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.