Letter 'C' on this question confuses me, please help!
Holly has joined a video rental club. After paying $6 a year to join, she
then has to pay only $1.25 for each new release she rents.
a. Write an equation in intercept form to represent Holly’s cost for movie rentals.
b. Graph this situation for up to 60 movie rentals.
c. Video Unlimited charges $60 for a year of unlimited movie rentals. How many movies would Holly have to rent for this to be a better deal?
I don't know if this is "intercept form," but here goes. Let x = # of rentals.
C = 6 + 1.25x
Cannot graph on this post.
60 < 6 + 1.25x
To find out how many movies Holly would have to rent for Video Unlimited to be a better deal, we need to compare the total cost of renting movies through Holly's video rental club with the cost of Video Unlimited.
Let's start by determining the equation in intercept form to represent Holly's cost for movie rentals.
a. To find the equation, we need to understand the cost structure. Holly pays $6 as a yearly fee, which is a fixed cost, and then she pays $1.25 for each new release she rents, which is a variable cost.
Let's represent the number of movie rentals as 'x' and the total cost as 'y.' The equation can be written as:
y = 1.25x + 6
Now, let's move on to graphing the situation for up to 60 movie rentals.
b. To graph this situation, we need to plot the number of movie rentals on the x-axis and the total cost on the y-axis.
Using the equation we found earlier (y = 1.25x + 6), we can plug in values for x (the number of movie rentals) and calculate the corresponding y (the total cost).
For example, if Holly rents 10 movies, the equation becomes:
y = 1.25 * 10 + 6
y = 12.5 + 6
y = 18.5
We can repeat this process for different values of x and plot these points on a graph. By connecting the points, we can visualize the data and see the relationship between movie rentals and the total cost.
c. To determine how many movies Holly would have to rent for Video Unlimited to be a better deal, we need to find the point where the cost of Holly's video rental club equals $60, which is the cost of Video Unlimited.
By substituting y = 60 into the equation we found earlier (y = 1.25x + 6), we can solve for x:
60 = 1.25x + 6
Rearranging the equation:
1.25x = 60 - 6
1.25x = 54
Dividing both sides by 1.25:
x = 54 / 1.25
x ≈ 43.2
Since Holly cannot rent a fraction of a movie, she would need to rent at least 44 movies for Video Unlimited to be a better deal in terms of cost.