Fanny, Victoria and Sarah each had some marbles and decided to play a game with their marbles. In round 1, Fanny lost ¹₅ of her marbles to Victoria. In round 2, Victoria lost ¹₅ of her total number of marbles to Sarah. In round 3, Sarah lost ¹₅ of her total number of marbles to Fanny. In the end, Fanny, Victoria and Sarah had 126, 96 and 72 marbles respectively. How many marbles did Victoria have at first?

	Fanny	Victoria	Sarah
		93
Before 1	5 b
Change 1	- 1 b	+ 1 b
After 1	4 b	120
Before 2	108	5 u
Change 2		- 1 u	+ 1 u
After 2		4 u	90
Before 3			5 p
Change 3	+ 1 p		- 1 p
After 3			4 p
Comparing Fanny, Victoria and Sarah in the end	126	96	72

Working backwards.

4 p = 72

1 p = 72 ÷ 4 = 18

At the start of Round 3:
Number of marbles that Sarah had
= 5 p
= 5 x 18
= 90

4 u = 96

1 u = 96 ÷ 4 = 24

At the start of Round 2:
Number of marbles that Victoria had
= 5 u
= 5 x 24
= 120

At the start of Round 2:
Number of marbles that Fanny had
= 126 - 18
= 108

4 b = 108

1 b = 108 ÷ 4 = 27

At the start of Round 1:
Number of marbles that Victoria had
= 120 - 1 b
= 120 - 27
= 93

Answer(s): 93