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You have uploaded two images, each showing a table of preferences and a voting scenario based on **Borda's method**. I'll guide you through the solution for both of them.

### First Image (Basketball team captain):

The table lists the preference rankings for **Cardona, Pitts-Jones, De Plata, and Vincent**, with corresponding numbers of voters. 

- **Step 1: Assign Borda scores**  
  Using Borda's method, points are awarded based on rank. If there are 4 candidates:
  - 1st choice gets 3 points,
  - 2nd choice gets 2 points,
  - 3rd choice gets 1 point,
  - 4th choice gets 0 points.

- **Step 2: Calculate Borda Scores**
  We need to multiply the number of voters for each ranking by the points given in Borda's system:

For **Cardona**:
- (3 points) x 1 voter = 3
- (2 points) x 4 voters = 8
- (1 point) x 1 voter = 1
- (0 points) x 2 voters = 0  
Total: \( 3 + 8 + 1 = 12 \)

For **Pitts-Jones**:
- (3 points) x 4 voters = 12
- (2 points) x 1 voter = 2
- (1 point) x 1 voter = 1
- (0 points) x 2 voters = 0  
Total: \( 12 + 2 + 1 = 15 \)

For **De Plata**:
- (3 points) x 1 voter = 3
- (2 points) x 2 voters = 4
- (1 point) x 4 voters = 4
- (0 points) x 1 voter = 0  
Total: \( 3 + 4 + 4 = 11 \)

For **Vincent**:
- (3 points) x 2 voters = 6
- (2 points) x 1 voter = 2
- (1 point) x 2 voters = 2
- (0 points) x 3 voters = 0  
Total: \( 6 + 2 + 2 = 10 \)

- **Step 3: Determine the Winner**
  The Borda scores are:
  - Cardona: 12 points
  - Pitts-Jones: 15 points
  - De Plata: 11 points
  - Vincent: 10 points
  
Thus, **Pitts-Jones** wins with 15 points.

---

### Second Image (School mascot voting):

In this table, the candidates are **Thomas, Walker, and Goodman**.

- **Step 1: Assign Borda scores**
  Since there are 3 candidates:
  - 1st choice gets 2 points,
  - 2nd choice gets 1 point,
  - 3rd choice gets 0 points.

- **Step 2: Calculate Borda Scores**

For **Thomas**:
- (2 points) x 3 voters = 6
- (1 point) x 2 voters = 2
- (0 points) x 3 voters = 0  
Total: \( 6 + 2 = 8 \)

For **Walker**:
- (2 points) x 1 voter = 2
- (1 point) x 3 voters = 3
- (0 points) x 4 voters = 0  
Total: \( 2 + 3 = 5 \)

For **Goodman**:
- (2 points) x 2 voters = 4
- (1 point) x 4 voters = 4
- (0 points) x 2 voters = 0  
Total: \( 4 + 4 = 8 \)

- **Step 3: Determine the Winner**
  The Borda scores are:
  - Thomas: 8 points
  - Walker: 5 points
  - Goodman: 8 points
  
There is a **tie** between **Thomas** and **Goodman** with 8 points each.

---

Would you like more details on any steps? Here are 5 related questions for deeper exploration:

1. What is the Borda count method, and how does it compare to other voting systems like plurality?
2. What happens in case of a tie in Borda count, and how can a winner be determined?
3. Can the Borda method lead to different outcomes if voters rank more than three or four candidates?
4. Why is the Borda method considered a "consensus" voting method?
5. How would the outcome change if there were more voters or different preferences?

**Tip:** Borda's method is designed to find a broadly acceptable candidate rather than just the most popular first choice.

Solve voting problems using Borda Count in a preference voting scenario. Learn how to assign points based on rankings and voter preferences for candidates, such as Cardona, Pitts-Jones, and more. Ideal for high school students in Grades 9-12.

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