Kimberly, Cindy and Usha each had some marbles and decided to play a game with their marbles. In round 1, Kimberly lost ¹₂ of her marbles to Cindy. In round 2, Cindy lost ¹₂ of her total number of marbles to Usha. In round 3, Usha lost ¹₂ of her total number of marbles to Kimberly. In the end, Kimberly, Cindy and Usha had 113, 102 and 75 marbles respectively. How many marbles did Cindy have at first?

	Kimberly	Cindy	Usha
Before  1	2 b	166
Change 1	- 1 b	+ 1 b
After 1	1 b	204
Before 2	38	2 u
Change 2		- 1 u	+1
After 2		1 u	150
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Kimberly, Cindy and Usha in the end	113	102	75

Working backwards.

1 p = 75

At the start of Round 3:
Number of marbles that Usha had
= 2 p
= 2 x 75 
= 150

At the start of Round 2:
Number of marbles that Kimberly had
= 113 - 1 p
= 113 - 75
= 38

At the end of Round 3:
Number of marbles that Cindy had = 102

1 u = 102

At the end of Round 1:
Number of marbles that Cindy had
= 2 u
= 2 x 102 
= 204

1 b = 38 

At the end of Round 1:
Number of marbles that Kimberly had = 38

At the start of Round 1:
Number of marbles that Cindy had
= 204 - 1 b
= 204 - 38
= 166

Answer(s): 166