Based on the problem statement, we need to form a system of equations that accurately represents the given situation with two variables: [tex]\( x \)[/tex] (number of adult tickets sold) and [tex]\( y \)[/tex] (number of student tickets sold).
1. Total number of tickets sold:
The first piece of information is that the museum had a total of 150 visitors. Since each visitor purchased one ticket, the equation will be:
[tex]\[
x + y = 150
\][/tex]
2. Total money collected:
The second piece of information is regarding the total amount of money collected from the tickets. Adult tickets cost [tex]$20 each and student tickets cost $[/tex]15 each, and together they collected a total of \$2500. Therefore, we can express this as:
[tex]\[
20x + 15y = 2500
\][/tex]
Therefore, the system of equations that describe this problem is:
[tex]\[
\begin{array}{l}
20x + 15y = 2500 \\
x + y = 150
\end{array}
\][/tex]
Let's compare this system with the given choices:
- [tex]\( 20x + 15y = 150 \)[/tex]
[tex]\( x + y = 2500 \)[/tex]
- [tex]\( 15x + 20y = 2500 \)[/tex]
[tex]\( x + y = 150 \)[/tex]
- [tex]\( 20x + 15y = 2500 \)[/tex]
[tex]\( x + y = 150 \)[/tex]
- [tex]\( 15x + 20y = 2500 \)[/tex]
[tex]\( x + y = 150 \)[/tex]
The correct system of equations that we need matches the third option:
[tex]\[
\begin{array}{l}
20x + 15y = 2500 \\
x + y = 150
\end{array}
\][/tex]
