https://file.aiquickdraw.com/mathbot/file/1726191186877qlgx0fd5.jpg

To solve the problem, we need to create a linear equation that represents the total amount collected from ticket sales for the 7:15 PM show.

### Step 1: Define Variables and Formulate the Equation
- Let $ A $ represent the number of adult tickets sold.
- Let $ C $ represent the number of children's tickets sold.
- Adult tickets cost $16 each, and children's tickets cost $10 each.
- The total amount collected is $1028.

The total amount collected can be expressed as:
\[
16A + 10C = 1028
\]

### Step 2: Determine the Number of Children’s Tickets Sold
If 53 adult tickets were sold, substitute $ A = 53 $ into the equation:

\[
16(53) + 10C = 1028
\]

Now, solve for $ C $:

\[
848 + 10C = 1028
\]

Subtract 848 from both sides:

\[
10C = 180
\]

Divide by 10:

\[
C = 18
\]

### Conclusion
There were **18 children** at the movie.

Would you like more details or have any questions? Here are some related questions to consider:
1. How would the equation change if the ticket prices were different?
2. How do you create a general formula for situations like this involving total sales?
3. What would happen if a different number of adult tickets were sold?
4. How can you use this equation to find the total number of tickets sold?
5. How do changes in the total amount collected affect the solution?

**Tip:** Always double-check your substitution and arithmetic when solving equations to avoid errors.

Tickets to a 3D movie cost $16 for an adult and $10 for each child. A total of $1028 was collected in ticket sales for the 7:15PM show. Write a linear equation in general form to represent this situation. Let C represent the number of children's tickets and A represent the number of adult tickets sold. If 53 adult tickets were sold, how many children were there?

Learn how to solve a linear equation problem involving movie ticket sales. Tickets to a 3D movie cost $16 for adults and $10 for children, with a total of $1028 collected for a show. Find out how many children's tickets were sold when 53 adult tickets were sold. Suitable for students in Grades 8-10.

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