Answer:
a) Amazon Cost per year with "x" movie rentals = 129 + 7.99 x
b) You Tube Cost per year with "x" movie rentals = 144 + 4.99 x
c) with exactly 5 movie rentals per year the annual costs will be equal
d) In such case the total annual cost would be $168.95
Step-by-step explanation:
a) Let's analyze how to represent Amazon charges per year as a function of number of movies rented. There is a fixed membership cost of $129, and there is a $7.99 per movie rented. So if we rent "x" movies over the year, the total cost for just movie rentals would be the product of the number of movies (x) times the price each rental involves ($7.99) that in math terms can be written as: "7.99 x". And the total Amazon cost (AC) will include not just the annual membership of $129 but the amount we just estimated due to x movie rentals per year (7.99 x):
AC = 129 + 7.99 x
and the cost will come in dollars ($)
b) Now, doing something similar for You Tube, considering again "x" movie rentals, the yearly cost for You Tube (YC) would be the fix flat rate of $144, plus what it would cost to rent "x" movies at the price of $4.99 each:
YC = 144 + 4.99 x
c) In order to find how many movies (x) we need to rent to have the bill from both companies equal each other, we set the equation that equal the amazon cost to the You Tube cost (AC = YC), and solve for "x":
[tex]AC = YC\\129+7.99\,x=144+4.99\,x\\7.99\,x-4.99\,x=144-129\\3\,x=15\\x=\frac{15}{3} \\x=5[/tex]
So this tells us that if we rent 5 videos per year, the cost of the two companies will be the same.
d) Now we need to find what that total cost would be, that we can do by using either cost expression (since for the 5 movie rental both should give the same cost). We use for example the You Tube cost equation and evaluate it for "x" (number of movie rentals) equal "5":
[tex]YC=144+4.99\,x\\YC=144+4.99\,(5)\\YC=168.95[/tex]
Therefore, the annual cost in this case would be $168.95
