Certainly! Let's go through and set up the problem step by step:
1. Define the Variables:
- The variable [tex]\(x\)[/tex] represents the number of general-admission tickets sold.
- The variable [tex]\(y\)[/tex] represents the number of preferred seats tickets sold.
2. Set up the Equation:
- Each general-admission ticket costs \[tex]$26.
- Each preferred seat ticket costs \$[/tex]65.
- Kyrsten needs to generate a total of \[tex]$1300 from selling these tickets.
3. Construct the Equation:
We need to use the costs of the tickets to form an equation that represents the total amount of money raised from selling the tickets. Therefore, the equation is:
\[ 26x + 65y = 1300 \]
This equation is in the standard form \(Ax + By = C\).
4. Graph the Equation:
When graphing the equation \(26x + 65y = 1300\), follow these steps:
- Find the x-intercept:
Set \(y = 0\) and solve for \(x\):
\[
26x + 65(0) = 1300 \\
26x = 1300 \\
x = \frac{1300}{26} \\
x = 50
\]
So, the x-intercept is \((50, 0)\).
- Find the y-intercept:
Set \(x = 0\) and solve for \(y\):
\[
26(0) + 65y = 1300 \\
65y = 1300 \\
y = \frac{1300}{65} \\
y = 20
\]
So, the y-intercept is \((0, 20)\).
- Plot the intercepts and draw the line:
Using the intercepts \((50, 0)\) and \((0, 20)\), plot these points on the coordinate plane and draw a straight line through them. This line represents all the combinations of general-admission and preferred seats tickets that will total \$[/tex]1300 in sales.
### Summary:
- The variable [tex]\(x\)[/tex] represents: the number of general-admission tickets sold.
- The variable [tex]\(y\)[/tex] represents: the number of preferred seats tickets sold.
- Equation: [tex]\(26x + 65y = 1300\)[/tex]
- Graph: Plot [tex]\((50, 0)\)[/tex] and [tex]\((0, 20)\)[/tex] and draw a line through these points.
By following these steps, you can visualize and understand all the different ways Kyrsten can sell enough tickets to pay the band.
