Question

Ama-zon charges a flat rate of $129 (yearly) for Ama-zon Pr-ime and $7.99 for each HD movie rental. You-tube 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 You-tube'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.

d) What would be the dollar amount when the bills are equal? How did you get that answer?

Answer 1

a) The equation which represents Ama-zon's charges is
`129+7.99x`

b) The equation which represents You-tube's charges is
`144+4.99x`

c) Total number of movies which need to be rented should 5 so that both have equal bills.

d) the amount will be $168.95 which would be same for both company after renting 5 movies.

Explanation:

Given:

Flat Rate of Ama-zon = $129

Price of each movie rental = $7.99

Let 'x' represents the number of movie to be rented.

Solving for part a

Hence Total amount charge by Ama-zon will be equal to sum of Flat Rate of Ama-zon and Price of each movie rental multiplied by number of movie to be rented.

Framing in equation form we get;

Total amount charge by Ama-zon =
`129+7.99x` (let it be equation 1)

Hence the equation which represents Ama-zon's charges is
`129+7.99x`

Also Given:

Flat Rate of You-tube = $144

Price of each movie rental = $4.99

Let 'x' represents the number of movie to be rented.

Solving for part b

Hence Total amount charge by You-tube will be equal to sum of Flat Rate of You-tube and Price of each movie rental multiplied by number of movie to be rented.

Framing in equation form we get;

Total amount charge by You-tube =
`144+4.99x` (Let this be equation 2)

Hence the equation which represents You-tube's charges is
`144+4.99x`

Solving for part c

To determine number of movies to be rented so that both have equal bills.

i.e we need to find the value of x

Total amount charge by Ama-zon = Total amount charge by You-tube

`129+7.99x=144+4.99x\\\\7.99x-4.99x=144-129\\\\3x=15\\\\x=(15)/(3)=5`

Hence Total number of movies which need to be rented should 5 so that both have equal bills.

Solving for part d.

Now Substituting the value of x = 5 which makes both the company charge equal we will find the dollar amount.

Total amount charge by Ama-zon =
`129+7.99x = 129 + 7.99* 5 = 129+39.95 = $168.95`

Total amount charge by You-tube =
`144+4.99x = 144 + 4.99* 5 = 144+24.95 = $168.95`

Hence the amount will be $168.95 which would be same for both company after renting 5 movies.