First, let's understand the given data and the formula:
- We are given the discount rate as [tex]\(40\%\)[/tex] or [tex]\(0.40\)[/tex] in decimal form.
- The discount amount is [tex]\(\$380\)[/tex].
Now, we need to find the original price and the sale price using the given formula:
[tex]\[ \text{Discount} = \text{Discount Rate} \times \text{Original Price} \][/tex]
We'll refer back to this information:
### Step-by-Step Calculation:
1. Find the Original Price:
We need to rearrange the formula to solve for the original price.
[tex]\[ \text{Original Price} = \frac{\text{Discount}}{\text{Discount Rate}} \][/tex]
Substituting the known values:
[tex]\[ \text{Original Price} = \frac{380}{0.40} \][/tex]
Simplifying this calculation gives us:
[tex]\[ \text{Original Price} = 950.0 \][/tex]
2. Find the Sale Price:
The sale price is calculated by subtracting the discount amount from the original price:
[tex]\[ \text{Sale Price} = \text{Original Price} - \text{Discount} \][/tex]
Substituting the known values:
[tex]\[ \text{Sale Price} = 950.0 - 380 \][/tex]
Simplifying this calculation gives us:
[tex]\[ \text{Sale Price} = 570.0 \][/tex]
### Completed Table:
\begin{tabular}{|c|c|c|c|}
\hline \begin{tabular}{c}
Original \\
Price
\end{tabular} & \begin{tabular}{c}
Discount \\
Rate
\end{tabular} & Discount & Sale Price \\
\hline\[tex]$950.0 & $[/tex]40 \%[tex]$ & $[/tex]\[tex]$ 380$[/tex] & [tex]$\$[/tex] 570.0[tex]$ \\
\hline
\end{tabular}
Therefore, the original price is \(\$[/tex]950.0\) and the sale price is [tex]\(\$570.0\)[/tex].
