Xuan, Dana and Sabrina each had some balls and decided to play a game with their balls. In round 1, Xuan lost ¹₂ of her balls to Dana. In round 2, Dana lost ¹₂ of her total number of balls to Sabrina. In round 3, Sabrina lost ¹₂ of her total number of balls to Xuan. In the end, Xuan, Dana and Sabrina had 115, 83 and 74 balls respectively. How many balls did Dana have at first?

	Xuan	Dana	Sabrina
Before  1	2 b	125
Change 1	- 1 b	+ 1 b
After 1	1 b	166
Before 2	41	2 u
Change 2		- 1 u	+1
After 2		1 u	148
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Xuan, Dana and Sabrina in the end	115	83	74

Working backwards.

1 p = 74

At the start of Round 3:
Number of balls that Sabrina had
= 2 p
= 2 x 74 
= 148

At the start of Round 2:
Number of balls that Xuan had
= 115 - 1 p
= 115 - 74
= 41

At the end of Round 3:
Number of balls that Dana had = 83

1 u = 83

At the end of Round 1:
Number of balls that Dana had
= 2 u
= 2 x 83 
= 166

1 b = 41 

At the end of Round 1:
Number of balls that Xuan had = 41

At the start of Round 1:
Number of balls that Dana had
= 166 - 1 b
= 166 - 41
= 125

Answer(s): 125