Question 1170871: Five candidates, Ruben, Bong, Angel, Louie and Melvin were nominated for president in the College
Student Council. After the polls close, ranked ballots were tallied, and the results are summarized
below. Determine the winner and what percent of the votes did the winner receive?
Rankings
Ruben 1 2 5 5 2 3 4
Bong 2 3 2 4 3 2 5
Angel 4 4 1 2 1 1 3
Louie 3 1 3 3 4 5 2
Melvin 5 5 4 1 5 4 1
Number of votes 10 7 12 16 11 4 10
Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website! Let's analyze the voting results using the Borda Count method, as it's often used with ranked ballots.
**1. Assign Points**
* For each ballot, assign points based on ranking:
* 1st place: 5 points
* 2nd place: 4 points
* 3rd place: 3 points
* 4th place: 2 points
* 5th place: 1 point
**2. Calculate Total Points for Each Candidate**
* **Ruben:**
* (1st place, 10 votes): 5 * 10 = 50
* (2nd place, 7 votes): 4 * 7 = 28
* (5th place, 12 votes): 1 * 12 = 12
* (5th place, 16 votes): 1 * 16 = 16
* (2nd place, 11 votes): 4 * 11 = 44
* (3rd place, 4 votes): 3 * 4 = 12
* (4th place, 10 votes): 2 * 10 = 20
* Total: 50 + 28 + 12 + 16 + 44 + 12 + 20 = 182
* **Bong:**
* (2nd place, 10 votes): 4 * 10 = 40
* (3rd place, 7 votes): 3 * 7 = 21
* (2nd place, 12 votes): 4 * 12 = 48
* (4th place, 16 votes): 2 * 16 = 32
* (3rd place, 11 votes): 3 * 11 = 33
* (2nd place, 4 votes): 4 * 4 = 16
* (5th place, 10 votes): 1 * 10 = 10
* Total: 40 + 21 + 48 + 32 + 33 + 16 + 10 = 200
* **Angel:**
* (4th place, 10 votes): 2 * 10 = 20
* (4th place, 7 votes): 2 * 7 = 14
* (1st place, 12 votes): 5 * 12 = 60
* (2nd place, 16 votes): 4 * 16 = 64
* (1st place, 11 votes): 5 * 11 = 55
* (1st place, 4 votes): 5 * 4 = 20
* (3rd place, 10 votes): 3 * 10 = 30
* Total: 20 + 14 + 60 + 64 + 55 + 20 + 30 = 263
* **Louie:**
* (3rd place, 10 votes): 3 * 10 = 30
* (1st place, 7 votes): 5 * 7 = 35
* (3rd place, 12 votes): 3 * 12 = 36
* (3rd place, 16 votes): 3 * 16 = 48
* (4th place, 11 votes): 2 * 11 = 22
* (5th place, 4 votes): 1 * 4 = 4
* (2nd place, 10 votes): 4 * 10 = 40
* Total: 30 + 35 + 36 + 48 + 22 + 4 + 40 = 215
* **Melvin:**
* (5th place, 10 votes): 1 * 10 = 10
* (5th place, 7 votes): 1 * 7 = 7
* (4th place, 12 votes): 2 * 12 = 24
* (1st place, 16 votes): 5 * 16 = 80
* (5th place, 11 votes): 1 * 11 = 11
* (4th place, 4 votes): 2 * 4 = 8
* (1st place, 10 votes): 5 * 10 = 50
* Total: 10 + 7 + 24 + 80 + 11 + 8 + 50 = 190
**3. Determine the Winner**
* Angel has the highest total points (263).
**4. Calculate Total Votes**
* Total votes: 10 + 7 + 12 + 16 + 11 + 4 + 10 = 70
**5. Calculate Percentage of Votes for Angel**
* Angel received the most points, so we need to calculate the percentage of total points Angel recieved compared to the total possible points.
* Total possible points: 5 points * 70 ballots = 350
* Angel's percentage: (263 / 350) * 100% ≈ 75.14%
**Winner:** Angel is the winner.
**Percentage:** Angel received approximately 75.14% of the possible points.
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