Adult tickets to the fall play cost $6

Question

and student tickets cost $3
. The drama class sold 25
more student tickets than adult tickets to the fall play. If the class collected $660
from ticket sales, how many student tickets were sold?

The drama class sold blank student tickets.

Answer 1

Let \( a \) represent the number of adult tickets sold, and let \( s \) represent the number of student tickets sold. We have the following information:

1. The class sold 25 more student tickets than adult tickets: \[ s = a + 25 \]

2. The total revenue from ticket sales was $660. The revenue from adult tickets (at $6 each) and student tickets (at $3 each) can be expressed as: \[ 6a + 3s = 660 \]

Now, we can substitute \( s \) from the first equation into the second equation: \[ 6a + 3(a + 25) = 660 \]

Expanding this gives: \[ 6a + 3a + 75 = 660 \]

Combining like terms results in: \[ 9a + 75 = 660 \]

Next, we subtract 75 from both sides: \[ 9a = 660 - 75 \] \[ 9a = 585 \]

Now, divide both sides by 9: \[ a = \frac{585}{9} = 65 \]

Having found the number of adult tickets sold, we can now find the number of student tickets sold: \[ s = a + 25 = 65 + 25 = 90 \]

Thus, the class sold \(\boxed{90}\) student tickets.