SOLUTION: A cell phone company charges a monthly fee of $10 for the first 1000 text messages and 10 cents for each additional text message. Miriam's bill for text messages for the month of J

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Question 163953This question is from textbook College Algebra
: A cell phone company charges a monthly fee of $10 for the first 1000 text messages and 10 cents for each additional text message. Miriam's bill for text messages for the month of June is $38.50. How many text messages did she send that month?
I can figure out the answer(1285 messages) but I don't know how to write the formula.
Thanks This question is from textbook College Algebra

Found 2 solutions by josmiceli, gonzo:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have the formula in your head
You just can't get it out
Let b= Miriam's monthly bill
Let t= the number of text messages sent in the
month of June by Miriam
t+-+1000= the number of text messages over 1000
Miriam's monthly bill is:
b+=+10+%2B+.1%2A%28t+-+1000%29 dollars
Her monthly bill is $38.50. I'll show it in terms of cents
3850+=+1000+%2B+10%2A%28t+-+1000%29 cents
Subtract 1000 from both sides
2850+=+10%2A%28t+-+1000%29
2850+=+10t+-+10000
Add 10000 to both sides
12850+=+10t
t+=+1285 messages
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It might help to go over the units involved in the 1st
formula which was
b+=+10+%2B+.1%2A%28t+-+1000%29 dollars
The 10 really stands for ($10/1000 messages)x(1000 messages)
And the other term is really (.1 dollars/message)x(t - 1000 messages)
The units work out to dollars for both terms
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You can check the answer
3850+=+1000+%2B+10%2A%28t+-+1000%29
3850+=+1000+%2B+10%2A%281285+-+1000%29
3850+=+1000+%2B+10%2A285
3850+=+1000+%2B+2850
3850+=+3850
OK

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
total messages for the month is 3850 as follows:
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let C = cost
let M = number of messages greater than 1000
formula is:
C = $10 + $.01*M
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substitute known values in equation.
$38.50 = $10 + $.01*M
subtract $10 from both sides of equation.
$28.5 = $.01*M
divide both sides of the equation by $.01.
2850 = M
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looks like number of messages greater than 1000 is 2850.
to prove, substitute in original equation.
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$38.50 = $10.00 + $.01*2850
$38.50 = $10.00 + $28.50
$38.50 = $38.50
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the value of 2850 for M is good.
total messages for the month would be 2850 + 1000 = 3850.
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