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

Algebra ->  Graphs -> 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      Log On


   

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) About Me  (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
graph%28400%2C300%2C-30%2C400%2C-10%2C200%2C20%2B0.5%28x-200%29%2C0.25x%29
=============
Cheers,
Stan H.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
First plan:
$29.99 a month for 200 minutes and $.45+each additional minute, and an activation fee of $90.00


If y+=mx+%2B+b,then
let x+=+the_+number_+of_+minutes
let total+_cost=+y
let m+=+.45 ……..cost per each additional minute
let b+=+%2829.99+%2B+90.00%29 ….sum of a monthly fee and activation fee

the a monthly fee for 200 minutes is $29.99; means, the first 200+min. cost $29.99
the remaining x-200 minutes cost $0.21 each
so the remaining x-1 minutes altogether costs $.45+%28x-200%29

your total cost:

y+=+.45+%28x-200%29+%2B+%2829.99+%2B+90.00%29+
y+=+.45+%28x-200%29+%2B+119.99


Second plan:
$29.99 a month for 300 minutes and $.40+each additional minute, and an activation fee of $90.00

your total cost:
y+=+.40+%28x-300%29+%2B+%2890.00%2B+29.99+%29
y+=+.40+%28x-300%29+%2B+119.99


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:


-45x%2By=11999

-40x%2By=11999





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


-45x%2By=11999 Start with the given equation



1y=11999%2B45x Add 45+x to both sides



1y=%2B45x%2B11999 Rearrange the equation



y=%28%2B45x%2B11999%29%2F%281%29 Divide both sides by 1



y=%28%2B45%2F1%29x%2B%2811999%29%2F%281%29 Break up the fraction



y=45x%2B11999 Reduce



Now lets graph y=45x%2B11999 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+45x%2B11999%29+ Graph of y=45x%2B11999




So let's solve for y on the second equation


-40x%2By=11999 Start with the given equation



1y=11999%2B40x Add 40+x to both sides



1y=%2B40x%2B11999 Rearrange the equation



y=%28%2B40x%2B11999%29%2F%281%29 Divide both sides by 1



y=%28%2B40%2F1%29x%2B%2811999%29%2F%281%29 Break up the fraction



y=40x%2B11999 Reduce





Now lets add the graph of y=40x%2B11999 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+45x%2B11999%2C40x%2B11999%29+ Graph of y=45x%2B11999(red) and y=40x%2B11999(green)


From the graph, we can see that the two lines intersect at the point (0,11999) (note: you might have to adjust the window to see the intersection)