Dana, Lynn and Hazel each had some marbles and decided to play a game with their marbles. In round 1, Dana lost ¹₂ of her marbles to Lynn. In round 2, Lynn lost ¹₂ of her total number of marbles to Hazel. In round 3, Hazel lost ¹₂ of her total number of marbles to Dana. In the end, Dana, Lynn and Hazel had 119, 96 and 54 marbles respectively. How many marbles did Lynn have at first?

	Dana	Lynn	Hazel
Before  1	2 b	127
Change 1	- 1 b	+ 1 b
After 1	1 b	192
Before 2	65	2 u
Change 2		- 1 u	+1
After 2		1 u	108
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Dana, Lynn and Hazel in the end	119	96	54

Working backwards.

1 p = 54

At the start of Round 3:
Number of marbles that Hazel had
= 2 p
= 2 x 54 
= 108

At the start of Round 2:
Number of marbles that Dana had
= 119 - 1 p
= 119 - 54
= 65

At the end of Round 3:
Number of marbles that Lynn had = 96

1 u = 96

At the end of Round 1:
Number of marbles that Lynn had
= 2 u
= 2 x 96 
= 192

1 b = 65 

At the end of Round 1:
Number of marbles that Dana had = 65

At the start of Round 1:
Number of marbles that Lynn had
= 192 - 1 b
= 192 - 65
= 127

Answer(s): 127