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.
Ideas???????
First, what we know:
membership flat fee: $20
dvd for members: $4
dvd for non-members: $5
Therefore, we know that the two equations are:
members:
y=5x
non-members:
y = 4x+20
if we put these two graphs into desmos.com, we can determine that when students buy more than 100 dvd's the membership is worth it.
So, when students buy more than 100 dvd's the membership is worth it.
not really
please this is really hard
20 + 4 x = 5 x
x = 20
To determine when the membership would be worth the money, we need to compare the total cost of renting DVDs as a member versus renting DVDs as a non-member.
Let's start by considering the cost of renting DVDs as a member. The membership fee is a flat fee of $20, and each DVD rental costs $4.
Therefore, the cost of renting 'x' DVDs as a member can be calculated with the equation: Cost as member = 20 + 4x.
On the other hand, as a non-member, the cost of renting DVDs is $5 per DVD rental.
The cost of renting 'x' DVDs as a non-member will be: Cost as non-member = 5x.
We need to find the point where the cost as a member becomes less than or equal to the cost as a non-member. Mathematically, this means that we need to solve the inequality:
20 + 4x ≤ 5x
To solve this inequality, we subtract 4x from both sides of the equation:
20 ≤ x
So, the membership would be worth the money if and only if the number of DVDs rented, 'x', is greater than or equal to 20.
In other words, if the number of DVDs rented is 20 or more, then the membership would be worth the money. If the number is less than 20, then it would be cheaper to rent DVDs as a non-member.
Graphically, we can plot the two equations, Cost as member = 20 + 4x and Cost as non-member = 5x, on a coordinate plane. The point(s) where the two lines intersect represent the number of DVDs at which the costs are equal, indicating when the membership becomes worth it.