A movie theater offers a special pricing for membership. The normal cost is $10 per ticket. The membership costs $7.50 per ticket but an initial fee of $50 . After how many tickets are both options the same price?

Answer 1

To find out how many tickets make the two pricing options equivalent, we can set up an equation.

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

1. The cost without membership for \( x \) tickets: \[ \text{Cost without membership} = 10x \]

2. The cost with membership, which includes the initial fee plus the lower ticket price for \( x \) tickets: \[ \text{Cost with membership} = 50 + 7.5x \]

Now, we set the two expressions equal to determine when the costs are the same: \[ 10x = 50 + 7.5x \]

Next, we solve for \( x \):

1. Subtract \( 7.5x \) from both sides: \[ 10x - 7.5x = 50 \] \[ 2.5x = 50 \]

2. Now, divide both sides by \( 2.5 \): \[ x = \frac{50}{2.5} = 20 \]

So, after 20 tickets, both pricing options are the same price.