Zara, Marion and Sabrina each had some balls and decided to play a game with their balls. In round 1, Zara lost ¹₃ of her balls to Marion. In round 2, Marion lost ¹₃ of her total number of balls to Sabrina. In round 3, Sabrina lost ¹₃ of her total number of balls to Zara. In the end, Zara, Marion and Sabrina had 139, 100 and 78 balls respectively. How many balls did Marion have at first?

	Zara	Marion	Sabrina
		100
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	150
Before 2	100	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	117
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Zara, Marion and Sabrina in the end	139	100	78

Working backwards.

2 p = 78

1 p = 78 ÷ 2 = 39

At the start of Round 3:
Number of balls that Sabrina had
= 3 p
= 3 x 39
= 117

2 u = 100

1 u = 100 ÷ 2 = 50

At the start of Round 2:
Number of balls that Marion had
= 3 u
= 3 x 50
= 150

At the start of Round 2:
Number of balls that Zara had
= 139 - 39
= 100

2 b = 100

1 b = 100 ÷ 2 = 50

At the start of Round 1:
Number of balls that Marion had
= 150 - 1 b
= 150 - 50
= 100

Answer(s): 100