SOLUTION: A plumber charged $110 for a three-hour job and $160 for a five-hour job. At this rate, how much would he charge for an eight-hour job? Assume that this situation can be described

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Question 198019This question is from textbook Algebra and trigonometry
: A plumber charged $110 for a three-hour job and $160 for a five-hour job. At this rate, how much would he charge for an eight-hour job?
Assume that this situation can be described by a linear function.
This question is from textbook Algebra and trigonometry

Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A plumber charged $110 for a three-hour job and $160 for a five-hour job. At this rate, how much would he charge for an eight-hour job?
Assume that this situation can be described by a linear function.
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The difference in charges is $50 for a difference of 2 hours, so the hourly rate is $25.
The overall charge is some base price, plust $25/hour.
$110 = b + $25*3
b = $35
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For 8 hours, charges = $35 + $25*8
= $235
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PS This must be an old math book - plumbers charge a LOT more than that.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I plot time on the horizontal and the charge on the vertical,
linear means that a straight line goes through the points
(3,110) and (5,160)
Let t= elapsed time in hours
Let c= charge in dollars
The formula to use is:
%28c+-+110%29+%2F+%28t+-+3%29+=+%28160+-+110%29+%2F+%285+-+3%29
%28c+-+110%29+%2F+%28t+-+3%29+=+50+%2F+2
%28c+-+110%29+%2F+%28t+-+3%29+=+25
Multiply both sides by t+-+3
c+-+110+=+25%2A%28t+-+3%29
c+-+110+=+25t+-+75
c+=+25t+%2B+35
Now plug in t+=+8
c+=+25%2A8+%2B+35
c+=+235
He charges $235 for an 8 hr job
I'll plot the line:
+graph%28+400%2C+400%2C+-1%2C+10%2C+-10%2C+250%2C+25x+%2B+35%29+