College

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

Answer :

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.