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.

Answer 1

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.

Answer 2

another 2 scenrio

Answer 3

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.