Raeann, Linda and Cathy each had some balls and decided to play a game with their balls. In round 1, Raeann lost ¹₄ of her balls to Linda. In round 2, Linda lost ¹₄ of her total number of balls to Cathy. In round 3, Cathy lost ¹₄ of her total number of balls to Raeann. In the end, Raeann, Linda and Cathy had 140, 75 and 78 balls respectively. How many balls did Linda have at first?

	Raeann	Linda	Cathy
		62
Before 1	4 b
Change 1	- 1 b	+ 1 b
After 1	3 b	100
Before 2	114	4 u
Change 2		- 1 u	+ 1 u
After 2		3 u	104
Before 3			4 p
Change 3	+ 1 p		- 1 p
After 3			3 p
Comparing Raeann, Linda and Cathy in the end	140	75	78

Working backwards.

3 p = 78

1 p = 78 ÷ 3 = 26

At the start of Round 3:
Number of balls that Cathy had
= 4 p
= 4 x 26
= 104

3 u = 75

1 u = 75 ÷ 3 = 25

At the start of Round 2:
Number of balls that Linda had
= 4 u
= 4 x 25
= 100

At the start of Round 2:
Number of balls that Raeann had
= 140 - 26
= 114

3 b = 114

1 b = 114 ÷ 3 = 38

At the start of Round 1:
Number of balls that Linda had
= 100 - 1 b
= 100 - 38
= 62

Answer(s): 62