SOLUTION: A rental company charges $65 a day and 30 cents a mile for renting a truck. Michael rents a truck for 3 days, and his bill comes to $275. How many miles did he drive? I can figure

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Question 163951This question is from textbook College Algebra
: A rental company charges $65 a day and 30 cents a mile for renting a truck. Michael rents a truck for 3 days, and his bill comes to $275. How many miles did he drive?
I can figure out that the answer is 400 miles, but I don't know how to put it in an algebraic equation form.
Thanks
This question is from textbook College Algebra

Found 2 solutions by gonzo, Edwin McCravy:
Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!
let C = cost to rent
let D = number of days
let M = number of miles.
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formula is:
C = ($65.00 * D) + ($.3 * M)
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in your problem,
C = $275.00
D = 3
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substitute known values in equation.
$275.00 = $65.00 * 3 + $.3 * M
perform indicated operations.
$275.00 = $195.00 + $.3 * M
subtract 195 from both sides of equation.
$275.00 - $195.00 = $.3 * M
perform indicated operations.
$80.00 = $.3 * M
divide both sides of equation by $.3
$80.00 / $.3 = M
perform indicated operations.
266.6666666667 = M
which is the same as
266 + 2/3 = M (.666666667 is same as 2/3)
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answer is 266 and 2/3 miles.
not sure how you got 400 but it isn't right.
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plugging values into original equation will help you to see this.
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C = 3*65 + .3*(400) = 195 + 120 = 315 (not equal to 275)
C = 3*65 + .3 (266 + 2/3) = 195 + 79.8 + .2 = 195 + 80 = 275
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Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
A rental company charges $65 a day and 30 cents a mile for renting a truck. Michael rents a truck for 3 days, and his bill comes to $275. How many miles did he drive?
I can figure out that the answer is 400 miles, but I don't know how to put it in an algebraic equation form.

400 miles cannot be correct, for 30 cents times 
400 miles gives $120. And $65 times 3 days gives $195. 

But adding $195 + $120 gives $315, not $275.

----------------------

Just think how the total bill was figured.  It was this way:

1.  $65 TIMES THE NUMBER OF DAYS 

PLUS 

2.  $0.30 TIMES THE NUMBER OF MILES

EQUALS

3.  THE TOTAL BILL 

---------------------

Let's look at 1.  That's $65 times 3 days or $195.

Let's look at 2.  We don't know the number of miles, so we let
the letter x represent this unknown number.  But we can
multiply $.30 by x anyway and get $.30x

Let's look at 3.  That's given as $275.

So we have

$195 PLUS $.30x EQUALS $275

or dropping the dollar signs, and using + for PLUS and = 
for EQUALS:

195 + .30x = 275

Now we subtract 195 from both sides:

      .30x = 80

Now we divide both sides by .30



       

So it's not 400 miles, it's 266.67 miles.

Edwin

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