A concert has seats 13,000 seats and two category of ticket prices,$17 and $27 assume all seats in each category can be sold. How many tickets of each category should be sold to being in each of the returns indicated in the table 

To solve this problem, we need to set up equations based on the information provided and the returns you want to achieve. Let's assume:

- $ x $ is the number of $17 tickets sold.
- $ y $ is the number of $27 tickets sold.

### 1. **Equation for Total Seats:**
Since there are 13,000 seats in total:
\[
x + y = 13,000
\]

### 2. **Equation for Total Revenue:**
The total revenue is a combination of the revenue from $17 tickets and $27 tickets. If the target revenue is $ R $, the equation is:
\[
17x + 27y = R
\]

To determine how many tickets of each category should be sold for different revenue targets, you can adjust $ R $ and solve the system of equations.

#### Example Solution
Let's say you want to determine the number of tickets to be sold to achieve a revenue of $250,000. The system of equations becomes:

\[
x + y = 13,000
\]
\[
17x + 27y = 250,000
\]

You can solve this system by substitution or elimination. Would you like to proceed with this example, or do you have specific revenue targets in the table that you want to calculate?

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**Relative Questions:**
1. What if the concert had 15,000 seats instead of 13,000?
2. How would the solution change if the ticket prices were different, say $20 and $30?
3. What happens if only 90% of the seats are expected to sell?
4. Can you solve for $ x $ and $ y $ given different revenue goals?
5. How would changing one ticket price affect the number of tickets needed to reach a specific revenue?

**Tip:** When dealing with linear systems, it’s often easier to use substitution if one of the equations is already solved for one variable.

A concert has 13,000 seats and two categories of ticket prices, $17 and $27. Assume all seats in each category can be sold. How many tickets of each category should be sold to bring in each of the returns indicated in the table?

Discover how to determine the number of $17 and $27 tickets that should be sold to achieve specific revenue targets for a 13,000 seat concert. This problem involves solving a system of linear equations and is suitable for students in Grades 9-12.

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