To determine the correct system of equations that represents the given situation, let's first define the variables and the relationships between them.
The problem provides the following information:
1. The cost of the home edition, [tex]\( x \)[/tex], is \[tex]$23.50.
2. The cost of the business edition, \( y \), is \$[/tex]58.75.
3. The total revenue from selling both editions is \$29,668.75.
4. The total number of copies sold is 745.
We need to write equations that incorporate all these details.
1. The first equation should represent the total revenue generated from selling [tex]\( x \)[/tex] copies of the home edition and [tex]\( y \)[/tex] copies of the business edition. The revenue from the home edition is given by the price per unit times the number of units sold, which is [tex]\( 23.50x \)[/tex]. Similarly, the revenue from the business edition is [tex]\( 58.75y \)[/tex]. The sum of these revenues should equal the total revenue:
[tex]\[
23.50x + 58.75y = 29,668.75
\][/tex]
2. The second equation should represent the total number of copies sold, which is the sum of the home editions and business editions sold:
[tex]\[
x + y = 745
\][/tex]
Therefore, the correct system of equations is:
[tex]\[
\begin{cases}
23.50x + 58.75y = 29,668.75 \\
x + y = 745
\end{cases}
\][/tex]
We now compare this system with the provided choices:
A. [tex]\( 58.75x + 23.50y = 29,668.75 \)[/tex] and [tex]\( x + y = 745 \)[/tex] – This does not match since the coefficients on [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are swapped.
B. [tex]\( 23.50x + 58.75y = 745 \)[/tex] and [tex]\( x + y = 29,668.75 \)[/tex] – This does not match since the constants on the right side of the equations are swapped.
C. [tex]\( 58.75x + 23.50y = 745 \)[/tex] and [tex]\( x + y = 29,668.75 \)[/tex] – This does not match since both the coefficients and constants are incorrect.
D. [tex]\( 23.50x + 58.75y = 29,668.75 \)[/tex] and [tex]\( x + y = 745 \)[/tex] – This correctly matches our derived system.
Thus, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
