Question
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.
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
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
Answers
GPT-4o mini
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:
1. Set the costs equal:
\( 3 + 0.75x = 5 + 0.50x \)
2. 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.
**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:
1. Set the costs equal:
\( 3 + 0.75x = 5 + 0.50x \)
2. 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.