Olivia, Opal and Jean each had some marbles and decided to play a game with their marbles. In round 1, Olivia lost ¹₂ of her marbles to Opal. In round 2, Opal lost ¹₂ of her total number of marbles to Jean. In round 3, Jean lost ¹₂ of her total number of marbles to Olivia. In the end, Olivia, Opal and Jean had 125, 86 and 71 marbles respectively. How many marbles did Opal have at first?

	Olivia	Opal	Jean
Before  1	2 b	118
Change 1	- 1 b	+ 1 b
After 1	1 b	172
Before 2	54	2 u
Change 2		- 1 u	+1
After 2		1 u	142
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Olivia, Opal and Jean in the end	125	86	71

Working backwards.

1 p = 71

At the start of Round 3:
Number of marbles that Jean had
= 2 p
= 2 x 71 
= 142

At the start of Round 2:
Number of marbles that Olivia had
= 125 - 1 p
= 125 - 71
= 54

At the end of Round 3:
Number of marbles that Opal had = 86

1 u = 86

At the end of Round 1:
Number of marbles that Opal had
= 2 u
= 2 x 86 
= 172

1 b = 54 

At the end of Round 1:
Number of marbles that Olivia had = 54

At the start of Round 1:
Number of marbles that Opal had
= 172 - 1 b
= 172 - 54
= 118

Answer(s): 118