Tickets to a 3D movie cost $12 for an adult and $6 for each child. A total of $726 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?  children

We are given the following information:

- The cost of an adult ticket is $12.
- The cost of a child's ticket is $6.
- The total revenue from ticket sales is $726.
- Let $ A $ represent the number of adult tickets sold and $ C $ represent the number of children's tickets sold.

### Step 1: Formulate the equation

We can write a linear equation based on the total amount of money collected:
\[
12A + 6C = 726
\]
This is the general form of the linear equation, where $ A $ and $ C $ represent the number of adult and children's tickets, respectively.

### Step 2: Solve for the number of children's tickets when $ A = 53 $

We are told that 53 adult tickets were sold, so we substitute $ A = 53 $ into the equation:

\[
12(53) + 6C = 726
\]
Now, calculate $ 12 \times 53 $:

\[
636 + 6C = 726
\]

Next, subtract 636 from both sides:

\[
6C = 726 - 636
\]

\[
6C = 90
\]

Now, divide both sides by 6 to solve for $ C $:

\[
C = \frac{90}{6} = 15
\]

### Final Answer:
There were 15 children at the 7:15 PM show.

Would you like more details, or have any questions about the process?

Here are some related questions:
1. How would the equation change if the adult ticket price increased to $15?
2. What if a total of $900 was collected? How would the number of children change?
3. Can you find how much more was collected from adult tickets than children's tickets?
4. What happens to the equation if no children attended the show?
5. How many total tickets were sold for this show?

**Tip**: Always check the reasonableness of your result by comparing the revenue from adult and children's tickets.

Tickets to a 3D movie cost $12 for an adult and $6 for each child. A total of $726 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 involving adult and children's ticket sales. The problem involves calculating the number of children's tickets sold when 53 adult tickets were sold, based on total revenue of $726. Suitable for Grades 6-8.

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