To determine the correct system of equations representing the given situation, follow these steps:
1. Identify the Variables:
- Let [tex]\(x\)[/tex] represent the number of copies of the home edition sold.
- Let [tex]\(y\)[/tex] represent the number of copies of the business edition sold.
2. Total Number of Copies Sold:
- The company sold a total of 745 copies.
- This relationship can be represented by the equation:
[tex]\[
x + y = 745
\][/tex]
3. Total Revenue:
- The home edition costs \[tex]$23.50 per copy.
- The business edition costs \$[/tex]58.75 per copy.
- The total revenue from selling these copies is \$29,668.75.
- This relationship can be represented by the equation:
[tex]\[
23.50x + 58.75y = 29,668.75
\][/tex]
Combining these two pieces of information into a system of equations, we get:
[tex]\[
\begin{cases}
23.50x + 58.75y = 29,668.75 \\
x + y = 745
\end{cases}
\][/tex]
We now compare this system of equations to the given options:
A.
[tex]\[
58.75x + 23.50y = 29,668.75 \\
x + y = 745
\][/tex]
This option swaps the coefficients and hence does not match our derived system.
B.
[tex]\[
23.50x + 58.75y = 745 \\
x + y = 29,668.75
\][/tex]
This option swaps the totals and the coefficients, so it does not match our derived system.
C.
[tex]\[
58.75x + 23.50y = 745 \\
x + y = 29,668.75
\][/tex]
This option swaps both the coefficients and the totals, so it does not match our derived system.
D.
[tex]\[
23.50x + 58.75y = 29,668.75 \\
x + y = 745
\][/tex]
This option matches perfectly with our derived system of equations.
Therefore, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
