Yen, Tammy and Fiona each had some marbles and decided to play a game with their marbles. In round 1, Yen lost ¹₂ of her marbles to Tammy. In round 2, Tammy lost ¹₂ of her total number of marbles to Fiona. In round 3, Fiona lost ¹₂ of her total number of marbles to Yen. In the end, Yen, Tammy and Fiona had 120, 92 and 67 marbles respectively. How many marbles did Tammy have at first?

	Yen	Tammy	Fiona
Before  1	2 b	131
Change 1	- 1 b	+ 1 b
After 1	1 b	184
Before 2	53	2 u
Change 2		- 1 u	+1
After 2		1 u	134
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Yen, Tammy and Fiona in the end	120	92	67

Working backwards.

1 p = 67

At the start of Round 3:
Number of marbles that Fiona had
= 2 p
= 2 x 67 
= 134

At the start of Round 2:
Number of marbles that Yen had
= 120 - 1 p
= 120 - 67
= 53

At the end of Round 3:
Number of marbles that Tammy had = 92

1 u = 92

At the end of Round 1:
Number of marbles that Tammy had
= 2 u
= 2 x 92 
= 184

1 b = 53 

At the end of Round 1:
Number of marbles that Yen had = 53

At the start of Round 1:
Number of marbles that Tammy had
= 184 - 1 b
= 184 - 53
= 131

Answer(s): 131