Jade, Linda and Wendy each had some marbles and decided to play a game with their marbles. In round 1, Jade lost ¹₃ of her marbles to Linda. In round 2, Linda lost ¹₃ of her total number of marbles to Wendy. In round 3, Wendy lost ¹₃ of her total number of marbles to Jade. In the end, Jade, Linda and Wendy had 130, 92 and 56 marbles respectively. How many marbles did Linda have at first?

	Jade	Linda	Wendy
		87
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	138
Before 2	102	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	84
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Jade, Linda and Wendy in the end	130	92	56

Working backwards.

2 p = 56

1 p = 56 ÷ 2 = 28

At the start of Round 3:
Number of marbles that Wendy had
= 3 p
= 3 x 28
= 84

2 u = 92

1 u = 92 ÷ 2 = 46

At the start of Round 2:
Number of marbles that Linda had
= 3 u
= 3 x 46
= 138

At the start of Round 2:
Number of marbles that Jade had
= 130 - 28
= 102

2 b = 102

1 b = 102 ÷ 2 = 51

At the start of Round 1:
Number of marbles that Linda had
= 138 - 1 b
= 138 - 51
= 87

Answer(s): 87