both companies charge the same amount when the total duration of monthly calls is...

eddy2017 · Jun 22, 2021

Two companies offer monthly cell phone plans, both of which include free text messaging. Company A charges a $25 monthly fee plus five cents per minute of phone conversation, while Company B charges a $50 monthly fee and offers unlimited calling. Both companies charge the same amount when the total duration of monthly calls is

8 hours and 33 minutes
5 hours
500 hours
8 hours and 20 minutes

I should have dealt quite easily with this type of problems by now only this one is presented in a different setting(or phrased differently and have stumped me), as opposed to the ones i have done having to do with cellphone costs.
info give
Company A charges a $25 monthly fee plus five cents per minute of phone conversation.
Company B charges a $50 monthly fee.
I do not know how to start this. Any hints?.

JeffM · Jun 22, 2021

What formula expresses in mathematical terms the monthly cost for Company A?

What formula expresses in mathematical terms the monthly cost for company B?

How can you use those formulas to answer the question?

eddy2017 · Jun 22, 2021

JeffM said:
What formula expresses in mathematical terms the monthly cost for Company A?

What formula expresses in mathematical terms the monthly cost for company B?

How can you use those formulas to answer the question?

for company A I'd say 25 + 5(m) m = minutes
for B.. don't have any idea, Jeff.

eddy2017 · Jun 22, 2021

eddy2017 said:
for company A I'd say 25 + 5(m) m = minutes
for B.. don't have any idea, Jeff.

i will send my work now

eddy2017 · Jun 22, 2021

25 + 0.05(m) =50 0.05 not 5 cos we're talking 5 out of the unit which would be 1 dollar
company B always charges the same fees. it is a flat rate with them
so i need to find when A reaches what B charges,ok,so
25 + 0.05 (m)=50 ( 50 being the B's flat rate)
will sub 25 from both sides
25 + -25 (0.05) (m)=50 -25
0.05(m)=25
m= 25/0.05
m=500 minutes
let's convert mi to hrs
500 * 1hr/60mi =8.33

Both companies charge the same amount when the total duration of monthly calls is 8 hours and 33 minutes.

eddy2017 · Jun 22, 2021

hey, the power of rational thinkin'!.

Otis · Jun 22, 2021

Hi Eddy. Your answer is not correct, but the good news is that your mistake occurred near the very end of your work. Did you use a calculator to divide 500 by 60? If so, the result 8.33333333 indicates a repeating decimal. And that means you're not looking at the exact answer; you're looking at a decimal approximation, instead.

When we divide by hand, the Integer part of the answer is 8 and the remainder is 20. We express the answer to Dividend÷Divisor as:

Integer Quotient + Remainder / Divisor

500÷60 = 8 + 20/60 = 8 + 1/3

In other words, $\frac{500}{60} = 8\frac{1}{3}$

In English, we could interpret that as "8 hours, plus a third of an hour more".

1/3 hr = ? min

?

eddy2017 · Jun 22, 2021

Otis said:
Hi Eddy. Your answer is not correct, but the good news is that your mistake occurred near the very end of your work. Did you use a calculator to divide 500 by 60? If so, the result 8.33333333 indicates a repeating decimal.

When we divide by hand, the answer is 8 with

Otis said:

Hi Eddy. Your answer is not correct, but the good news is that your mistake occurred near the very end of your work. Did you use a calculator to divide 500 by 60? If so, the result 8.33333333 indicates a repeating decimal.

When we divide by hand, the answer is 8 with remainder 20. We express that value as:

8 + remainder/divisor = 8 + 20/60

In other words, $\frac{500}{60} = 8\frac{1}{3}$

In English, we could interpret that as "8 hours, plus a third of an hour".

1/3 hr = ? min

?

Click to expand...

remainder 20. We express that value as:

8 + remainder/divisor = 8 + 20/60

In other words, $\frac{500}{60} = 8\frac{1}{3}$

In English, we could interpret that as "8 hours, plus a third of an hour".

1/3 hr = ? min

?

very interesting. yes, i used a calculator and the answer was 8.33 repeating. i never thought there'd be such a huge dif between the result off of a calc and a calculation by hand. amazing!

1/3of an hour * 1 hours/60 = 20 minutes

Deleted member 4993 · Jun 22, 2021

eddy2017 said:
25 + 0.05(m) =50 0.05 not 5 cos we're talking 5 out of the unit which would be 1 dollar
company B always charges the same fees. it is a flat rate with them
so i need to find when A reaches what B charges,ok,so
25 + 0.05 (m)=50 ( 50 being the B's flat rate)
will sub 25 from both sides
25 + -25 (0.05) (m)=50 -25
0.05(m)=25
m= 25/0.05
m=500 minutes
let's convert mi to hrs
500 * 1hr/60mi =8.33

Both companies charge the same amount when the total duration of monthly calls is 8 hours and 33 minutes......incorrect

1/3 hours = 20 minutes

Otis said:
In English, we could interpret that as "8 hours, plus a third of an hour".

