Shiyun, Raeann and Jean each had some marbles and decided to play a game with their marbles. In round 1, Shiyun lost ¹₃ of her marbles to Raeann. In round 2, Raeann lost ¹₃ of her total number of marbles to Jean. In round 3, Jean lost ¹₃ of her total number of marbles to Shiyun. In the end, Shiyun, Raeann and Jean had 124, 94 and 56 marbles respectively. How many marbles did Raeann have at first?

	Shiyun	Raeann	Jean
		93
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	141
Before 2	96	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	84
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Shiyun, Raeann and Jean in the end	124	94	56

Working backwards.

2 p = 56

1 p = 56 ÷ 2 = 28

At the start of Round 3:
Number of marbles that Jean had
= 3 p
= 3 x 28
= 84

2 u = 94

1 u = 94 ÷ 2 = 47

At the start of Round 2:
Number of marbles that Raeann had
= 3 u
= 3 x 47
= 141

At the start of Round 2:
Number of marbles that Shiyun had
= 124 - 28
= 96

2 b = 96

1 b = 96 ÷ 2 = 48

At the start of Round 1:
Number of marbles that Raeann had
= 141 - 1 b
= 141 - 48
= 93

Answer(s): 93