Question

a movie theater offers two options for memberships. The first shop cost $10 per ticket but in fee of $10 the second option cost five dollars per ticket by an Intel fee of 60 after how many tickets are both opponents at the same price

Answer 1

Let's break down the costs for each membership option to determine at what point they are equal.

1. **First membership option:**
- Cost per ticket = $10
- Monthly fee = $10
- Total cost for \( x \) tickets = \( 10 + 10x \)

2. **Second membership option:**
- Cost per ticket = $5
- Monthly fee = $60
- Total cost for \( x \) tickets = \( 60 + 5x \)

Now we want to find the number of tickets \( x \) where the total costs for both options are equal:

\[
10 + 10x = 60 + 5x
\]

Now, let's solve for \( x \):

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

\[
10 + 5x = 60
\]

2. Subtract 10 from both sides:

\[
5x = 50
\]

3. Divide both sides by 5:

\[
x = 10
\]

Thus, both options will cost the same after **10 tickets**.