Kathy, Tina and Mary each had some balls and decided to play a game with their balls. In round 1, Kathy lost ¹₃ of her balls to Tina. In round 2, Tina lost ¹₃ of her total number of balls to Mary. In round 3, Mary lost ¹₃ of her total number of balls to Kathy. In the end, Kathy, Tina and Mary had 133, 84 and 74 balls respectively. How many balls did Tina have at first?

	Kathy	Tina	Mary
		78
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	126
Before 2	96	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	111
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Kathy, Tina and Mary in the end	133	84	74

Working backwards.

2 p = 74

1 p = 74 ÷ 2 = 37

At the start of Round 3:
Number of balls that Mary had
= 3 p
= 3 x 37
= 111

2 u = 84

1 u = 84 ÷ 2 = 42

At the start of Round 2:
Number of balls that Tina had
= 3 u
= 3 x 42
= 126

At the start of Round 2:
Number of balls that Kathy had
= 133 - 37
= 96

2 b = 96

1 b = 96 ÷ 2 = 48

At the start of Round 1:
Number of balls that Tina had
= 126 - 1 b
= 126 - 48
= 78

Answer(s): 78