A movie theater offers a special pricing for membership. The normal cost is $15 per ticket. The membership costs $12.50 per ticket but an initial fee of $45 . After how many tickets are both options the same price? _tickets

Answer 1

To find out how many tickets would make both pricing options cost the same, let's set up the equations for the total cost of tickets under both options.

1. Without membership: The total cost for \( x \) tickets at $15 per ticket is: \[ C_1 = 15x \]

2. With membership: The total cost for \( x \) tickets at $12.50 per ticket plus a one-time membership fee of $45 is: \[ C_2 = 45 + 12.5x \]

Now we set the two equations equal to each other to find when the costs are the same: \[ 15x = 45 + 12.5x \]

To solve for \( x \), we first subtract \( 12.5x \) from both sides: \[ 15x - 12.5x = 45 \] \[ 2.5x = 45 \]

Next, divide both sides by \( 2.5 \): \[ x = \frac{45}{2.5} = 18 \]

Therefore, after 18 tickets, both options will cost the same price.