The managers of Prints Alive (a local silk-screening business) are planning a party for their 30 employees. There are three possible locations for the party: the warehouse (W), the park (P), or the beach (B). The employees are asked to rank these choices in order of preference, and the results are summarized in the table.Number of Ballots Cast6 7 12 51st choice P P B W2nd choice B W W B3rd choice W B P P(a) How many votes were cast? votes(b) Use the plurality method of voting to determine the winner.the beachthe park the warehouse(c) What percent of the votes did the winner in part (b) receive? (Round your answer to the nearest whole number.) %
Question
The managers of Prints Alive (a local silk-screening business) are planning a party for their 30 employees. There are three possible locations for the party: the warehouse (W), the park (P), or the beach (B). The employees are asked to rank these choices in order of preference, and the results are summarized in the table.Number of Ballots Cast6 7 12 51st choice P P B W2nd choice B W W B3rd choice W B P P(a) How many votes were cast? votes(b) Use the plurality method of voting to determine the winner.the beachthe park the warehouse(c) What percent of the votes did the winner in part (b) receive? (Round your answer to the nearest whole number.) %
Solution
(a) To determine the total number of votes cast, we need to sum the number of ballots in each column of the table.
Number of Ballots Cast:
- 6
- 7
- 12
- 5
Total votes = 6 + 7 + 12 + 5 = 30 votes
(b) Using the plurality method, we count the number of first-choice votes each location received.
- Park (P): 6 + 7 = 13 votes
- Beach (B): 12 votes
- Warehouse (W): 5 votes
The location with the most first-choice votes is the park (P) with 13 votes.
(c) To find the percentage of votes the winner received, we use the formula:
Percentage = (Number of votes for the winner / Total number of votes) * 100
For the park (P): Percentage = (13 / 30) * 100 ≈ 43.33%
Rounded to the nearest whole number, the park received 43% of the votes.
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