SOLUTION: I need to take a real-life situation and create an equation or inequality that could be used for analysis, prediction, or decision making. Then, draw a graph to depict the variable

Question 118510: I need to take a real-life situation and create an equation or inequality that could be used for analysis, prediction, or decision making. Then, draw a graph to depict the variables in my siuation. Use the graph and what you know about linear inequalities to discuss the significants of your finding.
My real-life siuation is comparing cell phone plans. I have two plans
29.99 a month for 200 minutes and $.45 each additional minute. The other is 29.99 a month for 300 minutes and $.40 each additional minute. They each have an activation fee of 90.00. I am confused on how to write this in a equation or inequality and how to create the graph. I believe once I figure out the equation then the graph should come out correctly. Thank you for any help that you can give.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I have two plans
29.99 a month for 200 minutes and $.45 each additional minute.
-------
Comment: Do you want an equation that covers one month or
one year. Do the "additional minutes" refer to one month
or to one year.
2nd Comment: I think you are making this much more complicated
than it needs to be. Why not compare monthly costs for the two
plans where one has fixed fee of $20 and 50 cents for all minutes
over 200, and the other charges 25 cents per minute with no fixed
fee.
Then you would have:
1st Plan:
C(x) = 20+1.50(x-200)
2nd Plan:
C(x) = 0.25x

=============
Cheers,
Stan H.

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
First plan:
$ a month for minutes and $each additional minute, and an activation fee of $

If ,then
let
let
let ��..cost per each additional minute
let �.sum of a monthly fee and activation fee

the a monthly fee for minutes is $; means, the first cost $
the remaining minutes cost $ each
so the remaining minutes altogether costs $

your total cost:

Second plan:
$ a month for minutes and $each additional minute, and an activation fee of $

your total cost:

Here is the graph:
you can compare your plans and see which one is better plan

Solved by pluggable solver: Solve the System of Equations by Graphing

Start with the given system of equations:

In order to graph these equations, we need to solve for y for each equation.

So let's solve for y on the first equation

Start with the given equation

Add to both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Add to both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

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