Lucy, Eva and Hilda each had some balls and decided to play a game with their balls. In round 1, Lucy lost ¹₇ of her balls to Eva. In round 2, Eva lost ¹₇ of her total number of balls to Hilda. In round 3, Hilda lost ¹₇ of her total number of balls to Lucy. In the end, Lucy, Eva and Hilda had 111, 90 and 54 balls respectively. How many balls did Eva have at first?

	Lucy	Eva	Hilda
		88
Before 1	7 b
Change 1	- 1 b	+ 1 b
After 1	6 b	105
Before 2	102	7 u
Change 2		- 1 u	+ 1 u
After 2		6 u	63
Before 3			7 p
Change 3	+ 1 p		- 1 p
After 3			6 p
Comparing Lucy, Eva and Hilda in the end	111	90	54

Working backwards.

6 p = 54

1 p = 54 ÷ 6 = 9

At the start of Round 3:
Number of balls that Hilda had
= 7 p
= 7 x 9
= 63

6 u = 90

1 u = 90 ÷ 6 = 15

At the start of Round 2:
Number of balls that Eva had
= 7 u
= 7 x 15
= 105

At the start of Round 2:
Number of balls that Lucy had
= 111 - 9
= 102

6 b = 102

1 b = 102 ÷ 6 = 17

At the start of Round 1:
Number of balls that Eva had
= 105 - 1 b
= 105 - 17
= 88

Answer(s): 88