for an annual fee of $30 you can join a movie club that will allow you to purchase tickets for $5.50 each at you local theater. If the theater charges $8 for movie tickets write an solve an equation to determine how many movie tickets you will have to buy through the movie club for the cost to equal that of buying regularly priced tickets.

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To solve this problem, we need to set up an equation that represents the cost of purchasing movie tickets through the movie club and the cost of buying regularly priced tickets. Let's break it down step by step:

Let's assume the number of movie tickets you need to buy through the movie club to make the cost equal is "x".

Regular Price: Each movie ticket costs $8.
So, the cost of buying x movie tickets at the regular price is 8x dollars.

Movie Club Price: Each movie ticket costs $5.50 when purchased through the movie club.
Since you have already paid an annual fee of $30, you do not need to consider it while calculating the ticket price.
Therefore, the cost of buying x movie tickets through the movie club is 5.50x dollars.

Now we can set up the equation to find x:

8x = 5.50x + 30

Explanation: The total cost of buying regular tickets (8x) should be equal to the total cost of buying tickets through the movie club (5.50x) plus the annual fee ($30).

Now, let's solve the equation to find x:

8x - 5.50x = 30
2.50x = 30
x = 30 / 2.50
x = 12

Therefore, you will have to buy 12 movie tickets through the movie club for the cost to equal that of buying regularly priced tickets.