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Let's work through this problem step by step.

We know the following:
- The rental company charges a base fee of $18.95.
- In addition, they charge $0.16 per mile driven.
- Laverne has $40 to spend in total.

We can write the equation for the total cost of driving $ x $ miles as:

\[
\text{Total Cost} = 18.95 + 0.16x
\]

where $ x $ is the number of miles driven.

We need to determine the maximum $ x $ such that the total cost does not exceed $40:

\[
18.95 + 0.16x \leq 40
\]

Now, let's solve for $ x $:

\[
0.16x \leq 40 - 18.95
\]
\[
0.16x \leq 21.05
\]
\[
x \leq \frac{21.05}{0.16}
\]

I will calculate this value for $ x $.Laverne can drive a maximum of 131 miles without exceeding the $40 limit.

Would you like more details or have any other questions?

Here are some related questions you could explore:
1. What if the rental fee increased to $20? How many miles could Laverne drive then?
2. How would the equation change if Laverne had a $50 budget instead?
3. What would happen if the rental company reduced the per-mile charge to $0.12?
4. How can you graph this equation to visually understand the relationship between miles and cost?
5. What is the minimum number of miles Laverne could drive to exactly spend $40?

**Tip:** When solving cost-related problems, always break down the equation into fixed and variable costs for clarity.

Laverne needs to rent a car while on vacation. The rental company charges $18.95, plus 16 cents for each mile driven. If Laverne only has $40 to spend on the car rental, what is the maximum number of miles she can drive? Round your answer down to the nearest mile.

This problem involves calculating the maximum number of miles Laverne can drive while staying within a $40 budget. The rental company charges a base fee of $18.95 and $0.16 per mile driven. The solution explores linear equations and inequalities, suitable for students in Grades 8-10.

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