A car can be rented from a local rental business for [tex]$100[/tex] per week plus [tex]$0.30[/tex] per mile.

How many miles can be driven if you can spend at most [tex]$1000[/tex] on a one-week rental?

Write an inequality and solve.

Select one:
A. At most 500 miles
B. At most 2000 miles
C. At most 3000 miles
D. At most 4000 miles
E. At most 1000 miles

To determine how many miles can be driven if you can spend at most [tex]$1000 on a one-week rental, let's set up and solve an inequality based on the rental cost structure.

1. Rental Cost Structure:
- Fixed cost: $[/tex]100 per week
- Variable cost: [tex]$0.30 per mile

2. Maximum Spending Allowance: $[/tex]1000

3. Inequality Setup:
- The total cost must be less than or equal to [tex]$1000. The total cost includes the fixed weekly cost plus the variable cost based on miles driven. Therefore, we can set up the following inequality:

\[ 100 + 0.30 \times \text{miles} \leq 1000 \]

4. Solve for Miles:
- First, subtract the fixed weekly cost from both sides:

\[ 0.30 \times \text{miles} \leq 1000 - 100 \]

\[ 0.30 \times \text{miles} \leq 900 \]

- Next, divide both sides by the cost per mile ($[/tex]0.30) to solve for the number of miles:

[tex]\[ \text{miles} \leq \frac{900}{0.30} \][/tex]

[tex]\[ \text{miles} \leq 3000 \][/tex]

5. Conclusion:
- The maximum number of miles that can be driven while keeping the total rental cost at or below $1000 is 3000 miles.

So, the answer is: At most 3000 miles, which corresponds to option c.