You have purchased a VCR for $180. You also joined a video rental store where you can rent movies for $3 each.
Suppose that the cost of admission to a movie theater is $6.00. How many videos must you rent to make your average cost per video less than $6.00?
To determine how many videos you must rent to make your average cost per video less than $6.00, we can set up an equation based on the given information.
Let's assume you rent "x" videos from the video rental store.
The total amount spent on the VCR and video rentals can be calculated as:
Total Cost = Cost of VCR + Cost of Video Rentals
Given:
Cost of VCR = $180
Cost of Video Rentals = $3 per video
Number of Videos Rented = x
Total Cost = 180 + 3x
To calculate the average cost per video, divide the total cost by the number of videos rented:
Average Cost = Total Cost / Number of Videos Rented
Average Cost = (180 + 3x) / x
You want the average cost per video to be less than $6.00:
Average Cost < $6.00
Therefore, the equation becomes:
(180 + 3x) / x < 6
To solve this inequality, we'll multiply both sides of the inequality by "x" since "x" is positive (you can't rent a negative number of videos):
180 + 3x < 6x
Now, subtract 3x from both sides:
180 < 6x - 3x
180 < 3x
Divide both sides by 3:
60 < x
So, you must rent more than 60 videos to make your average cost per video less than $6.00.