Xylia, Jade and Eva each had some balls and decided to play a game with their balls. In round 1, Xylia lost ¹₃ of her balls to Jade. In round 2, Jade lost ¹₃ of her total number of balls to Eva. In round 3, Eva lost ¹₃ of her total number of balls to Xylia. In the end, Xylia, Jade and Eva had 149, 90 and 58 balls respectively. How many balls did Jade have at first?

	Xylia	Jade	Eva
		75
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	135
Before 2	120	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	87
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Xylia, Jade and Eva in the end	149	90	58

Working backwards.

2 p = 58

1 p = 58 ÷ 2 = 29

At the start of Round 3:
Number of balls that Eva had
= 3 p
= 3 x 29
= 87

2 u = 90

1 u = 90 ÷ 2 = 45

At the start of Round 2:
Number of balls that Jade had
= 3 u
= 3 x 45
= 135

At the start of Round 2:
Number of balls that Xylia had
= 149 - 29
= 120

2 b = 120

1 b = 120 ÷ 2 = 60

At the start of Round 1:
Number of balls that Jade had
= 135 - 1 b
= 135 - 60
= 75

Answer(s): 75