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.



We can set up the equation by comparing the total cost for both services:

- **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:
\[
C_{\text{Movies Plus}} = 20 + 5m
\]
- **Movies-To-Go** charges $7 per movie, with no additional fees. So, the total cost for renting $ m $ movies from Movies-To-Go is:
\[
C_{\text{Movies-To-Go}} = 7m
\]

To find when the costs are the same, we set the two cost equations equal to each other:
\[
20 + 5m = 7m
\]

This is the equation representing the problem. Now, let's solve it.

### Solving the equation:

\[
20 + 5m = 7m
\]
Subtract $ 5m $ from both sides:
\[
20 = 2m
\]
Divide both sides by 2:
\[
m = 10
\]

Thus, the cost of renting movies from both companies is the same when Monique rents **10 movies**.

---

Would you like a detailed breakdown of any part of the solution, or do you have any questions? Here are five related questions to expand on this concept:

1. What would be the total cost for Monique to rent 10 movies from both services?
2. What happens if Monique rents fewer than 10 movies? Which service would be cheaper?
3. If Movies-To-Go increased their price to $8 per movie, how would the equation change?
4. How much would Monique save by choosing Movies Plus if she rents only 5 movies?
5. If the one-time fee for Movies Plus is reduced to $10, how many movies must Monique rent for the costs to be equal?

**Tip:** Always check whether fixed costs, like the one-time fee, influence your decision, especially for smaller quantities.

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?

Discover how to solve a cost comparison problem between Movies Plus and Movies-To-Go using linear equations. This solution involves calculating when the cost of renting movies from both services is equal, using algebraic methods. Suitable for students in Grades 6-8.

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