https://file.aiquickdraw.com/mathbot/file/17264565091526iix4tur.jpg

To solve the problem presented in the image, let's denote the number of student tickets sold as $ S $ and the number of adult tickets sold as $ A $.

From the problem, we have the following information:
1. The total number of people at the concert is 600.
2. There are 150 more adults than students at the concert.
3. The total revenue from the concert is $3150.

Let's translate these into mathematical equations.

### Step 1: Setting Up the Equations
1. The total number of people:
   \[
   S + A = 600
   \]

2. The number of adults is 150 more than the number of students:
   \[
   A = S + 150
   \]

3. Assuming ticket prices (this is typically given in such problems, but since it's not provided, we might need to deduce it from additional information, which seems to be missing in the image provided):
   \[
   \text{Let's assume the ticket prices: } \text{Student ticket price} = x, \text{Adult ticket price} = y
   \]
   However, without ticket prices, the total revenue equation won't be solvable. Let's just proceed with the given details and solve for $ S $ and $ A $.

### Step 2: Solve the Equations
Substitute the second equation into the first equation:
\[
S + (S + 150) = 600
\]
Simplify and solve for $ S $:
\[
2S + 150 = 600
\]
\[
2S = 450
\]
\[
S = 225
\]

Now, find $ A $ using $ A = S + 150 $:
\[
A = 225 + 150
\]
\[
A = 375
\]

### Conclusion
There are 225 student tickets and 375 adult tickets sold.

Do you want details or have any questions?

Here are five relative questions expanding on this topic:
1. How would the solution change if the number of adults was 200 more than the number of students?
2. What if the total revenue from the concert was $3600? How would you approach finding the ticket prices?
3. If the student tickets were priced at $10 each and the adult tickets at $20 each, what would the revenue be?
4. How would you set up the equations if there were 100 fewer adults than students?
5. What is the significance of defining variables when solving such word problems?

**Tip:** Always define your variables clearly and ensure your equations correctly represent the given conditions in word problems.

A school band performs a spring concert for a crowd of 600 people. The revenue for the concert is $3150. There are 150 more adults at the concert than students. How many of each type of ticket are sold?

Learn how to solve a system of equations involving ticket sales for a school concert. This problem involves algebraic concepts such as systems of linear equations to find the number of student and adult tickets sold. Ideal for Grades 7-10.

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