Julie, Erika and Jade each had some balls and decided to play a game with their balls. In round 1, Julie lost ¹₃ of her balls to Erika. In round 2, Erika lost ¹₃ of her total number of balls to Jade. In round 3, Jade lost ¹₃ of her total number of balls to Julie. In the end, Julie, Erika and Jade had 121, 92 and 66 balls respectively. How many balls did Erika have at first?

	Julie	Erika	Jade
		94
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	138
Before 2	88	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 Julie, Erika and Jade in the end	121	92	66

Working backwards.

2 p = 66

1 p = 66 ÷ 2 = 33

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

2 u = 92

1 u = 92 ÷ 2 = 46

At the start of Round 2:
Number of balls that Erika had
= 3 u
= 3 x 46
= 138

At the start of Round 2:
Number of balls that Julie had
= 121 - 33
= 88

2 b = 88

1 b = 88 ÷ 2 = 44

At the start of Round 1:
Number of balls that Erika had
= 138 - 1 b
= 138 - 44
= 94

Answer(s): 94