Xuan, Sabrina and Xylia each had some beads and decided to play a game with their beads. In round 1, Xuan lost ¹₅ of her beads to Sabrina. In round 2, Sabrina lost ¹₅ of her total number of beads to Xylia. In round 3, Xylia lost ¹₅ of her total number of beads to Xuan. In the end, Xuan, Sabrina and Xylia had 124, 76 and 80 beads respectively. How many beads did Sabrina have at first?

	Xuan	Sabrina	Xylia
		69
Before 1	5 b
Change 1	- 1 b	+ 1 b
After 1	4 b	95
Before 2	104	5 u
Change 2		- 1 u	+ 1 u
After 2		4 u	100
Before 3			5 p
Change 3	+ 1 p		- 1 p
After 3			4 p
Comparing Xuan, Sabrina and Xylia in the end	124	76	80

Working backwards.

4 p = 80

1 p = 80 ÷ 4 = 20

At the start of Round 3:
Number of beads that Xylia had
= 5 p
= 5 x 20
= 100

4 u = 76

1 u = 76 ÷ 4 = 19

At the start of Round 2:
Number of beads that Sabrina had
= 5 u
= 5 x 19
= 95

At the start of Round 2:
Number of beads that Xuan had
= 124 - 20
= 104

4 b = 104

1 b = 104 ÷ 4 = 26

At the start of Round 1:
Number of beads that Sabrina had
= 95 - 1 b
= 95 - 26
= 69

Answer(s): 69