Question

A company sells two versions of an antivirus software. The home edition cost $23.50, and the business edition cost $58.75. Last week, the company earned $29,668.75 from selling 745 copies of the software. If x represents the number of copies of the home edition and y represents the number of copies of the business edition sold, which system of equations represents this situation.

Answer 1

To represent the situation with a system of equations, we can establish two equations based on the information given:

1. **Equation for the total number of copies sold:**
The total number of copies sold is the sum of the home edition copies (x) and the business edition copies (y). This gives us our first equation:
\[
x + y = 745
\]

2. **Equation for the total revenue earned:**
The total revenue from selling x copies of the home edition at $23.50 each and y copies of the business edition at $58.75 each should equal the total earnings of $29,668.75. This gives us our second equation:
\[
23.50x + 58.75y = 29,668.75
\]

Putting these two equations together, we have the following system of equations:

\[
\begin{align*}
1) & \quad x + y = 745 \\
2) & \quad 23.50x + 58.75y = 29,668.75
\end{align*}
\]

This system of equations can now be used to determine the values of \(x\) (copies of the home edition sold) and \(y\) (copies of the business edition sold).