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

1 answer

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.