Amazon charges a flat rate of $129 (yearly) for Amazon Prime and $7.99 for each HD movie rental.
Youtube Red charges a flat rate of $144 (yearly) and $4.99 for each movie rental.
a) Write an equation to represent Amazon's charges. Explain how you got that equation.
b) Write an equation to represent Youtube's charges. Explain how you got that equation.
c) Solve the system of equations to determine how many movies you must rent from each company to have equal bills.
***DO NOT just give an answer. You must show your work and explain what you did.***
d) What would be the dollar amount when the bills are equal? How did you get that answer?
A = 129 + 7.99 n
Y = 144 + 4.99 m
if Y = A and m = n then
129 + 7.99 n = 144 + 4.99 n
3 n = 15
n = m = 5 of either
put that back as n in the A equation or as m in Y
Y = 144 + 4.99 * 5
a) To represent Amazon's charges, we need to consider the fixed annual fee for Amazon Prime and the variable cost per HD movie rental.
Let's use the variable "x" to represent the number of HD movie rentals from Amazon. The equation for Amazon's charges can be written as follows:
Total Charges for Amazon = Annual Fee for Amazon Prime + (Cost per HD Movie Rental * Number of HD Movie Rentals)
Total Charges for Amazon = $129 + ($7.99 * x)
b) Similarly, to represent Youtube's charges, we consider the fixed annual fee for Youtube Red and the variable cost per movie rental.
Using the variable "y" to represent the number of movie rentals from Youtube, the equation for Youtube's charges would be:
Total Charges for Youtube = Annual Fee for Youtube Red + (Cost per Movie Rental * Number of Movie Rentals)
Total Charges for Youtube = $144 + ($4.99 * y)
c) To determine the number of movies you must rent from each company to have equal bills, we need to solve the system of equations:
Total Charges for Amazon = Total Charges for Youtube
$129 + ($7.99 * x) = $144 + ($4.99 * y)
We need to find the values of "x" and "y" that satisfy this equation.
d) To find the dollar amount when the bills are equal, we need to solve the system of equations and determine the values of "x" and "y". Once we have these values, we can substitute them into either equation to find the equal bill amount.
Substituting the value of "x" from equation (a) into equation (b):
$129 + ($7.99 * x) = $144 + ($4.99 * y)
$129 + ($7.99 * (y - $144)) = $144 + ($4.99 * y)
Now, we can solve this equation to find the values of "x" and "y" that satisfy the equation.