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.
Answers
GPT-4o mini
To determine when each video rental store would be the more cost-effective option, we can set up a comparison based on the membership fees and rental costs.
**Blockbuster Costs:**
- Membership Fee: $3 per month
- Cost per Movie Rented: $0.75
The total cost for renting movies from Blockbuster can be described by the equation:
\[ \text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75m \]
where \( m \) is the number of movies rented in a month.
**Hollywood Video Costs:**
- Membership Fee: $5 per month
- Cost per Movie Rented: $0.50
The total cost for renting movies from Hollywood Video can be described by the equation:
\[ \text{Total Cost}_{\text{Hollywood}} = 5 + 0.50m \]
### Scenario 1: Cheaper to Rent from Blockbuster
Let’s find a scenario where renting from Blockbuster is cheaper.
Assume a family rents **4 movies** in a month.
**Blockbuster Costs:**
\[ \text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(4) = 3 + 3 = 6 \]
**Hollywood Video Costs:**
\[ \text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(4) = 5 + 2 = 7 \]
In this scenario, renting 4 movies results in a total cost of **$6** at Blockbuster, which is **$1 cheaper** than renting at Hollywood Video, which costs **$7**.
### Scenario 2: Cheaper to Rent from Hollywood Video
Now, let’s find a scenario where renting from Hollywood Video is the more affordable option.
Assume a family rents **10 movies** in a month.
**Blockbuster Costs:**
\[ \text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(10) = 3 + 7.5 = 10.5 \]
**Hollywood Video Costs:**
\[ \text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(10) = 5 + 5 = 10 \]
In this scenario, renting 10 movies results in a total cost of **$10** at Hollywood Video, which is **$0.50 cheaper** than renting at Blockbuster, which costs **$10.5**.
### Conclusion
To summarize, renting from Blockbuster is cheaper when renting **4 movies** in a month, while renting from Hollywood Video becomes cheaper when renting **10 movies**. The threshold for determining which service is cheaper shifts based on the number of rentals, highlighting the importance of considering usage patterns when choosing membership options.
**Blockbuster Costs:**
- Membership Fee: $3 per month
- Cost per Movie Rented: $0.75
The total cost for renting movies from Blockbuster can be described by the equation:
\[ \text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75m \]
where \( m \) is the number of movies rented in a month.
**Hollywood Video Costs:**
- Membership Fee: $5 per month
- Cost per Movie Rented: $0.50
The total cost for renting movies from Hollywood Video can be described by the equation:
\[ \text{Total Cost}_{\text{Hollywood}} = 5 + 0.50m \]
### Scenario 1: Cheaper to Rent from Blockbuster
Let’s find a scenario where renting from Blockbuster is cheaper.
Assume a family rents **4 movies** in a month.
**Blockbuster Costs:**
\[ \text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(4) = 3 + 3 = 6 \]
**Hollywood Video Costs:**
\[ \text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(4) = 5 + 2 = 7 \]
In this scenario, renting 4 movies results in a total cost of **$6** at Blockbuster, which is **$1 cheaper** than renting at Hollywood Video, which costs **$7**.
### Scenario 2: Cheaper to Rent from Hollywood Video
Now, let’s find a scenario where renting from Hollywood Video is the more affordable option.
Assume a family rents **10 movies** in a month.
**Blockbuster Costs:**
\[ \text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(10) = 3 + 7.5 = 10.5 \]
**Hollywood Video Costs:**
\[ \text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(10) = 5 + 5 = 10 \]
In this scenario, renting 10 movies results in a total cost of **$10** at Hollywood Video, which is **$0.50 cheaper** than renting at Blockbuster, which costs **$10.5**.
### Conclusion
To summarize, renting from Blockbuster is cheaper when renting **4 movies** in a month, while renting from Hollywood Video becomes cheaper when renting **10 movies**. The threshold for determining which service is cheaper shifts based on the number of rentals, highlighting the importance of considering usage patterns when choosing membership options.
another 2 scenrio
GPT-4o mini
Certainly! Let's explore two more scenarios to further illustrate when each video rental service would be more affordable.
