SOLUTION: Ana wants to subscribe to a movie streaming service on her TV. She has two options: Option A charges a fee of $13.00 per month and provides unlimited movies. Option B charge

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Question 1189714: Ana wants to subscribe to a movie streaming service on her TV. She has two options:
Option A charges a fee of $13.00 per month and provides unlimited movies.
Option B charges a fee of $4.00 per month plus $2.50 for each movie watched.
How many movies does Ana need to watch to make Option A worth the cost?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
optioon A = 13 per month with unlimited movies.
option B = 4 per month plus 2.50 for each movie.

the breakeven point is when cost for option A equals cost for option B.
that occurs when 13 = 4 + 2.5 * x
x is the number of movies watched.
subtract 4 from sides of the equation to get 9 = 2.5 * x
solve for x to get x = 9/2.5 = 3.6
at less than or equal to 3 movies, option A is more expensive.
at greater than or equal to 4 movies, option B is more expensive.

you have two equations.
they are:
y = 13 and y = 4 + 2.5 * x
subtract the second equation from the first to get:
y = 13 - 4 - 2.5 * x
simplify to get:
y = 9 - 2.5 * x
when the graph is positive, option A is more expensive.
when the graph is negative, option B is more expensive.
the graph looks like this.



you can also graph the equations separately.
you would graph y = 13 and y = 4 + 2.5 * x
that graph looks like this.



you can also create a table around the breakeven point.
the table would look like this:
x           y1 = 13          y1 = 4 + 2.5 * x        y1 - y2
2              13                  9                    4
3              13                  11.5                 1.5
4              13                  14                   -1
5              13                  16.5                 -3.5


all graphs and tables point to the fact that, at 3 movies or less per month, option A is more expensive, while at 4 movies or more per month, option B is more expensive.

ana would need to watch 4 movies or more per month to make option A worth the cost.