Gillian, Yen and Cindy each had some beads and decided to play a game with their beads. In round 1, Gillian lost ¹₄ of her beads to Yen. In round 2, Yen lost ¹₄ of her total number of beads to Cindy. In round 3, Cindy lost ¹₄ of her total number of beads to Gillian. In the end, Gillian, Yen and Cindy had 116, 78 and 60 beads respectively. How many beads did Yen have at first?

	Gillian	Yen	Cindy
		72
Before 1	4 b
Change 1	- 1 b	+ 1 b
After 1	3 b	104
Before 2	96	4 u
Change 2		- 1 u	+ 1 u
After 2		3 u	80
Before 3			4 p
Change 3	+ 1 p		- 1 p
After 3			3 p
Comparing Gillian, Yen and Cindy in the end	116	78	60

Working backwards.

3 p = 60

1 p = 60 ÷ 3 = 20

At the start of Round 3:
Number of beads that Cindy had
= 4 p
= 4 x 20
= 80

3 u = 78

1 u = 78 ÷ 3 = 26

At the start of Round 2:
Number of beads that Yen had
= 4 u
= 4 x 26
= 104

At the start of Round 2:
Number of beads that Gillian had
= 116 - 20
= 96

3 b = 96

1 b = 96 ÷ 3 = 32

At the start of Round 1:
Number of beads that Yen had
= 104 - 1 b
= 104 - 32
= 72

Answer(s): 72