Gwen, Vanessa and Jade each had some marbles and decided to play a game with their marbles. In round 1, Gwen lost ¹₂ of her marbles to Vanessa. In round 2, Vanessa lost ¹₂ of her total number of marbles to Jade. In round 3, Jade lost ¹₂ of her total number of marbles to Gwen. In the end, Gwen, Vanessa and Jade had 121, 85 and 61 marbles respectively. How many marbles did Vanessa have at first?

	Gwen	Vanessa	Jade
Before  1	2 b	110
Change 1	- 1 b	+ 1 b
After 1	1 b	170
Before 2	60	2 u
Change 2		- 1 u	+1
After 2		1 u	122
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Gwen, Vanessa and Jade in the end	121	85	61

Working backwards.

1 p = 61

At the start of Round 3:
Number of marbles that Jade had
= 2 p
= 2 x 61 
= 122

At the start of Round 2:
Number of marbles that Gwen had
= 121 - 1 p
= 121 - 61
= 60

At the end of Round 3:
Number of marbles that Vanessa had = 85

1 u = 85

At the end of Round 1:
Number of marbles that Vanessa had
= 2 u
= 2 x 85 
= 170

1 b = 60 

At the end of Round 1:
Number of marbles that Gwen had = 60

At the start of Round 1:
Number of marbles that Vanessa had
= 170 - 1 b
= 170 - 60
= 110

Answer(s): 110