1/3 hr = ? min

Deleted member 4993 · Jun 22, 2021

eddy2017 said:
very interesting. yes, i used a calculator and the answer was 8.33 repeating. i never thought there'd be such a huge dif between the result off of a calc and a calculation by hand. amazing!

There is no difference - you are changing "units"

8.33 hours ~ 8 hrs and 20 minutes

Watch the units!!!

eddy2017 · Jun 22, 2021

Subhotosh Khan said:
There is no difference - you are changing "units"

8.33 hours ~ 8 hrs and 20 minutes

Watch the units!!!

Oh yes, that is it.

eddy2017 · Jun 22, 2021

eddy2017 said:
Oh yes, that is it.

Thanks, Doc. I understand now.

Otis · Jun 22, 2021

eddy2017 said:
… i never thought there'd be such a huge dif …

For those using Company A, the difference amounts to 65 cents.

You've probably already memorized the decimal form of some basic Rational numbers. In time, you'll recognize even more.

$\displaystyle \frac{1}{9} = 0.11111…$

$\displaystyle \frac{1}{5} = 0.2$

$\displaystyle \frac{2}{9} = 0.22222…$

$\displaystyle \frac{1}{4} = 0.25$

$\displaystyle \frac{1}{3} = 0.33333…$

$\displaystyle \frac{2}{5} = 0.4$

$\displaystyle \frac{4}{9} = 0.44444…$

$\displaystyle \frac{1}{2} = 0.5$

$\displaystyle \frac{5}{9} = 0.55555…$

$\displaystyle \frac{3}{5} = 0.6$

$\displaystyle \frac{2}{3} = 0.66666…$

$\displaystyle \frac{3}{4} = 0.75$

$\displaystyle \frac{7}{9} = 0.77777…$

$\displaystyle \frac{4}{5} = 0.8$

$\displaystyle \frac{8}{9} = 0.88888…$

$\displaystyle 1 = 0.99999…$

When a decimal form eventually repeats the digits 142857, that indicates a factor of 7 in the denominator. For example:

$\displaystyle \frac{1}{7} = 0.142857142857…$

$\displaystyle \frac{2}{7} = 0.2857142857142857…$

$\displaystyle \frac{3}{7} = 0.42857142857142857…$

$\displaystyle \frac{5}{14} = 0.357142857142857…$

When the decimal part terminates with the digits 125, 375, 625, or 875, that indicates a factor of 8 in the denominator. For example:

$\displaystyle \frac{1}{8} = 0.125$

$\displaystyle \frac{3}{8} = 0.375$

$\displaystyle \frac{5}{8} = 0.625$

$\displaystyle \frac{7}{8} = 0.875$

$\displaystyle \frac{3}{16} = 0.1875$

$\displaystyle \frac{9}{16} = 0.5625$

?

eddy2017 · Jun 22, 2021

?
That's juicy grist to my mathematic mill!!!

Otis · Jun 22, 2021

In schoolwork, we often simplify fractions by dividing numerator and denominator by the same amount. When numerator and denominator both end with zero, we may divide each by 10. Those divisions result in dropping the ending zeros.

$\displaystyle \frac{500}{60} = \frac{500÷10}{60÷10} = \frac{50\cancel{0}}{6\cancel{0}} = \frac{50}{6}$

When numerator and denominator are both even, we may divide by 2.

$\displaystyle \frac{50}{6} = \frac{(\cancel{2})(25)}{(\cancel{2})(3)} = \frac{25}{3}$

We know that 25 contains eight 3s (because we've memorized the multiplication table: 8×3=24).

$\displaystyle \frac{25}{3} = \frac{24 + 1}{3} = \frac{24}{3} + \frac{1}{3} = 8\frac{1}{3}$

?

eddy2017 · Jun 22, 2021

Wow!. Thanks!!. Very useful info to have. Will speed things up when simplifying.

eddy2017 · Jun 22, 2021

Otis said:
In schoolwork, we often simplify fractions by dividing numerator and denominator by the same amount. When numerator and denominator both end with zero(s), we may divide each by 10.

$\displaystyle \frac{500}{60} = \frac{500÷10}{60÷10} = \frac{50\cancel{0}}{6\cancel{0}} = \frac{50}{6}$

When numerator and denominator are both even, we may divide by 2.

$\displaystyle \frac{50}{6} = \frac{(\cancel{2})(25)}{(\cancel{2})(3)} = \frac{25}{3}$

We know that 25 contains eight 3s (because we've memorized the multiplication table: 8×3=24).

$\displaystyle \frac{25}{3} = \frac{24 + 1}{3} = \frac{24}{3} + \frac{1}{3} = 8\frac{1}{3}$

?

This is neat!

eddy2017 · Jun 23, 2021

JeffM said:
What formula expresses in mathematical terms the monthly cost for Company A?

What formula expresses in mathematical terms the monthly cost for company B?

How can you use those formulas to answer the question?

i forgot to address your question. let me do it now.
A: y = 25 + 0.05 x ( x represents the time for calls in minutes)

B: y = 50
these are two straight lines, only that B line is horizontal.

eddy2017 · Jun 23, 2021

i liked this thread. i could glean good information here. thanks

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