Answer :
To determine the number of points that Tacos receive using the Borda count method, we need to allocate points based on voters' preferences. The Borda count method gives a certain number of points based on the ranking: the highest rank gets the most points, the second rank gets fewer points, and so on.
Here is the breakdown for the given survey results:
\begin{tabular}{|l|l|l|l|l|}
\hline & 8 voters & 6 voters & 3 voters & 3 voters \\
\hline First choice & Tacos & Pizza & Sandwiches & Pizza \\
\hline Second choice & Pizza & Tacos & Tacos & Sandwiches \\
\hline Third choice & Sandwiches & Sandwiches & Pizza & Tacos \\
\hline
\end{tabular}
### Points Allocation:
- 1st choice: 3 points
- 2nd choice: 2 points
- 3rd choice: 1 point
### Calculating the Borda count points for Tacos:
1. Points from First Choice Votes for Tacos:
- 8 voters choose Tacos as their 1st choice.
- Points from 1st choice: \(8 \times 3 = 24\)
2. Points from Second Choice Votes for Tacos:
- 6 voters choose Tacos as their 2nd choice.
- 3 voters choose Tacos as their 2nd choice.
- Points from 2nd choice: \( (6 + 3) \times 2 = 9 \times 2 = 18\)
3. Points from Third Choice Votes for Tacos:
- 3 voters choose Tacos as their 3rd choice.
- Points from 3rd choice: \( 3 \times 1 = 3\)
### Total Points for Tacos:
Adding up all the points from each category:
[tex]\[ 24 \text{ (First choice points)} + 18 \text{ (Second choice points)} + 3 \text{ (Third choice points)} = 45 \][/tex]
Therefore, Tacos receive 45 points using the Borda count method.
Here is the breakdown for the given survey results:
\begin{tabular}{|l|l|l|l|l|}
\hline & 8 voters & 6 voters & 3 voters & 3 voters \\
\hline First choice & Tacos & Pizza & Sandwiches & Pizza \\
\hline Second choice & Pizza & Tacos & Tacos & Sandwiches \\
\hline Third choice & Sandwiches & Sandwiches & Pizza & Tacos \\
\hline
\end{tabular}
### Points Allocation:
- 1st choice: 3 points
- 2nd choice: 2 points
- 3rd choice: 1 point
### Calculating the Borda count points for Tacos:
1. Points from First Choice Votes for Tacos:
- 8 voters choose Tacos as their 1st choice.
- Points from 1st choice: \(8 \times 3 = 24\)
2. Points from Second Choice Votes for Tacos:
- 6 voters choose Tacos as their 2nd choice.
- 3 voters choose Tacos as their 2nd choice.
- Points from 2nd choice: \( (6 + 3) \times 2 = 9 \times 2 = 18\)
3. Points from Third Choice Votes for Tacos:
- 3 voters choose Tacos as their 3rd choice.
- Points from 3rd choice: \( 3 \times 1 = 3\)
### Total Points for Tacos:
Adding up all the points from each category:
[tex]\[ 24 \text{ (First choice points)} + 18 \text{ (Second choice points)} + 3 \text{ (Third choice points)} = 45 \][/tex]
Therefore, Tacos receive 45 points using the Borda count method.
