To find the linear equation that represents a cost of [tex]$130 when renting a car from a company that charges $[/tex]0.50 per mile and a flat rate of [tex]$30.00, we can follow these steps:
1. Identify the components of the problem:
- The cost per mile is $[/tex]0.50.
- The flat rate is [tex]$30.00.
- The total cost represents a combination of both the variable cost (based on miles driven, \(m\)) and the flat rate.
- The total cost given is $[/tex]130.
2. Define the variables:
- Let [tex]\(m\)[/tex] represent the number of miles driven.
- Let [tex]\(C(m)\)[/tex] represent the total cost.
3. Set up the linear equation:
- The total cost [tex]\(C(m)\)[/tex] can be represented by the equation combining the flat rate and the mileage cost:
[tex]\[
C(m) = 0.50 \times m + 30
\][/tex]
4. Substitute the given total cost into the equation:
- We are given that the total cost is [tex]$130. Therefore, we can substitute $[/tex]130[tex]$ for \(C(m)\):
\[
130 = 0.50 \times m + 30
\]
Thus, the linear equation that represents the total cost of $[/tex]130 when [tex]\(m\)[/tex] miles are driven is:
[tex]\[
130 = 0.50 m + 30
\][/tex]
This matches the third option from the list:
[tex]\[
\boxed{130=0.50 m+30}
\][/tex]
