Kimberly, Gillian and Shannon each had some balls and decided to play a game with their balls. In round 1, Kimberly lost ¹₃ of her balls to Gillian. In round 2, Gillian lost ¹₃ of her total number of balls to Shannon. In round 3, Shannon lost ¹₃ of her total number of balls to Kimberly. In the end, Kimberly, Gillian and Shannon had 120, 94 and 56 balls respectively. How many balls did Gillian have at first?

	Kimberly	Gillian	Shannon
		95
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	141
Before 2	92	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	84
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Kimberly, Gillian and Shannon in the end	120	94	56

Working backwards.

2 p = 56

1 p = 56 ÷ 2 = 28

At the start of Round 3:
Number of balls that Shannon had
= 3 p
= 3 x 28
= 84

2 u = 94

1 u = 94 ÷ 2 = 47

At the start of Round 2:
Number of balls that Gillian had
= 3 u
= 3 x 47
= 141

At the start of Round 2:
Number of balls that Kimberly had
= 120 - 28
= 92

2 b = 92

1 b = 92 ÷ 2 = 46

At the start of Round 1:
Number of balls that Gillian had
= 141 - 1 b
= 141 - 46
= 95

Answer(s): 95