# Two Phone Companies

Discussion in 'Algebra' started by nycmathguy, May 18, 2022.

1. ### nycmathguy

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Math 004 sample test questions for anyone seeking NYS certification as a high school math teacher. This is just one of several exams required for NYS high school teacher certification.

You have no idea how terribly frustrating it is to say that I completed a thorough review of precalculus, now learning first semester calculus but can't figure out this word problem.

I know there are two phone companies.
The confusing part of the wording for me is UNLIMITED CALLING for Company B but 0.05 for each minute of conversation for A.

If you are taking the teacher certification timed test, and come across a problem like this one (assuming you never saw this question before), how would you reason your way to the right set up?

nycmathguy, May 18, 2022
2. ### MathLover1

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The expression representing the monthly charge for Company A is $25+$0.05m, where m is the time in minutes spent talking on the phone.

Set this expression equal to the monthly charge for Company B, which is $50. Solve for m to find the number of minutes for which the two companies charge the same amount:$25 + $0.05m =$50
$0.05m =$25
m = 500 minutes
convert minutes into hours:

Since there are 60 minutes in an hour, m = 500/60 hours = 8 1/3 hours.
One-third of an hour is 20 minutes, so m = 8 hours, 20 minutes

MathLover1, May 18, 2022
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3. ### nycmathguy

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I understood what you did after setting up your equation. What I don't understand is how you worked your way to the proper equation.

You said:

"The expression representing the monthly charge for Company A is $25+$0.05m, where m is the time in minutes spent talking on the phone."

What information in the problem led you to form
$25 +$0.05m, where m represents minutes?

You said:

"Set this expression equal to the monthly charge for Company B, which is $50." What information led you to equate$25 + $0.05m to$50?

If at all possible, I would like for you to break down word problems in this fashion. I want to think like a mathematician not just a student learning short cuts on a website.

nycmathguy, May 18, 2022
4. ### MathLover1

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given:
company A charges a $25 plus 5 cents=$0.05 per minute => $25+0.05m company B charges a$50 (unlimited plan, does not matter how many minutes)

so, to find m set

$25+0.05m=50 0.05m=25 m=500 minutes now jus convert min to hours MathLover1, May 18, 2022 nycmathguy likes this. 5. ### nycmathguy Joined: Jun 27, 2021 Messages: 5,386 Likes Received: 422 I understand what you are saying here. What remains unclear, however, is why we must set Company A to Company B to find m. Where in the wording does it say to do that? nycmathguy, May 19, 2022 6. ### MathLover1 Joined: Jun 27, 2021 Messages: 2,989 Likes Received: 2,884 why we must set Company A to Company B to find m did you ever compare two phone companies plans to decide which one has better plan Company A has plan$25+0.05m -> so, how much you will pay depends on how many minutes you used
Company B is offering you plane $50 a month, does not care how many minutes you will use, minutes are unlimited if you want to see how many minutes you will have available using Company A for$50, must set Company A to Company B to find m

and, as you can see, using Company A you will have only 8h 20min ( for $50), + you will pay more if you use more min Company B you will have unlimited # min ( for$50)

in your opinion, which plan is better?

MathLover1, May 19, 2022
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