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]
