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.