Question

A movie theater offers two options for membership. The first option costs $7.50\$7.50$7.50 per ticket but an initial fee of $5\$5$5. The second option costs $5\$5$5 per ticket but an initial fee of $50\$50$50 . After how many tickets are both options the same price? Click Here for Help Video



____ tickets

Answer 1

To find the number of tickets after which both membership options cost the same, we can set up an equation.

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

1. **First Option**:
- Initial fee: $5
- Cost per ticket: $7.50
- Total cost: \( 5 + 7.50x \)

2. **Second Option**:
- Initial fee: $50
- Cost per ticket: $5
- Total cost: \( 50 + 5x \)

Now, we want to set the total costs of both options equal to each other:

\[
5 + 7.50x = 50 + 5x
\]

Next, we will solve the equation for \( x \):

1. Subtract \( 5x \) from both sides:

\[
5 + 7.50x - 5x = 50
\]

2. Simplify:

\[
5 + 2.50x = 50
\]

3. Subtract 5 from both sides:

\[
2.50x = 45
\]

4. Divide both sides by 2.50:

\[
x = \frac{45}{2.50} = 18
\]

Therefore, both options cost the same after **18 tickets**.

So the answer is:

\[
\boxed{18}
\]