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.
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.