Two Phone Companies

[nycmathguy]

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?

 

[MathLover1]

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

 

[nycmathguy]

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

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.

 

[MathLover1]

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

 

[nycmathguy]

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

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?

 

[MathLover1]

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?

 

[nycmathguy]

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?

You asked if I ever compared two phone companies. I have compared more than two in real life. In terms of this application, Company B is better than A. None of this tells me to equate A to B to solve for m. If you post this question on the board in a CUNY classroom and ask students to solve this problem, no one would know what to do. In my opinion, Company B is the better choice. Still, nothing I said here leads me to create the equations you found to solve the problem. Moving on. . . .