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Sam is planning to start a pool cleaning business from his home. He has developed the following cost analysis for the setup and operation for the first year of his business. He has [tex]$\$[/tex]9,000[tex]$ in savings and $[/tex]\[tex]$23,000$[/tex] in credit that he can use for the business. Approximately what percent of the initial setup and operation costs will Sam need to finance with a lender or investor?

\begin{tabular}{|l|l|}
\hline
\textbf{Item} & \textbf{Cost} \\
\hline
Truck & [tex]$\$[/tex]9,000$ \\
\hline
Pool Cleaning Supplies & [tex]$\$[/tex]6,000$ \\
\hline
Payroll & [tex]$\$[/tex]23,000$ \\
\hline
Advertising & [tex]$\$[/tex]1,500$ \\
\hline
\end{tabular}

a. [tex]$19 \%$[/tex]
b. [tex]$23 \%$[/tex]
c. [tex]$33 \%$[/tex]
d. [tex]$78 \%$[/tex]

Please select the best answer from the choices provided.

Sagot :

GinnyAnswer
To determine the percentage of the initial setup and operation costs that Sam will need to finance with a lender or investor, we need to go through the following steps:

1. Sum up the total initial setup and operation costs.
[tex]\[ \text{Total Cost} = \text{Truck Cost} + \text{Supplies Cost} + \text{Payroll Cost} + \text{Advertising Cost} \][/tex]
Substituting the given values:
[tex]\[ \text{Total Cost} = \[tex]$9,000 + \$[/tex]6,000 + \[tex]$23,000 + \$[/tex]1,500 = \$39,500
\][/tex]

2. Calculate the total funds available from savings and credit.
[tex]\[ \text{Total Funds} = \text{Savings} + \text{Credit} \][/tex]
Substituting the given values:
[tex]\[ \text{Total Funds} = \[tex]$9,000 + \$[/tex]23,000 = \$32,000
\][/tex]

3. Find the amount Sam still needs to finance.
[tex]\[ \text{Amount Needed} = \text{Total Cost} - \text{Total Funds} \][/tex]
Substituting the known values:
[tex]\[ \text{Amount Needed} = \[tex]$39,500 - \$[/tex]32,000 = \$7,500
\][/tex]

4. Calculate the percentage of the total cost that needs to be financed.
[tex]\[ \text{Percentage Needed} = \left( \frac{\text{Amount Needed}}{\text{Total Cost}} \right) \times 100 \% \][/tex]

5. Compute the percentage.
[tex]\[ \text{Percentage Needed} = \left( \frac{\[tex]$7,500}{\$[/tex]39,500} \right) \times 100 \% \approx 18.99\%
\][/tex]

6. Choose the closest percentage from the provided options.
The provided options are:
- a. \(19 \%\)
- b. \(23 \%\)
- c. \(33 \%\)
- d. \(78 \%\)

The closest option to \(18.99\%\) is \(19\%\).

Therefore, the best answer is:

a. [tex]\(19 \%\)[/tex]
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