Rachel, Tina and Kylie each had some marbles and decided to play a game with their marbles. In round 1, Rachel lost ¹₂ of her marbles to Tina. In round 2, Tina lost ¹₂ of her total number of marbles to Kylie. In round 3, Kylie lost ¹₂ of her total number of marbles to Rachel. In the end, Rachel, Tina and Kylie had 118, 94 and 58 marbles respectively. How many marbles did Tina have at first?

	Rachel	Tina	Kylie
Before  1	2 b	128
Change 1	- 1 b	+ 1 b
After 1	1 b	188
Before 2	60	2 u
Change 2		- 1 u	+1
After 2		1 u	116
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Rachel, Tina and Kylie in the end	118	94	58

Working backwards.

1 p = 58

At the start of Round 3:
Number of marbles that Kylie had
= 2 p
= 2 x 58 
= 116

At the start of Round 2:
Number of marbles that Rachel had
= 118 - 1 p
= 118 - 58
= 60

At the end of Round 3:
Number of marbles that Tina had = 94

1 u = 94

At the end of Round 1:
Number of marbles that Tina had
= 2 u
= 2 x 94 
= 188

1 b = 60 

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

At the start of Round 1:
Number of marbles that Tina had
= 188 - 1 b
= 188 - 60
= 128

Answer(s): 128