Risa, Ivory and Xuan each had some balls and decided to play a game with their balls. In round 1, Risa lost ¹₂ of her balls to Ivory. In round 2, Ivory lost ¹₂ of her total number of balls to Xuan. In round 3, Xuan lost ¹₂ of her total number of balls to Risa. In the end, Risa, Ivory and Xuan had 125, 103 and 50 balls respectively. How many balls did Ivory have at first?

	Risa	Ivory	Xuan
Before  1	2 b	131
Change 1	- 1 b	+ 1 b
After 1	1 b	206
Before 2	75	2 u
Change 2		- 1 u	+1
After 2		1 u	100
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Risa, Ivory and Xuan in the end	125	103	50

Working backwards.

1 p = 50

At the start of Round 3:
Number of balls that Xuan had
= 2 p
= 2 x 50 
= 100

At the start of Round 2:
Number of balls that Risa had
= 125 - 1 p
= 125 - 50
= 75

At the end of Round 3:
Number of balls that Ivory had = 103

1 u = 103

At the end of Round 1:
Number of balls that Ivory had
= 2 u
= 2 x 103 
= 206

1 b = 75 

At the end of Round 1:
Number of balls that Risa had = 75

At the start of Round 1:
Number of balls that Ivory had
= 206 - 1 b
= 206 - 75
= 131

Answer(s): 131