Adult tickets to the fall play cost $8

Question

and student tickets cost $4
. The drama class sold 30
more adult tickets than student tickets to the fall play. If the class collected $840 from ticket sales, how many adult tickets were sold?

The drama class sold _____ adult tickets.

Answer 1

Let's denote the number of student tickets sold as \( x \). According to the problem, the adult tickets sold are \( x + 30 \).

The cost of adult tickets is $8, which means the revenue from adult tickets is: \[ 8(x + 30) \] The cost of student tickets is $4, hence the revenue from student tickets is: \[ 4x \]

The total revenue from both ticket types is given as $840. Therefore, we can write the equation: \[ 8(x + 30) + 4x = 840 \]

Now, let's simplify the equation:

1. Distribute the 8: \[ 8x + 240 + 4x = 840 \]

2. Combine like terms: \[ 12x + 240 = 840 \]

3. Subtract 240 from both sides: \[ 12x = 600 \]

4. Divide both sides by 12: \[ x = 50 \]

Now, we know the number of student tickets sold is 50. To find the number of adult tickets sold, we substitute \( x \) back into the expression for the number of adult tickets: \[ x + 30 = 50 + 30 = 80 \]

Thus, the drama class sold \( \boxed{80} \) adult tickets.