Problem 1
This answer will vary from person to person. And as your teacher says, you can also randomly pick a value if you aren't sure.
Let's say you spend an hour each day talking on your phone. This means voice calls and not texting. Video calling could also be part of voice calling, though it will depend on how your cell phone company structures the cell phone plan.
Anyways, let's go with 1 hour. This converts to 60 minutes.
If you talk for 60 minutes per day, then you spend 60*30 = 1800 minutes per month talking on the phone. This is an average value. I'm using 30 days per month.
Answer: 1800 minutes
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Problem 2
For each of the 6 companies, form their respective equations
x = number of minutes
y = total cost per month
We get the following equations for each company:
With those 6 plans in mind, we will plug x = 1800 into each equation
Doing so leads to...
So we can see that clearly Public Mobile has the lowest cost per month at $24 a month. The cost per minute of $0 means that we have unlimited minutes here. The other costs are really high and far from $24. The next smallest value is $190, which is far from $24.
Is Public Mobile always the best choice? It depends. Refer to the chart below (attached image) and you'll see that the yellow cells are instances when Public Mobile isn't the cheapest option. However, note how small x has to be for this to occur and note how the yellow cells don't show up very often. Sure we could make more yellow cells pop up if we used even smaller x values, but at a certain point, it's likely not to be realistic. Why have a cell phone plan if you don't use the minutes to talk on it? Of course, everyone is different.
Anyway, for the x value chosen in problem 1, the Public Mobile plan is the cheapest option at $24 per month.
Answer: Public Mobile
