Mary's yard is a mess. She needs to hire someone to prune her trees and shrubs. A landscaping service she calls quotes her a price of \[tex]$15 consultation fee plus \$[/tex]8 an hour for the actual work. Mary's neighbor has offered to help her out. She doesn't charge a consultation fee but does charge \[tex]$10 an hour for her work.

Write two equations, one that describes the landscaping service charge and one that describes your neighbor's charge. Let $[/tex]C[tex]$ equal the charge as a function of $[/tex]h$, the number of hours worked.

a.
[tex]\[
\begin{array}{l}
C = 15 + 10h \\
C = 8h
\end{array}
\][/tex]

b.
[tex]\[
\begin{array}{l}
C = 10h + 8h \\
C = 15
\end{array}
\][/tex]

c.
[tex]\[
\begin{array}{l}
C = 15 + 8h \\
C = 10h
\end{array}
\][/tex]

d.
[tex]\[
\begin{array}{l}
C = 18h \\
C = 15
\end{array}
\][/tex]



Answer :

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]