of balls that Tammy had
= 129 - 1 p
= 129 - 61
= 68

At the end of Round 3:
Number of balls that Usha had = 93

1 u = 93

At the end of Round 1:
Number of balls that Usha had
= 2 u
= 2 x 93 
= 186

1 b = 68 

At the end of Round 1:
Number of balls that Tammy had = 68

At the start of Round 1:
Number of balls that Usha had
= 186 - 1 b
= 186 - 68
= 118

Answer(s): 118