Consider the weighted voting system [75: 31, 29, 23, 16, 8, 7]. Find each:
a. The total number of players
b. The total number of votes
c. The weight of P3
d. The minimum percentage of the votes needed to pass a motion 9rounded to the next whole percent)
This is for my general education math homework of which I have 10 questions similar to this, any help would be appreciated.
Sure! I would be happy to help you with these questions.
a. To find the total number of players, you need to count the number of elements in the weighted voting system. In this case, the system has 6 players: P1, P2, P3, P4, P5, and P6.
b. To find the total number of votes, you need to sum up the weights of all the players. In this case, the total number of votes can be calculated by adding up the numbers in the brackets: 31 + 29 + 23 + 16 + 8 + 7 = 114.
c. To find the weight of P3, you need to look at the number corresponding to P3 in the weighted voting system. In this case, the weight of P3 is 23.
d. To calculate the minimum percentage of the votes needed to pass a motion, you need to find the majority of the total number of votes. The majority is defined as more than half of the total votes.
In this case, the total number of votes is 114. To find the minimum percentage needed to pass a motion, divide half of the total votes by the total number of votes, and then multiply by 100.
(50/114) * 100 = 43.8596 (rounded to 43%)
So, the minimum percentage of votes needed to pass a motion is 43%.