Linda, Wendy and Hazel each had some marbles and decided to play a game with their marbles. In round 1, Linda lost ¹₂ of her marbles to Wendy. In round 2, Wendy lost ¹₂ of her total number of marbles to Hazel. In round 3, Hazel lost ¹₂ of her total number of marbles to Linda. In the end, Linda, Wendy and Hazel had 122, 83 and 74 marbles respectively. How many marbles did Wendy have at first?

	Linda	Wendy	Hazel
Before  1	2 b	118
Change 1	- 1 b	+ 1 b
After 1	1 b	166
Before 2	48	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 Linda, Wendy and Hazel in the end	122	83	74

Working backwards.

1 p = 74

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

At the start of Round 2:
Number of marbles that Linda had
= 122 - 1 p
= 122 - 74
= 48

At the end of Round 3:
Number of marbles that Wendy had = 83

1 u = 83

At the end of Round 1:
Number of marbles that Wendy had
= 2 u
= 2 x 83 
= 166

1 b = 48 

At the end of Round 1:
Number of marbles that Linda had = 48

At the start of Round 1:
Number of marbles that Wendy had
= 166 - 1 b
= 166 - 48
= 118

Answer(s): 118