Vanessa, Cathy and Linda each had some balls and decided to play a game with their balls. In round 1, Vanessa lost ¹₃ of her balls to Cathy. In round 2, Cathy lost ¹₃ of her total number of balls to Linda. In round 3, Linda lost ¹₃ of her total number of balls to Vanessa. In the end, Vanessa, Cathy and Linda had 141, 88 and 66 balls respectively. How many balls did Cathy have at first?

	Vanessa	Cathy	Linda
		78
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	132
Before 2	108	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	99
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Vanessa, Cathy and Linda in the end	141	88	66

Working backwards.

2 p = 66

1 p = 66 ÷ 2 = 33

At the start of Round 3:
Number of balls that Linda had
= 3 p
= 3 x 33
= 99

2 u = 88

1 u = 88 ÷ 2 = 44

At the start of Round 2:
Number of balls that Cathy had
= 3 u
= 3 x 44
= 132

At the start of Round 2:
Number of balls that Vanessa had
= 141 - 33
= 108

2 b = 108

1 b = 108 ÷ 2 = 54

At the start of Round 1:
Number of balls that Cathy had
= 132 - 1 b
= 132 - 54
= 78

Answer(s): 78