This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Monique wants to rent online movies. Movies Plus charges a one-time fee of $20 plus $5 per movie. Movies-To-Go charges $7 per movie. For how many movies is the cost of renting movies from Movies Plus and Movies-To-Go the same?

 

Write an equation to represent the problem, where m is the number of movies rented.

To solve this problem, we need to find when the cost of renting movies from Movies Plus and Movies-To-Go is the same.

### Step 1: Define the costs for both companies.

1. **Movies Plus** charges a one-time fee of $20 plus $5 per movie. So, the total cost for renting *m* movies from Movies Plus is:

   \[
   \text{Cost of Movies Plus} = 20 + 5m
   \]

2. **Movies-To-Go** charges $7 per movie, with no one-time fee. So, the total cost for renting *m* movies from Movies-To-Go is:

   \[
   \text{Cost of Movies-To-Go} = 7m
   \]

### Step 2: Set up an equation.

We want to find the number of movies, *m*, where the costs are equal. Set the two cost expressions equal to each other:

\[
20 + 5m = 7m
\]

This is the equation that represents the problem. Now we can move on to solving for *m*.

Do you want me to proceed with solving Part B? Also, would you like further explanation of Part A? 

Here are 5 related questions:

1. How would the equation change if Movies-To-Go offered a one-time discount?
2. What if Movies Plus charged a different one-time fee?
3. How do linear equations like this apply to real-world budgeting?
4. Can you graph the two cost functions to see the intersection visually?
5. How does changing the per-movie price affect the solution?

**Tip:** Always make sure to set up equations based on the variables and conditions given to understand the problem clearly.

Monique wants to rent online movies. Movies Plus charges a one-time fee of $20 plus $5 per movie. Movies-To-Go charges $7 per movie. For how many movies is the cost of renting movies from Movies Plus and Movies-To-Go the same? Write an equation to represent the problem, where m is the number of movies rented.

Discover how to determine the number of movies Monique needs to rent for the costs of Movies Plus and Movies-To-Go to be equal. This problem involves algebra and setting up linear equations. Suitable for students in Grades 6-8.

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