Let x represent the number of movies you need to buy for the cost of each movie club to be the same.
For the first movie club, the cost would be $100 for the membership fee plus $10 for each movie, so the total cost would be 100 + 10x.
For the second movie club, there is no membership fee, and each movie costs $15, so the total cost would be 15x.
Therefore, the equation would be:
100 + 10x = 15x
To solve the equation:
First, subtract 10x from both sides:
100 = 5x
Then, divide both sides by 5:
20 = x
So, you would need to buy 20 movies for the cost of each movie club to be the same.