Jaslyn, Victoria and Lynn each had some marbles and decided to play a game with their marbles. In round 1, Jaslyn lost ¹₂ of her marbles to Victoria. In round 2, Victoria lost ¹₂ of her total number of marbles to Lynn. In round 3, Lynn lost ¹₂ of her total number of marbles to Jaslyn. In the end, Jaslyn, Victoria and Lynn had 130, 101 and 55 marbles respectively. How many marbles did Victoria have at first?

	Jaslyn	Victoria	Lynn
Before  1	2 b	127
Change 1	- 1 b	+ 1 b
After 1	1 b	202
Before 2	75	2 u
Change 2		- 1 u	+1
After 2		1 u	110
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Jaslyn, Victoria and Lynn in the end	130	101	55

Working backwards.

1 p = 55

At the start of Round 3:
Number of marbles that Lynn had
= 2 p
= 2 x 55 
= 110

At the start of Round 2:
Number of marbles that Jaslyn had
= 130 - 1 p
= 130 - 55
= 75

At the end of Round 3:
Number of marbles that Victoria had = 101

1 u = 101

At the end of Round 1:
Number of marbles that Victoria had
= 2 u
= 2 x 101 
= 202

1 b = 75 

At the end of Round 1:
Number of marbles that Jaslyn had = 75

At the start of Round 1:
Number of marbles that Victoria had
= 202 - 1 b
= 202 - 75
= 127

Answer(s): 127