https://file.aiquickdraw.com/mathbot/file/1726679927895j4sx3h0u.jpg

To solve the problem from the screenshot, the costs for parking at Lot A and Lot B are given in terms of hours:

- For Lot A: 
  - 1 hour: $8.50 
  - 4 hours: $19.00

- For Lot B: 
  - 1 hour: $12.00 
  - 4 hours: $21.00

### Step 1: Find the hourly rate and set fee for each lot.

#### Lot A:
- For 1 hour: $8.50
- For 4 hours: $19.00

The total cost can be modeled as:
\[
\text{Cost for Lot A} = \text{set fee} + \text{hourly rate} \times \text{hours}
\]

Using 1 hour:
\[
\text{Cost for 1 hour} = \text{set fee} + \text{hourly rate} \times 1 = 8.50
\]

Using 4 hours:
\[
\text{Cost for 4 hours} = \text{set fee} + \text{hourly rate} \times 4 = 19.00
\]

Subtracting the 1-hour equation from the 4-hour equation:
\[
\left(\text{set fee} + 4 \times \text{hourly rate}\right) - \left(\text{set fee} + \text{hourly rate} \times 1\right) = 19.00 - 8.50
\]
\[
3 \times \text{hourly rate} = 10.50 \quad \Rightarrow \quad \text{hourly rate for Lot A} = 3.50
\]

Now substitute back to find the set fee:
\[
8.50 = \text{set fee} + 3.50 \quad \Rightarrow \quad \text{set fee for Lot A} = 5.00
\]

Thus, the equation for Lot A is:
\[
\text{Cost for Lot A} = 5.00 + 3.50 \times h
\]

#### Lot B:
- For 1 hour: $12.00
- For 4 hours: $21.00

Using a similar approach:
\[
\text{Cost for Lot B} = \text{set fee} + \text{hourly rate} \times \text{hours}
\]
Using 1 hour:
\[
\text{Cost for 1 hour} = \text{set fee} + \text{hourly rate} \times 1 = 12.00
\]
Using 4 hours:
\[
\text{Cost for 4 hours} = \text{set fee} + \text{hourly rate} \times 4 = 21.00
\]

Subtracting the 1-hour equation from the 4-hour equation:
\[
3 \times \text{hourly rate} = 9.00 \quad \Rightarrow \quad \text{hourly rate for Lot B} = 3.00
\]

Substitute back to find the set fee:
\[
12.00 = \text{set fee} + 3.00 \quad \Rightarrow \quad \text{set fee for Lot B} = 9.00
\]

Thus, the equation for Lot B is:
\[
\text{Cost for Lot B} = 9.00 + 3.00 \times h
\]

### Step 2: Set the equations equal to each other.

To find when the costs are the same:
\[
5.00 + 3.50h = 9.00 + 3.00h
\]

Simplifying:
\[
0.50h = 4.00 \quad \Rightarrow \quad h = 8
\]

### Conclusion:
Mr. Diaz needs to park for 8 hours for the costs to be the same at both Lot A and Lot B.

Would you like further details or clarifications?

### Follow-up questions:
1. How would the cost change if the hourly rates were slightly different for each lot?
2. How does the set fee influence the cost comparison over more or fewer hours?
3. Can you determine a general rule for when parking costs in two lots are equal based on rates and fees?
4. How would the equation change if additional discounts were applied for long-term parking?
5. How can this method be extended to solve for more than two parking lots?

### Tip:
Always compare linear equations by aligning terms and using algebraic simplifications to isolate variables easily!

Mr. Diaz needs to park his car and realizes that it would cost the same in both parking lots A and B. How many hours does Mr. Diaz need to park?

Solve the parking cost comparison problem where Mr. Diaz must park for an equal cost in Lot A and Lot B. This involves solving systems of linear equations to find the number of hours required. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation