5. A group of eighth-graders at your school is thinking of forming a club whose members rent DVDs. The club would also rent DVDs to non-members but at a higher price.

They decided to create a membership for $20 flat fee and then charge $4 per DVD for members. Non-members could also rent a DVD, but for $5 per DVD.
When would the membership be worth the money? Show all of your work, graphs, equations to answer this question.

1 answer

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Did you know?

Did you know that when deciding whether a membership is worth the money, it is important to consider the number of DVDs rented? In the case of the eighth-graders' club, let's do some math to find out. Let's assume the number of DVDs rented per month is denoted by x. For members, the cost equation would be "y = 4x + 20", where y represents the total cost including the membership fee. For non-members, the equation would be "y = 5x". To determine when the membership is worth the money, we need to find the point where the total cost for non-members equals the total cost for members. In other words, we need to find the intersection point of the two equations. By setting the equations equal to each other, we have: 4x + 20 = 5x Rearranging the equation, we get: 20 = x Hence, when the number of DVDs rented is equal to 20, the membership would be worth the money. Beyond that, members would save money compared to non-members. Graphically, we can plot the two cost equations on a graph and look for the point of intersection. The point where the lines cross would represent the number of DVDs rented at which the membership becomes financially beneficial.