Question

A movie theater sold 125 tickets for a a movie. A children’s ticket costs $6 and an adult ticket costs $12. If the theater sold $1,170 worth of tickets, how many adult tickets were sold?(1 point)
adult tickets

Answer 1

Let \( x \) be the number of adult tickets sold and \( y \) be the number of children's tickets sold. We have the following two equations based on the problem:

1. The total number of tickets sold:
\[
x + y = 125
\]

2. The total revenue generated from the ticket sales:
\[
12x + 6y = 1170
\]

Now, we can solve these equations simultaneously.

From the first equation, we can express \( y \) in terms of \( x \):
\[
y = 125 - x
\]

Next, we substitute this expression for \( y \) into the second equation:
\[
12x + 6(125 - x) = 1170
\]

Expanding the equation:
\[
12x + 750 - 6x = 1170
\]

Combining like terms:
\[
6x + 750 = 1170
\]

Subtracting 750 from both sides gives:
\[
6x = 420
\]

Dividing both sides by 6:
\[
x = 70
\]

Now that we have \( x \), we can find \( y \):
\[
y = 125 - x = 125 - 70 = 55
\]

Thus, the number of adult tickets sold is \( \boxed{70} \).