Question

A movie theater offers a special pricing for membership. The normal cost is $11\$11$11 per ticket. The membership costs $8.50\$8.50$8.50 per ticket but an initial fee of $60\$60$60 . After how many tickets are both options the same price?

Answer 1

To find out after how many tickets both pricing options are the same, we can let \( n \) represent the number of tickets purchased.

1. **Normal ticket price:**
The cost per ticket is \( 11 \) dollars, so the cost for \( n \) tickets is:
\[
\text{Cost}_\text{normal} = 11n
\]

2. **Membership ticket price:**
The membership has an initial fee of \( 60 \) dollars and a cost of \( 8.50 \) dollars per ticket. So the total cost for \( n \) tickets with the membership is:
\[
\text{Cost}_\text{membership} = 60 + 8.50n
\]

3. **Setting the costs equal:**
We want to find \( n \) such that:
\[
11n = 60 + 8.50n
\]

4. **Solving for \( n \):**
First, subtract \( 8.50n \) from both sides:
\[
11n - 8.50n = 60
\]
This simplifies to:
\[
2.5n = 60
\]

Next, divide both sides by \( 2.5 \):
\[
n = \frac{60}{2.5} = 24
\]

Thus, the two options will cost the same after purchasing **24 tickets**.