To solve this problem, we need to write two separate equations describing the charges for the landscaping service and Mary's neighbor. We will let [tex]\( C \)[/tex] represent the total charge and [tex]\( h \)[/tex] represent the number of hours worked.
First, let's define the charge for the landscaping service:
1. Landscaping Service Charge:
- The service includes a consultation fee of \[tex]$15.
- The charge for the actual work is \$[/tex]8 per hour.
Therefore, the total charge [tex]\( C \)[/tex] as a function of hours [tex]\( h \)[/tex] can be written as:
[tex]\[
C = 15 + 8h
\][/tex]
Next, let's define the charge for Mary's neighbor:
2. Neighbor's Charge:
- The neighbor does not charge a consultation fee.
- The charge for the work is \$10 per hour.
Therefore, the total charge [tex]\( C \)[/tex] as a function of hours [tex]\( h \)[/tex] can be written as:
[tex]\[
C = 10h
\][/tex]
Now, we will match these pairs of equations with the given multiple choice options:
a.
[tex]\[
\begin{array}{l}
C = 15 + 10h \\
C = 8h
\end{array}
\][/tex]
This option does not match our equations.
b.
[tex]\[
\begin{array}{l}
C = 10h + 8h \\
C = 15
\end{array}
\][/tex]
This option does not match our equations.
c.
[tex]\[
\begin{array}{l}
C = 15 + 8h \\
C = 10h
\end{array}
\][/tex]
This option matches our equations exactly.
d.
[tex]\[
\begin{array}{l}
C = 18h \\
C = 15
\end{array}
\][/tex]
This option does not match our equations.
Therefore, the correct answer is:
[tex]\[
c.
\begin{array}{l}
C = 15 + 8h \\
C = 10h
\end{array}
\][/tex]
