Question

A movie theater has two ticket prices. $8 for adults, and $5 for kids. If the box office took in $4116 from the sale of 600 tickets, how many of each kind were sold?

Answer 1

Let's denote the number of adult tickets sold as \( x \) and the number of kids' tickets sold as \( y \).

We can set up the following system of equations based on the information provided:

1. The total number of tickets sold:
\[
x + y = 600
\]

2. The total revenue from ticket sales:
\[
8x + 5y = 4116
\]

Now we can solve this system of equations.

From the first equation, we can express \( y \) in terms of \( x \):
\[
y = 600 - x
\]

Now we can substitute this expression for \( y \) into the second equation:
\[
8x + 5(600 - x) = 4116
\]

Expanding this gives:
\[
8x + 3000 - 5x = 4116
\]

Combining like terms:
\[
3x + 3000 = 4116
\]

Now, isolate \( x \):
\[
3x = 4116 - 3000
\]
\[
3x = 1116
\]
\[
x = \frac{1116}{3} = 372
\]

Now that we have \( x \), we can find \( y \) using the first equation:
\[
y = 600 - x = 600 - 372 = 228
\]

Thus, the number of adult tickets sold is \( \boxed{372} \), and the number of kids' tickets sold is \( \boxed{228} \).

Answer 2

Write the first equation

Answer 3

The first equation based on the total number of tickets sold is:

\[
x + y = 600
\]

where:
- \( x \) is the number of adult tickets sold,
- \( y \) is the number of kids' tickets sold.