Let's break down the problem step by step:
1. We need to determine the system of equations that represents the sales of hot dogs and hamburgers at the concession stand.
2. From the problem, we know:
- Each hot dog earns \[tex]$0.50 for the programs.
- Each hamburger earns \$[/tex]0.75 for the programs.
- The total number of hot dogs and hamburgers sold together is 230.
- The total earnings from the sales of these items is \$138.50.
3. We use [tex]\( x \)[/tex] to represent the number of hot dogs sold and [tex]\( y \)[/tex] to represent the number of hamburgers sold.
4. First, we need an equation that represents the total number of hot dogs and hamburgers sold:
[tex]\[ x + y = 230 \][/tex]
5. Next, we need an equation that represents the total earnings from the sales:
[tex]\[ 0.50x + 0.75y = 138.50 \][/tex]
Let's review the given choices now:
A. [tex]\( 0.50x + 0.75y = 138.50 \)[/tex]
[tex]\[
x + y = 230
\][/tex]
B. [tex]\( 0.75x + 0.50y = 230 \)[/tex]
[tex]\[
x + y = 138.50
\][/tex]
C. [tex]\( 0.50x + 0.75y = 230 \)[/tex]
[tex]\[
x + y = 138.50
\][/tex]
D. [tex]\( 0.75x + 0.50y = 138.50 \)[/tex]
[tex]\[
x + y = 230
\][/tex]
The correct system of equations that represents the situation is:
[tex]\[0.50x + 0.75y = 138.50\][/tex]
[tex]\[x + y = 230\][/tex]
So, the correct answer is:
A.
[tex]\[
\begin{align*}
0.50x + 0.75y &= 138.50 \\
x + y &= 230
\end{align*}
\][/tex]
