Tickets for a school place sells for eight dollars for floor seats and six for balcony seats for one performance 72 tickets are sold Bringing In 516 how many of each tickets were sold?

Answer 1

Let's denote the number of floor seats sold as \( x \) and the number of balcony seats sold as \( y \).

We have two pieces of information that lead to the following system of equations:

1. The total number of tickets sold: \[ x + y = 72 \]

2. The total revenue from ticket sales: \[ 8x + 6y = 516 \]

We can solve this system step-by-step.

First, let's solve the first equation for \( y \): \[ y = 72 - x \]

Now, we can substitute this expression for \( y \) into the second equation: \[ 8x + 6(72 - x) = 516 \] Distributing the \( 6 \): \[ 8x + 432 - 6x = 516 \] Combine like terms: \[ 2x + 432 = 516 \] Subtract \( 432 \) from both sides: \[ 2x = 84 \] Divide by \( 2 \): \[ x = 42 \]

Now that we have \( x \), we can find \( y \): \[ y = 72 - x = 72 - 42 = 30 \]

Thus, the number of tickets sold is:

• Floor seats (x): 42
• Balcony seats (y): 30

To summarize, 42 floor seats and 30 balcony seats were sold.