Before streaming became popular, families had to visit video rental stores like Blockbuster and Hollywood Video to rent movies. The graph compares the costs at both locations: Blockbuster charges a $3 monthly membership fee and $0.75 for each movie rented, while Hollywood Video charges a $5 monthly membership fee but only $0.50 per movie rented.

Question

Describe a scenario in which it would be cheaper to have a Blockbuster membership, and then describe a scenario where a Hollywood Video membership would be the more affordable option

GPT-4o mini · Answer

To determine when each membership would be cheaper, we can set up a cost comparison based on the number of movies rented in a month.

Blockbuster Membership Cost:

Monthly fee: $3
Cost per movie rented: $0.75
Total cost for $ x $ movies rented: $ 3 + 0.75x $

Hollywood Video Membership Cost:

Monthly fee: $5
Cost per movie rented: $0.50
Total cost for $ x $ movies rented: $ 5 + 0.50x $

Scenario Favoring Blockbuster

Let’s determine the crossover point where both memberships cost the same:

Set the costs equal: $ 3 + 0.75x = 5 + 0.50x $
Solve for $ x $:
- $ 0.75x - 0.50x = 5 - 3 $
- $ 0.25x = 2 $
- $ x = 8 $

This means that Blockbuster is cheaper when renting less than 8 movies per month.

Scenario: A family that rents 6 movies in a month would find it cheaper to have a Blockbuster membership:

Blockbuster Cost: $ 3 + (0.75 \times 6) = 3 + 4.50 = $7.50 $
Hollywood Video Cost: $ 5 + (0.50 \times 6) = 5 + 3 = $8.00 $

Scenario Favoring Hollywood Video

In contrast, if a family rents more movies, Hollywood Video becomes the better option.

Scenario: A family that rents 10 movies in a month would find it cheaper to have a Hollywood Video membership:

Blockbuster Cost: $ 3 + (0.75 \times 10) = 3 + 7.50 = $10.50 $
Hollywood Video Cost: $ 5 + (0.50 \times 10) = 5 + 5 = $10.00 $

Summary

For renting less than 8 movies, Blockbuster membership is cheaper.
For renting 8 or more movies, Hollywood Video membership is more affordable.