To determine the correct system of equations representing this situation, we need to translate the given information about sales and earnings into mathematical equations.
1. Understand the Variables:
- Let [tex]\( x \)[/tex] represent the number of hot dogs sold.
- Let [tex]\( y \)[/tex] represent the number of hamburgers sold.
2. Total Earnings Equation:
- Each hot dog sold earns \[tex]$0.50: therefore, the earnings from hot dogs would be \( 0.50x \).
- Each hamburger sold earns \$[/tex]0.75: therefore, the earnings from hamburgers would be [tex]\( 0.75y \)[/tex].
- The total earnings from selling both hot dogs and hamburgers this week is \$138.50.
- This relationship can be written as:
[tex]\[
0.50x + 0.75y = 138.50
\][/tex]
3. Total Number of Items Sold Equation:
- The total number of hot dogs and hamburgers sold is 230.
- This relationship can be written as:
[tex]\[
x + y = 230
\][/tex]
Now, we need to look at the given answer choices and see which one matches our equations:
A.
[tex]\[
0.75x + 0.50y = 138.50
\][/tex]
[tex]\[
x + y = 230
\][/tex]
B.
[tex]\[
0.50x + 0.75y = 138.50
\][/tex]
[tex]\[
x + y = 230
\][/tex]
C.
[tex]\[
0.50x + 0.75y = 230
\][/tex]
[tex]\[
x + y = 138.50
\][/tex]
D.
[tex]\[
0.75x + 0.50y = 230
\][/tex]
[tex]\[
x + y = 138.50
\][/tex]
From the analysis, 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:
(B)
[tex]\[
\begin{aligned}
0.50x + 0.75y & = 138.50 \\
x + y & = 230
\end{aligned}
\][/tex]
