Wendy, Ivory and Emily each had some marbles and decided to play a game with their marbles. In round 1, Wendy lost ¹₅ of her marbles to Ivory. In round 2, Ivory lost ¹₅ of her total number of marbles to Emily. In round 3, Emily lost ¹₅ of her total number of marbles to Wendy. In the end, Wendy, Ivory and Emily had 111, 72 and 60 marbles respectively. How many marbles did Ivory have at first?

	Wendy	Ivory	Emily
		66
Before 1	5 b
Change 1	- 1 b	+ 1 b
After 1	4 b	90
Before 2	96	5 u
Change 2		- 1 u	+ 1 u
After 2		4 u	75
Before 3			5 p
Change 3	+ 1 p		- 1 p
After 3			4 p
Comparing Wendy, Ivory and Emily in the end	111	72	60

Working backwards.

4 p = 60

1 p = 60 ÷ 4 = 15

At the start of Round 3:
Number of marbles that Emily had
= 5 p
= 5 x 15
= 75

4 u = 72

1 u = 72 ÷ 4 = 18

At the start of Round 2:
Number of marbles that Ivory had
= 5 u
= 5 x 18
= 90

At the start of Round 2:
Number of marbles that Wendy had
= 111 - 15
= 96

4 b = 96

1 b = 96 ÷ 4 = 24

At the start of Round 1:
Number of marbles that Ivory had
= 90 - 1 b
= 90 - 24
= 66

Answer(s): 66