Xandra, Pamela and Barbara each had some beads and decided to play a game with their beads. In round 1, Xandra lost ¹₅ of her beads to Pamela. In round 2, Pamela lost ¹₅ of her total number of beads to Barbara. In round 3, Barbara lost ¹₅ of her total number of beads to Xandra. In the end, Xandra, Pamela and Barbara had 127, 96 and 76 beads respectively. How many beads did Pamela have at first?

	Xandra	Pamela	Barbara
		93
Before 1	5 b
Change 1	- 1 b	+ 1 b
After 1	4 b	120
Before 2	108	5 u
Change 2		- 1 u	+ 1 u
After 2		4 u	95
Before 3			5 p
Change 3	+ 1 p		- 1 p
After 3			4 p
Comparing Xandra, Pamela and Barbara in the end	127	96	76

Working backwards.

4 p = 76

1 p = 76 ÷ 4 = 19

At the start of Round 3:
Number of beads that Barbara had
= 5 p
= 5 x 19
= 95

4 u = 96

1 u = 96 ÷ 4 = 24

At the start of Round 2:
Number of beads that Pamela had
= 5 u
= 5 x 24
= 120

At the start of Round 2:
Number of beads that Xandra had
= 127 - 19
= 108

4 b = 108

1 b = 108 ÷ 4 = 27

At the start of Round 1:
Number of beads that Pamela had
= 120 - 1 b
= 120 - 27
= 93

Answer(s): 93