Jade, Vanessa and Victoria each had some beads and decided to play a game with their beads. In round 1, Jade lost ¹₃ of her beads to Vanessa. In round 2, Vanessa lost ¹₃ of her total number of beads to Victoria. In round 3, Victoria lost ¹₃ of her total number of beads to Jade. In the end, Jade, Vanessa and Victoria had 143, 74 and 66 beads respectively. How many beads did Vanessa have at first?

	Jade	Vanessa	Victoria
		56
Before 1	3 b
Change 1	- 1 b	+ 1 b
After 1	2 b	111
Before 2	110	3 u
Change 2		- 1 u	+ 1 u
After 2		2 u	99
Before 3			3 p
Change 3	+ 1 p		- 1 p
After 3			2 p
Comparing Jade, Vanessa and Victoria in the end	143	74	66

Working backwards.

2 p = 66

1 p = 66 ÷ 2 = 33

At the start of Round 3:
Number of beads that Victoria had
= 3 p
= 3 x 33
= 99

2 u = 74

1 u = 74 ÷ 2 = 37

At the start of Round 2:
Number of beads that Vanessa had
= 3 u
= 3 x 37
= 111

At the start of Round 2:
Number of beads that Jade had
= 143 - 33
= 110

2 b = 110

1 b = 110 ÷ 2 = 55

At the start of Round 1:
Number of beads that Vanessa had
= 111 - 1 b
= 111 - 55
= 56

Answer(s): 56