Cindy, Jade and Wendy each had some balls and decided to play a game with their balls. In round 1, Cindy lost ¹₄ of her balls to Jade. In round 2, Jade lost ¹₄ of her total number of balls to Wendy. In round 3, Wendy lost ¹₄ of her total number of balls to Cindy. In the end, Cindy, Jade and Wendy had 142, 72 and 75 balls respectively. How many balls did Jade have at first?

	Cindy	Jade	Wendy
		57
Before 1	4 b
Change 1	- 1 b	+ 1 b
After 1	3 b	96
Before 2	117	4 u
Change 2		- 1 u	+ 1 u
After 2		3 u	100
Before 3			4 p
Change 3	+ 1 p		- 1 p
After 3			3 p
Comparing Cindy, Jade and Wendy in the end	142	72	75

Working backwards.

3 p = 75

1 p = 75 ÷ 3 = 25

At the start of Round 3:
Number of balls that Wendy had
= 4 p
= 4 x 25
= 100

3 u = 72

1 u = 72 ÷ 3 = 24

At the start of Round 2:
Number of balls that Jade had
= 4 u
= 4 x 24
= 96

At the start of Round 2:
Number of balls that Cindy had
= 142 - 25
= 117

3 b = 117

1 b = 117 ÷ 3 = 39

At the start of Round 1:
Number of balls that Jade had
= 96 - 1 b
= 96 - 39
= 57

Answer(s): 57