Question: User: 1. Movie Rentals
Movie Store A charges a $12 membership fee plus $3 per movie rented. Movie Store B has no membership fee but charges $5 per movie.
Write a system of equations to represent this relationship. Graph the equations and use the graph to determine the number of movies rented that would cost the same from each store.
Be sure to use let statements to define variables!
1. **State the problem:**
We want to find the number of movies rented where the total cost from Movie Store A equals the total cost from Movie Store B.
2. **Define variables:**
Let $x$ = number of movies rented.
Let $y$ = total cost.
3. **Write the equations:**
- Movie Store A charges a $12 membership fee plus $3 per movie, so:
$$y = 12 + 3x$$
- Movie Store B charges $5 per movie with no membership fee, so:
$$y = 5x$$
4. **Set the equations equal to find the break-even point:**
$$12 + 3x = 5x$$
5. **Solve for $x$:**
$$12 = 5x - 3x$$
$$12 = 2x$$
$$x = \frac{12}{2}$$
$$x = 6$$
6. **Interpretation:**
At $6$ movies rented, the total cost from both stores is the same.
7. **Calculate the cost at $x=6$:**
$$y = 12 + 3(6) = 12 + 18 = 30$$
$$y = 5(6) = 30$$
**Final answer:**
The cost is the same at $6$ movies rented, costing $30$ at both stores.