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compare cell phones plans

How do you use systems of equations to compare cell phone plans?

Here’s a simple example. I’m going to ignore text messaging and mobile web prices because I don’t know how complicated you want it to be.
I’m just going to assume there is a monthly charge (no matter how many minutes you use) and a charge per minute for the amount of minutes that you go over your allowed minutes.

Let’s say plan A is 39.99/month for 500 minutes, and then it is $0.65 per minute after you use the 500 minutes.
Let’s say plan B is $34.99/month for 450 minutes, and then it is $0.60 per minute after the 450 minutes.

Let x = number of minutes you use each month.
The cost of plan A would be
C = 39.99 if you use less than 500 minutes or
C = 39.99 + 0.65(x-500) if you use 500 minutes or more.

The cost of plan B would be
C = 34.99 if you use less than 450 minutes or
C = 34.99 + 0.60(x-450) if you use more than 450 minutes.

Right away you can see that Plan B is cheaper if you don’t use more than 450 minutes.
You can find when the plans cost the same amount by setting the cost of each plan equal to each other.
39.99 + 0.65(x-500) = 34.99 +0.60(x-450)
Then solve for x.

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