### Scenario 3: Cheaper to Rent from Blockbuster
Let's consider a situation where a family rents **2 movies** in a month.
**Blockbuster Costs:**
\[
\text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(2) = 3 + 1.5 = 4.5
\]
**Hollywood Video Costs:**
\[
\text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(2) = 5 + 1 = 6
\]
In this scenario, renting **2 movies** results in a total cost of **$4.5** at Blockbuster, which is **$1.5 cheaper** than renting at Hollywood Video, which costs **$6**.
### Scenario 4: Cheaper to Rent from Hollywood Video
Now let’s take a look at a scenario where renting from Hollywood Video is the more affordable option, specifically when a user rents **8 movies** in a month.
**Blockbuster Costs:**
\[
\text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(8) = 3 + 6 = 9
\]
**Hollywood Video Costs:**
\[
\text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(8) = 5 + 4 = 9
\]
In this case, the total costs for both Blockbuster and Hollywood Video come out to be **$9** when renting **8 movies**. However, let’s increase the rentals to **11 movies** to see when Hollywood Video becomes more favorable.
**Now for renting 11 movies:**
**Blockbuster Costs:**
\[
\text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(11) = 3 + 8.25 = 11.25
\]
**Hollywood Video Costs:**
\[
\text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(11) = 5 + 5.5 = 10.5
\]
In this revised scenario, renting **11 movies** results in a total cost of **$10.5** at Hollywood Video, which is **$0.75 cheaper** than renting from Blockbuster, which costs **$11.25**.
### Summary of Scenarios
1. **Blockbuster is cheaper** when renting **2 movies** (Blockbuster: $4.5 vs. Hollywood: $6).
2. **Hollywood Video is cheaper** when renting **11 movies** (Blockbuster: $11.25 vs. Hollywood: $10.5).
These scenarios demonstrate how the choice of video rental service can vary depending on the number of movies rented in a month.
### Scenario 3: Cheaper to Rent from Blockbuster
Let's consider a situation where a family rents **2 movies** in a month.
**Blockbuster Costs:**
\[
\text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(2) = 3 + 1.5 = 4.5
\]
**Hollywood Video Costs:**
\[
\text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(2) = 5 + 1 = 6
\]
In this scenario, renting **2 movies** results in a total cost of **$4.5** at Blockbuster, which is **$1.5 cheaper** than renting at Hollywood Video, which costs **$6**.
### Scenario 4: Cheaper to Rent from Hollywood Video
Now let’s take a look at a scenario where renting from Hollywood Video is the more affordable option, specifically when a user rents **8 movies** in a month.
**Blockbuster Costs:**
\[
\text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(8) = 3 + 6 = 9
\]
**Hollywood Video Costs:**
\[
\text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(8) = 5 + 4 = 9
\]
In this case, the total costs for both Blockbuster and Hollywood Video come out to be **$9** when renting **8 movies**. However, let’s increase the rentals to **11 movies** to see when Hollywood Video becomes more favorable.
**Now for renting 11 movies:**
**Blockbuster Costs:**
\[
\text{Total Cost}_{\text{Blockbuster}} = 3 + 0.75(11) = 3 + 8.25 = 11.25
\]
**Hollywood Video Costs:**
\[
\text{Total Cost}_{\text{Hollywood}} = 5 + 0.50(11) = 5 + 5.5 = 10.5
\]
In this revised scenario, renting **11 movies** results in a total cost of **$10.5** at Hollywood Video, which is **$0.75 cheaper** than renting from Blockbuster, which costs **$11.25**.
### Summary of Scenarios
1. **Blockbuster is cheaper** when renting **2 movies** (Blockbuster: $4.5 vs. Hollywood: $6).
2. **Hollywood Video is cheaper** when renting **11 movies** (Blockbuster: $11.25 vs. Hollywood: $10.5).
These scenarios demonstrate how the choice of video rental service can vary depending on the number of movies rented in a month.