Let's break down the question step by step and address the potential answers.
We need to provide a detailed solution for a given question related to calculating parking fees based on certain conditions. Here's the step-by-step breakdown:
### Given Information
1. Initial Fee for the First Two Hours: [tex]$8
2. Hourly Fee After the First Two Hours: $[/tex]2 per hour
3. Total Hours Parked: 14 hours
### Calculation Steps
1. Step 1: Calculating the Fee for the First Two Hours
- The fee for the first two hours of parking is fixed at [tex]$8.
2. Step 2: Determining the Remaining Hours
- The total parking time is 14 hours.
- Since we have already calculated the fee for the first 2 hours, we need to find the remaining hours by subtracting 2 from the total hours.
- Remaining Hours = Total Hours - First Two Hours = 14 - 2 = 12 hours.
3. Step 3: Calculating the Fee for the Remaining Hours
- The fee for each hour after the first two hours is $[/tex]2.
- Remaining Hours Fee = Remaining Hours Hourly Fee After Two Hours = 12 [tex]$2 = $[/tex]24.
4. Step 4: Calculating the Total Parking Fee
- The total parking fee is the sum of the fee for the first two hours and the fee for the remaining hours.
- Total Parking Fee = First Two Hours Fee + Remaining Hours Fee
- Total Parking Fee = [tex]$8 + $[/tex]24 = [tex]$32.
### Summary of Results
- First Two Hours Fee: $[/tex]8
- Remaining Hours: 12 hours
- Remaining Hours Fee: [tex]$24
- Total Parking Fee: $[/tex]32
By following these steps, we have comprehensively determined how the total parking fee of [tex]$32 is calculated.
### Evaluating the Sample Response
- Student B is correct.
- Reasoning: The response correctly identifies that as per the calculations, tickets sold represent the input \((x)\) and the donation amount \(y\) is correctly represented by the equation $[/tex]5 = \frac{1}{2}(10)[tex]$, which aligns with the output of the valid `B` explanation provided in the example above.
### Select All That Apply
1. Student B is correct because the tickets sold represent the input \((x)\) and the amount donated represents the output \((y)\).
2. Student B is correct because the donated amount is represented by $[/tex]5 = \frac{1}{2}(10)$.
3. Student B is correct because Student A's equation [tex]\(y = 2x\)[/tex] represents [tex]\(5 = 2(10)\)[/tex], which is incorrect.
In summary, all mentioned points are relevant to the correctness of Student B's explanation.
