Natalie, Tiffany and Eva each had some marbles and decided to play a game with their marbles. In round 1, Natalie lost ¹₂ of her marbles to Tiffany. In round 2, Tiffany lost ¹₂ of her total number of marbles to Eva. In round 3, Eva lost ¹₂ of her total number of marbles to Natalie. In the end, Natalie, Tiffany and Eva had 114, 94 and 62 marbles respectively. How many marbles did Tiffany have at first?

	Natalie	Tiffany	Eva
Before  1	2 b	136
Change 1	- 1 b	+ 1 b
After 1	1 b	188
Before 2	52	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 Natalie, Tiffany and Eva in the end	114	94	62

Working backwards.

1 p = 62

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

At the start of Round 2:
Number of marbles that Natalie had
= 114 - 1 p
= 114 - 62
= 52

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

1 u = 94

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

1 b = 52 

At the end of Round 1:
Number of marbles that Natalie had = 52

At the start of Round 1:
Number of marbles that Tiffany had
= 188 - 1 b
= 188 - 52
= 136

Answer(s): 136