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Sagot :
Let's complete the table step by step with the given data and numerical results.
### First, Calculate the Monthly Charges
1. Copy Machine:
- List Price: \[tex]$5,210.85 - Rental Rate: 12.0% \[ \text{Monthly Charge} = \left( \frac{12.0}{100} \right) \times 5,210.85 = 625.302 \] 2. Tent: - List Price: \$[/tex]1,900.00
- Rental Rate: 9.0%
[tex]\[ \text{Monthly Charge} = \left( \frac{9.0}{100} \right) \times 1,900.00 = 171.0 \][/tex]
Therefore:
[tex]\[ \text{Monthly Charge for Copy Machine (a.)} = 625.302 \][/tex]
[tex]\[ \text{Monthly Charge for Tent (a.)} = 171.0 \][/tex]
### Next, Calculate the Total Rental Costs
1. Copy Machine:
- Rental Period: 6 months
- Monthly charge: 625.302
- Usage Tax: 6.5%
[tex]\[ \text{Total Rental Cost} = 625.302 \times 6 = 3751.812 \][/tex]
[tex]\[ \text{Usage Tax} = \left( \frac{6.5}{100} \right) \times 3751.812 = 243.86778 \][/tex]
[tex]\[ \text{Total Rental Cost with Tax (b.)} = 3751.812 + 243.86778 = 3995.67978 \][/tex]
2. Tent:
- Rental Period: 2 months
- Monthly charge: 171.0
- Usage Tax: 4.5%
[tex]\[ \text{Total Rental Cost} = 171.0 \times 2 = 342.0 \][/tex]
[tex]\[ \text{Usage Tax} = \left( \frac{4.5}{100} \right) \times 342.0 = 15.39 \][/tex]
[tex]\[ \text{Total Rental Cost with Tax (b.)} = 342.0 + 15.39 = 357.39 \][/tex]
Therefore:
[tex]\[ \text{Total Rental Cost for Copy Machine (b.)} = 3995.67978 \][/tex]
[tex]\[ \text{Total Rental Cost for Tent (b.)} = 357.39 \][/tex]
### Completed Table:
[tex]\[ \begin{tabular}{|c|l|l|l|l|l|l|} \hline Item & List Price & \begin{tabular}{c} Rental \\ Rate \end{tabular} & \begin{tabular}{c} Monthly \\ Charge \end{tabular} & \begin{tabular}{c} Number \\ of \\ Months \end{tabular} & \begin{tabular}{c} Usage \\ Tax \end{tabular} & \begin{tabular}{c} Total Rental \\ Cost \end{tabular} \\ \hline \begin{tabular}{c} copy \\ machine \end{tabular} & \$5,210.85 & \begin{tabular}{c} \$12.0 \% \\ of list \end{tabular} & \emph{625.302} & 6 & \$6.5 \% & \emph{3995.67978} \\ \hline tent & \$1,900.00 & \begin{tabular}{c} \$9.0 \% \\ of list \end{tabular} & \emph{171.0} & 2 & \$4.5 \% & \emph{357.39} \\ \hline \end{tabular} \][/tex]
### First, Calculate the Monthly Charges
1. Copy Machine:
- List Price: \[tex]$5,210.85 - Rental Rate: 12.0% \[ \text{Monthly Charge} = \left( \frac{12.0}{100} \right) \times 5,210.85 = 625.302 \] 2. Tent: - List Price: \$[/tex]1,900.00
- Rental Rate: 9.0%
[tex]\[ \text{Monthly Charge} = \left( \frac{9.0}{100} \right) \times 1,900.00 = 171.0 \][/tex]
Therefore:
[tex]\[ \text{Monthly Charge for Copy Machine (a.)} = 625.302 \][/tex]
[tex]\[ \text{Monthly Charge for Tent (a.)} = 171.0 \][/tex]
### Next, Calculate the Total Rental Costs
1. Copy Machine:
- Rental Period: 6 months
- Monthly charge: 625.302
- Usage Tax: 6.5%
[tex]\[ \text{Total Rental Cost} = 625.302 \times 6 = 3751.812 \][/tex]
[tex]\[ \text{Usage Tax} = \left( \frac{6.5}{100} \right) \times 3751.812 = 243.86778 \][/tex]
[tex]\[ \text{Total Rental Cost with Tax (b.)} = 3751.812 + 243.86778 = 3995.67978 \][/tex]
2. Tent:
- Rental Period: 2 months
- Monthly charge: 171.0
- Usage Tax: 4.5%
[tex]\[ \text{Total Rental Cost} = 171.0 \times 2 = 342.0 \][/tex]
[tex]\[ \text{Usage Tax} = \left( \frac{4.5}{100} \right) \times 342.0 = 15.39 \][/tex]
[tex]\[ \text{Total Rental Cost with Tax (b.)} = 342.0 + 15.39 = 357.39 \][/tex]
Therefore:
[tex]\[ \text{Total Rental Cost for Copy Machine (b.)} = 3995.67978 \][/tex]
[tex]\[ \text{Total Rental Cost for Tent (b.)} = 357.39 \][/tex]
### Completed Table:
[tex]\[ \begin{tabular}{|c|l|l|l|l|l|l|} \hline Item & List Price & \begin{tabular}{c} Rental \\ Rate \end{tabular} & \begin{tabular}{c} Monthly \\ Charge \end{tabular} & \begin{tabular}{c} Number \\ of \\ Months \end{tabular} & \begin{tabular}{c} Usage \\ Tax \end{tabular} & \begin{tabular}{c} Total Rental \\ Cost \end{tabular} \\ \hline \begin{tabular}{c} copy \\ machine \end{tabular} & \$5,210.85 & \begin{tabular}{c} \$12.0 \% \\ of list \end{tabular} & \emph{625.302} & 6 & \$6.5 \% & \emph{3995.67978} \\ \hline tent & \$1,900.00 & \begin{tabular}{c} \$9.0 \% \\ of list \end{tabular} & \emph{171.0} & 2 & \$4.5 \% & \emph{357.39} \\ \hline \end{tabular} \][/tex]
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