You try: A particular movie theater charges $9 per adult and $4.5 per child. If 750 people attended a movie and the total revenue from ticket sales was $5175. How many adults and children attended?

Let:
- $ x $ be the number of adults
- $ y $ be the number of children

We have two pieces of information:
1. The total number of people who attended the movie: 
   \[
   x + y = 750
   \]
2. The total revenue from ticket sales was $5175, and the prices are $9 for adults and $4.5 for children:
   \[
   9x + 4.5y = 5175
   \]

Now, let's solve the system of equations.

### Step 1: Solve the first equation for $ y $
\[
y = 750 - x
\]

### Step 2: Substitute $ y = 750 - x $ into the second equation
\[
9x + 4.5(750 - x) = 5175
\]
Expand:
\[
9x + 4.5 \times 750 - 4.5x = 5175
\]
\[
9x + 3375 - 4.5x = 5175
\]
Simplify:
\[
4.5x + 3375 = 5175
\]
Subtract 3375 from both sides:
\[
4.5x = 1800
\]
Solve for $ x $:
\[
x = \frac{1800}{4.5} = 400
\]

### Step 3: Substitute $ x = 400 $ into $ y = 750 - x $
\[
y = 750 - 400 = 350
\]

### Conclusion:
- Number of adults ($ x $): 400
- Number of children ($ y $): 350

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What would be the revenue if 500 adults and 250 children attended?
2. How much would the revenue decrease if only 600 people attended with the same adult-to-child ratio?
3. If the theater charged $10 for adults and $5 for children, how would that change the total revenue?
4. What is the ratio of adults to children in this case?
5. If only 650 people attended, how many adults and children would there be if the ratio of prices stayed the same?

**Tip:** For solving systems of linear equations, substitution or elimination methods are effective approaches.

A particular movie theater charges $9 per adult and $4.5 per child. If 750 people attended a movie and the total revenue from ticket sales was $5175, how many adults and children attended?

Learn how to solve a system of linear equations to find the number of adults and children attending a movie theater. This problem involves algebraic concepts such as total revenue and ticket prices, suitable for students in Grades 8-10.

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