Question

a movie theater offers a special pricing for membership. The normal cost is $7.50 per ticket. The membership cost is five dollars per ticket but an initial fee of $30 after how many tickets are both options the same price
______tickets

Answer 1

To determine the number of tickets at which the cost of the membership option equals the cost of the regular ticket option, we can set up an equation.

Let \( x \) be the number of tickets.

**Cost of regular tickets:**
\[
\text{Cost} = 7.50x
\]

**Cost of membership tickets:**
The initial fee is $30 and the membership ticket price is $5:
\[
\text{Cost} = 30 + 5x
\]

Now, we can set the two costs equal to each other to find the point at which they are the same:

\[
7.50x = 30 + 5x
\]

Now, let's solve for \( x \):

1. Subtract \( 5x \) from both sides:
\[
7.50x - 5x = 30
\]
\[
2.50x = 30
\]

2. Now divide by 2.50:
\[
x = \frac{30}{2.50}
\]
\[
x = 12
\]

So, after **12 tickets**, both options will cost the same price.