A video store offers two rental plans. The yearly membership fee and the daily charge per video for each plan are shown below. How many one-night rentals can be made per year if the No-fee plan is to be the less expensive of the plans? Rental Plan Yearly Fee Daily Charge per Video Low-Rate $30.00 $2.49 No-Fee None $3.99

Question

Quizplus · Accepted Answer

For the No-Fee plan to be less expensive, the total cost of one-night rentals for the year must be less than $30.00 (the yearly fee for the Low-Rate plan).

Let's calculate the total cost of one-night rentals for the year under each plan:

No-Fee Plan: 
Daily charge per video = $3.99
Number of one-night rentals for the year = x

Total cost = 3.99x

Low-Rate Plan:
Yearly fee = $30.00
Daily charge per video = $2.49
Number of one-night rentals for the year = y

Total cost = 30.00 + (2.49y)

We want the total cost under the No-Fee Plan to be less than $30.00.

3.99x < 30.00

x < 7.52

This means that the maximum number of one-night rentals that can be made under the No-Fee Plan for it to be less expensive than the Low-Rate Plan is 7.

Let's check the total cost of one-night rentals for the year under each plan for 7 rentals:

No-Fee Plan:
Total cost = 3.99(7) = $27.93

Low-Rate Plan:
Total cost = 30.00 + (2.49(7)) = $48.43

Since the total cost of one-night rentals for the year under the No-Fee Plan is less than $30.00, and also less than the total cost under the Low-Rate Plan for 7 rentals, the best choice is:

D) 20 rentals or less

A Video Store Offers Two Rental Plans