Question

Movie theater charges five dollars for an adult ticket and two dollars for a child’s ticket on Saturday. The theater sold for 785 tickets for $3280. How many of each type of ticket was sold

Answer 1

Let \( x \) represent the number of adult tickets sold, and let \( y \) represent the number of child tickets sold. We know the following from the problem statement:

1. The total number of tickets sold:
\[
x + y = 785
\]

2. The total revenue from the tickets:
\[
5x + 2y = 3280
\]

Now, we have a system of equations:

\[
\begin{align*}
1. & \quad x + y = 785 \quad \text{(1)} \\
2. & \quad 5x + 2y = 3280 \quad \text{(2)}
\end{align*}
\]

We can solve for \( y \) from equation (1):

\[
y = 785 - x
\]

Now, substitute this expression for \( y \) into equation (2):

\[
5x + 2(785 - x) = 3280
\]

Distributing the \( 2 \):

\[
5x + 1570 - 2x = 3280
\]

Combining like terms:

\[
3x + 1570 = 3280
\]

Subtract \( 1570 \) from both sides:

\[
3x = 3280 - 1570
\]
\[
3x = 1710
\]

Now, divide by \( 3 \):

\[
x = \frac{1710}{3} = 570
\]

Now that we have \( x \), we can find \( y \):

\[
y = 785 - x = 785 - 570 = 215
\]

Thus, the number of adult tickets sold is \( 570 \) and the number of child tickets sold is \( 215 \).

To summarize:
- Adult tickets sold: **570**
- Child tickets sold: **215**

We can verify this by checking both conditions:

1. Total tickets: \( 570 + 215 = 785 \) (valid)
2. Total revenue: \( 5(570) + 2(215) = 2850 + 430 = 3280 \) (valid)

Everything checks out, so the solution is correct.