Yoko, Erika and Jen each had some beads and decided to play a game with their beads. In round 1, Yoko lost ¹₅ of her beads to Erika. In round 2, Erika lost ¹₅ of her total number of beads to Jen. In round 3, Jen lost ¹₅ of her total number of beads to Yoko. In the end, Yoko, Erika and Jen had 142, 80 and 56 beads respectively. How many beads did Erika have at first?

	Yoko	Erika	Jen
		68
Before 1	5 b
Change 1	- 1 b	+ 1 b
After 1	4 b	100
Before 2	128	5 u
Change 2		- 1 u	+ 1 u
After 2		4 u	70
Before 3			5 p
Change 3	+ 1 p		- 1 p
After 3			4 p
Comparing Yoko, Erika and Jen in the end	142	80	56

Working backwards.

4 p = 56

1 p = 56 ÷ 4 = 14

At the start of Round 3:
Number of beads that Jen had
= 5 p
= 5 x 14
= 70

4 u = 80

1 u = 80 ÷ 4 = 20

At the start of Round 2:
Number of beads that Erika had
= 5 u
= 5 x 20
= 100

At the start of Round 2:
Number of beads that Yoko had
= 142 - 14
= 128

4 b = 128

1 b = 128 ÷ 4 = 32

At the start of Round 1:
Number of beads that Erika had
= 100 - 1 b
= 100 - 32
= 68

Answer(s): 68