At Mr.Vid's Rentals you can join his VID Club for a monthly membership fee of $30.Club members pay only $.85 to rent each movie. If you are not a member of the VID Club, the movies rent for $2.25 each.How many videos would you have to rent each month to make a membership worth the investment?

Question

At Mr.Vid's Rentals you can join his VID Club for a monthly membership fee of $30.Club members pay only $.85 to rent each movie. If you are not a member of the VID Club, the movies rent for $2.25 each.How many videos would you have to rent each month to make a membership worth the investment?

Answer 1

30 + .85x < 2.25x

Solve for x.

Answer 2

To determine the number of videos you would have to rent each month to make a membership worth the investment, we need to calculate the break-even point.

Let's assume the number of videos rented per month is represented by x.

For non-members, the rental cost per video is $2.25. So without the membership, the total cost per month would be 2.25x.

For VID Club members, the rental cost per video is $0.85. In addition, there is a monthly membership fee of $30. Therefore, the total cost per month for club members would be 0.85x + 30.

To find the break-even point, we set the two costs equal to each other:

2.25x = 0.85x + 30

Subtracting 0.85x from both sides of the equation:

2.25x - 0.85x = 0.85x + 30 - 0.85x

1.4x = 30

Now, we can solve for x by dividing both sides of the equation by 1.4:

x = 30 / 1.4

x ≈ 21.43

Therefore, you would have to rent approximately 21.43 videos per month to make the membership worth the investment. Since it is not possible to rent a fraction of a video, you would have to round up to the nearest whole number. In this case, you would need to rent at least 22 videos per month to break even.

Answer 3

To determine how many videos you would have to rent each month to make a membership worth the investment, we need to compare the cost of renting as a member versus the cost of renting without a membership.

If you are a member of the VID Club, the cost to rent each movie is $0.85. Without a membership, the cost to rent each movie is $2.25.

Let's calculate the breakeven point:

1. Subtract the cost per movie with a membership from the cost per movie without a membership: $2.25 - $0.85 = $1.40
2. Divide the monthly membership fee by the price difference calculated in step 1: $30 / $1.40 = approximately 21.43

To make the membership worth the investment, you would need to rent more than 21 movies per month. Since you cannot rent a fraction of a movie, the rounded-up value of 22 would be the minimum number of videos you would have to rent each month to make the membership worth it.