Find linear cost fcn C(t), fixed monthly fee from 2 bills

[whytehaze]

A phone company charges a fixed monthly fee plus a charge per minute of phone time. A person using 200 minutes of phone time is charged $25 for the month, and a person using 360 minutes of phone time is charged $37 for the month.

a. Find a formula for the linear function C(t) relating cost in dollars for the month to minutes t of phone time.

b. How much is the monthly fee?

 

[tkhunny]

Re: Calc Question

i sincerely hope you posted this in the Calculus section by accident. A calculus student should find this problem 'second nature" at worst.

Having said that, simply set it up. Rule #1 - Name Stuff.

"A phone company charges a fixed monthly fee plus a charge per minute of phone time."

F = Fixed Monthly fee
M = per minute Charge.

"A person using 200 minutes of phone time is charged $25 for the month,"

F + 200*M = $25 <== Stare at this until you see from whence it hails.

"and a person using 360 minutes of phone time is charged $37 for the month."

F + 360*M = $37 <== Stare at this until you see from whence it hails.

This gives two linear equations in two variables - a piece o'cake for a calculus student.

Let's see what you get.

 

[whytehaze]

Re: Calc Question

I have no idea how to figure out the monthly fee. I am sorry that I am not as smart as you. If anyone could help me out with that, I would appreciate it.

 

[stapel]

I have no idea how to figure out the monthly fee. I am sorry that I am not as smart as you.

Um... It's not a matter of "being as smart as" anybody in particular. It is, as the tutor suggested, a matter of having taken pre-algebra, algebra, and pre-calculus before hitting your current calculus course. This was covered, at length, back in those courses, which is why it should be "a piece of cake" for any calculus student. It does not involve anything past beginning calculus.

The fact that you "have no idea how to figure out" this exercise suggests that you may need to have a SERIOUS talk with your academic advisor, specifically with respect to appropriate course placement. There is almost zero chance of passing calculus when one is missing the year or two of prerequisite courses. :shock:

My best wishes to you!

Eliz.

 

[whytehaze]

Re: Calc Question

Well I am not the only one in the calc class having trouble with this problem. I also took pre-calc this summer, and received an 87% in the class. I was hoping that somebody would be willing to help me with this one problem, as the name of the site has the word help in it instead of people calling me stupid and predicting that I will fail the class before I even start. Thank you.

 

[galactus]

Re: Calc Question

But tkhunny showed you how to do it. It is a matter of two equations in two unknowns.

I read the posts and I see no one calling you stupid.

Let F=the fixed rate and M=the cost per minute.

Then

\(\displaystyle F+200M=25\)

\(\displaystyle F+360M=37\)

Solve for F and M.

Does that help?.

 

[tkhunny]

Re: Calc Question

Well I am not the only one in the calc class having trouble with this problem. I also took pre-calc this summer, and received an 87% in the class. I was hoping that somebody would be willing to help me with this one problem, as the name of the site has the word help in it instead of people calling me stupid and predicting that I will fail the class before I even start. Thank you.

We would love to help you with your mathematics. Again, but more stongly, if you have a large portion of a calculus class that cannot solve this problem, you have some serious, threatening academic problems in your school district. This simply is WRONG!

You MUST have learned to manipulate algebraic expressions.

F + 200M = 25 ==> F = 25 - 200M

You MUST have learned how to substitute.

F + 360M = 37 ==> (25 - 200M) + 350M = 37

You MUST have learned how to solve such equations.

(25 - 200M) + 350M = 37 ==> 25 - 200M + 350M = 37 ==> 25 + 150M = 37 ==> 150M = 37 - 25 ==> 150M = 12 ==> M = 12/150 = 6/75 = 2/25 = 8/100 = 0.08

Really, I dare you to tell me that one whole row or column of your calculus class cannot do this. I will be truly stunned. You just cannot have a calculus class where a significant percentage of the students cannot do 1st year algebra.

Note: No one called you stupid. No one predicted that you would fail. No one claimed to be smarter than you. Please abandon these self-destructive impressions and simply answer the questions asked and provide the demonstrations requested. We are trying to help you, but so far you have provided no evidence that you are willing to be helped. It is time for you to change an attitude or two.