Jean, Shannon and Gwen each had some beads and decided to play a game with their beads. In round 1, Jean lost ¹₆ of her beads to Shannon. In round 2, Shannon lost ¹₆ of her total number of beads to Gwen. In round 3, Gwen lost ¹₆ of her total number of beads to Jean. In the end, Jean, Shannon and Gwen had 111, 100 and 80 beads respectively. How many beads did Shannon have at first?

	Jean	Shannon	Gwen
		101
Before 1	6 b
Change 1	- 1 b	+ 1 b
After 1	5 b	120
Before 2	95	6 u
Change 2		- 1 u	+ 1 u
After 2		5 u	96
Before 3			6 p
Change 3	+ 1 p		- 1 p
After 3			5 p
Comparing Jean, Shannon and Gwen in the end	111	100	80

Working backwards.

5 p = 80

1 p = 80 ÷ 5 = 16

At the start of Round 3:
Number of beads that Gwen had
= 6 p
= 6 x 16
= 96

5 u = 100

1 u = 100 ÷ 5 = 20

At the start of Round 2:
Number of beads that Shannon had
= 6 u
= 6 x 20
= 120

At the start of Round 2:
Number of beads that Jean had
= 111 - 16
= 95

5 b = 95

1 b = 95 ÷ 5 = 19

At the start of Round 1:
Number of beads that Shannon had
= 120 - 1 b
= 120 - 19
= 101

Answer(s): 101