Cindy, Tina and Pamela each had some balls and decided to play a game with their balls. In round 1, Cindy lost ¹₂ of her balls to Tina. In round 2, Tina lost ¹₂ of her total number of balls to Pamela. In round 3, Pamela lost ¹₂ of her total number of balls to Cindy. In the end, Cindy, Tina and Pamela had 123, 97 and 65 balls respectively. How many balls did Tina have at first?

	Cindy	Tina	Pamela
Before  1	2 b	136
Change 1	- 1 b	+ 1 b
After 1	1 b	194
Before 2	58	2 u
Change 2		- 1 u	+1
After 2		1 u	130
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Cindy, Tina and Pamela in the end	123	97	65

Working backwards.

1 p = 65

At the start of Round 3:
Number of balls that Pamela had
= 2 p
= 2 x 65 
= 130

At the start of Round 2:
Number of balls that Cindy had
= 123 - 1 p
= 123 - 65
= 58

At the end of Round 3:
Number of balls that Tina had = 97

1 u = 97

At the end of Round 1:
Number of balls that Tina had
= 2 u
= 2 x 97 
= 194

1 b = 58 

At the end of Round 1:
Number of balls that Cindy had = 58

At the start of Round 1:
Number of balls that Tina had
= 194 - 1 b
= 194 - 58
= 136

Answer(s): 136