Jen, Elyse and Ivory each had some balls and decided to play a game with their balls. In round 1, Jen lost ¹₂ of her balls to Elyse. In round 2, Elyse lost ¹₂ of her total number of balls to Ivory. In round 3, Ivory lost ¹₂ of her total number of balls to Jen. In the end, Jen, Elyse and Ivory had 120, 100 and 60 balls respectively. How many balls did Elyse have at first?

	Jen	Elyse	Ivory
Before  1	2 b	140
Change 1	- 1 b	+ 1 b
After 1	1 b	200
Before 2	60	2 u
Change 2		- 1 u	+1
After 2		1 u	120
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Jen, Elyse and Ivory in the end	120	100	60

Working backwards.

1 p = 60

At the start of Round 3:
Number of balls that Ivory had
= 2 p
= 2 x 60 
= 120

At the start of Round 2:
Number of balls that Jen had
= 120 - 1 p
= 120 - 60
= 60

At the end of Round 3:
Number of balls that Elyse had = 100

1 u = 100

At the end of Round 1:
Number of balls that Elyse had
= 2 u
= 2 x 100 
= 200

1 b = 60 

At the end of Round 1:
Number of balls that Jen had = 60

At the start of Round 1:
Number of balls that Elyse had
= 200 - 1 b
= 200 - 60
= 140

Answer(s): 140