Tammy, Julie and Roshel each had some marbles and decided to play a game with their marbles. In round 1, Tammy lost ¹₃ of her marbles to Julie. In round 2, Julie lost ¹₃ of her total number of marbles to Roshel. In round 3, Roshel lost ¹₃ of her total number of marbles to Tammy. In the end, Tammy, Julie and Roshel had 123, 86 and 50 marbles respectively. How many marbles did Julie have at first?

	Tammy	Julie	Roshel
		80
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	129
Before 2	98	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	75
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Tammy, Julie and Roshel in the end	123	86	50

Working backwards.

2 p = 50

1 p = 50 ÷ 2 = 25

At the start of Round 3:
Number of marbles that Roshel had
= 3 p
= 3 x 25
= 75

2 u = 86

1 u = 86 ÷ 2 = 43

At the start of Round 2:
Number of marbles that Julie had
= 3 u
= 3 x 43
= 129

At the start of Round 2:
Number of marbles that Tammy had
= 123 - 25
= 98

2 b = 98

1 b = 98 ÷ 2 = 49

At the start of Round 1:
Number of marbles that Julie had
= 129 - 1 b
= 129 - 49
= 80

Answer(s): 80