Question

Andres is deciding between two different movie streaming sites to subscribe to. Plan A costs $12 per month plus $1 per movie watched. Plan B costs $8 per month plus $2 per movie watched. Let AA represent the monthly cost of Plan A if Andres watches xx per month, and let BB represent the monthly cost of Plan B if Andres watches xx movies per month. Graph each function and determine the number of monthly movies watched, x, commax, that would make the two plans have an equal monthly cost.

Answer 1

At 4 movies/month, both plans cost the same. Beyond 4, Plan B costs more; below 4, Plan A is pricier.

To represent the monthly cost for each plan as a function of the number of movies watched per month x, we'll use the provided information:

For Plan A:

Monthly cost (AA) = $12 (fixed cost) + $1 (cost per movie) × x (number of movies watched).

The function for Plan A can be written as: A(x) = 12 + x.

For Plan B:

Monthly cost (BB) = $8 (fixed cost) + $2 (cost per movie) × x (number of movies watched).

The function for Plan B can be written as: B(x) = 8 + 2x.

To find the number of movies x that would make the two plans have an equal monthly cost, we'll set the equations A(x) and B(x) equal to each other and solve for x:

12 + x = 8 + 2x

x = 4

At x = 4 movies per month, both plans have an equal monthly cost. To visualize this, we can plot the functions A(x) and B(x) on a graph, where the x-axis represents the number of movies watched per month and the y-axis represents the monthly cost in dollars.

At x = 4 on the graph, the two lines representing Plan A and Plan B intersect, signifying the point where both plans have the same monthly cost. Beyond this point, Plan B becomes more expensive, and below this point, Plan A is more expensive.