Mary, Esther and Jaslyn each had some marbles and decided to play a game with their marbles. In round 1, Mary lost ¹₃ of her marbles to Esther. In round 2, Esther lost ¹₃ of her total number of marbles to Jaslyn. In round 3, Jaslyn lost ¹₃ of her total number of marbles to Mary. In the end, Mary, Esther and Jaslyn had 142, 96 and 80 marbles respectively. How many marbles did Esther have at first?

	Mary	Esther	Jaslyn
		93
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	144
Before 2	102	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	120
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Mary, Esther and Jaslyn in the end	142	96	80

Working backwards.

2 p = 80

1 p = 80 ÷ 2 = 40

At the start of Round 3:
Number of marbles that Jaslyn had
= 3 p
= 3 x 40
= 120

2 u = 96

1 u = 96 ÷ 2 = 48

At the start of Round 2:
Number of marbles that Esther had
= 3 u
= 3 x 48
= 144

At the start of Round 2:
Number of marbles that Mary had
= 142 - 40
= 102

2 b = 102

1 b = 102 ÷ 2 = 51

At the start of Round 1:
Number of marbles that Esther had
= 144 - 1 b
= 144 - 51
= 93

Answer(s): 93