Question

Two video rental clubs offer two different rental fee plans.Club A charges $12 for membership and $2 for each rented video.Club B charges $4 for membership fee and charges $4 for each rented video.Which video rental club is the better deal and why?

Answer 1

Answer: Club A

 

EXPLANATION

Given,

Club A charges $12 for membership and $2 for each rented video.

The deal in Club A can be represented by the function, f(x) = 12 + 2x

 

Club B charges $4 for membership fee and charges $4 for each rented video.

The deal in Club B can be represented by the function, f(x) = 4 + 4x

 

 

To determine which video rental club is the better deal

First, we find the number of videos where the amount spent will be the same

 

That is, when 4 + 4x = 12 + 2x

 

Subtract 4 from both sides of the equation

4 + 4x – 4 = 12 + 2x – 4

4x = 8 + 2x

 

Subtract 2x from both sides of the equation

4x – 2x = 8 + 2x – 2x

2x = 8

 

Divide both sides by 2

2x/2 = 8/2

x = 4

 

Since the deals for club B and club B will be of equal expense by the time a total of 4 videos have been rented, the better deal is the one that is cheaper when more than 4 videos have been rented.

 

Take a random value of x that is greater than 4, say 6

 

For the deal in Club A, f(x) = 12 + 2x

= 12 + 2(6)

= 12 + 12

= $24

 

For the deal in Club A, f(x) = 4 + 4x

= 4 + 4(6)

= 4 + 24

= $28

 

Since the deal in Club A is cheaper on the long run (i.e for 5 videos and above), it is a better deal than that of Club B