Rachel, Anna and Pamela each had some marbles and decided to play a game with their marbles. In round 1, Rachel lost ¹₂ of her marbles to Anna. In round 2, Anna lost ¹₂ of her total number of marbles to Pamela. In round 3, Pamela lost ¹₂ of her total number of marbles to Rachel. In the end, Rachel, Anna and Pamela had 116, 85 and 74 marbles respectively. How many marbles did Anna have at first?

	Rachel	Anna	Pamela
Before  1	2 b	128
Change 1	- 1 b	+ 1 b
After 1	1 b	170
Before 2	42	2 u
Change 2		- 1 u	+1
After 2		1 u	148
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Rachel, Anna and Pamela in the end	116	85	74

Working backwards.

1 p = 74

At the start of Round 3:
Number of marbles that Pamela had
= 2 p
= 2 x 74 
= 148

At the start of Round 2:
Number of marbles that Rachel had
= 116 - 1 p
= 116 - 74
= 42

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

1 u = 85

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

1 b = 42 

At the end of Round 1:
Number of marbles that Rachel had = 42

At the start of Round 1:
Number of marbles that Anna had
= 170 - 1 b
= 170 - 42
= 128

Answer(s): 128