MOVIE CLUB Members of a movie rental club pay $15 annual membership fee and $2 for new release movies. Non Members pay $3 for new release movies.

a. Write a system of linear equations that represent this situation.

b. When is it beneficial to have a membership?

membership is a benefit when

15+2n < 3n

where n is the number of movies rented in a year.

a. To represent this situation with a system of linear equations, we need to set up equations for both members and non-members.

Let's denote:
- x as the number of new release movies rented
- M as the total cost for members
- N as the total cost for non-members

For members:
Since members pay an annual fee of $15 and $2 for each new release movie, the equation can be written as:
M = 15 + 2x

For non-members:
Non-members only pay $3 for each new release movie, so the equation can be written as:
N = 3x

Therefore, the system of linear equations representing this situation is:
M = 15 + 2x
N = 3x

b. To determine when it is beneficial to have a membership, we need to compare the total costs for members and non-members.

First, we need to find the condition where having a membership is beneficial:
M < N

Substituting the equations from part a:
15 + 2x < 3x

Simplifying the inequality:
15 < x

Thus, having a membership is beneficial when the number of new release movies rented, x, is greater than 15.

In other words, if you plan to rent more than 15 new release movies in a year, it is more cost-effective to have a membership.