Cathy, Gillian and Jane each had some marbles and decided to play a game with their marbles. In round 1, Cathy lost ¹₂ of her marbles to Gillian. In round 2, Gillian lost ¹₂ of her total number of marbles to Jane. In round 3, Jane lost ¹₂ of her total number of marbles to Cathy. In the end, Cathy, Gillian and Jane had 112, 96 and 62 marbles respectively. How many marbles did Gillian have at first?

	Cathy	Gillian	Jane
Before  1	2 b	142
Change 1	- 1 b	+ 1 b
After 1	1 b	192
Before 2	50	2 u
Change 2		- 1 u	+1
After 2		1 u	124
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Cathy, Gillian and Jane in the end	112	96	62

Working backwards.

1 p = 62

At the start of Round 3:
Number of marbles that Jane had
= 2 p
= 2 x 62 
= 124

At the start of Round 2:
Number of marbles that Cathy had
= 112 - 1 p
= 112 - 62
= 50

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

1 u = 96

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

1 b = 50 

At the end of Round 1:
Number of marbles that Cathy had = 50

At the start of Round 1:
Number of marbles that Gillian had
= 192 - 1 b
= 192 - 50
= 142

Answer(s): 142