Penelope, Emma and Tina each had some balls and decided to play a game with their balls. In round 1, Penelope lost ¹₂ of her balls to Emma. In round 2, Emma lost ¹₂ of her total number of balls to Tina. In round 3, Tina lost ¹₂ of her total number of balls to Penelope. In the end, Penelope, Emma and Tina had 121, 101 and 61 balls respectively. How many balls did Emma have at first?

	Penelope	Emma	Tina
Before  1	2 b	142
Change 1	- 1 b	+ 1 b
After 1	1 b	202
Before 2	60	2 u
Change 2		- 1 u	+1
After 2		1 u	122
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Penelope, Emma and Tina in the end	121	101	61

Working backwards.

1 p = 61

At the start of Round 3:
Number of balls that Tina had
= 2 p
= 2 x 61 
= 122

At the start of Round 2:
Number of balls that Penelope had
= 121 - 1 p
= 121 - 61
= 60

At the end of Round 3:
Number of balls that Emma had = 101

1 u = 101

At the end of Round 1:
Number of balls that Emma had
= 2 u
= 2 x 101 
= 202

1 b = 60 

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

At the start of Round 1:
Number of balls that Emma had
= 202 - 1 b
= 202 - 60
= 142

Answer(s): 142