document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104890>Question 104890</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "need help. have tried. my answer was $200. please correct me if i am wrong<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76324 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Figure the rates per hr.<BR>\n" );
document.write( "110/3 = 36 2/3<BR>\n" );
document.write( "160/5 = 32.<BR>\n" );
document.write( "So, the rates are not the same. <BR>\n" );
document.write( "Knowing a bit about plumbers, they normally charge a basic fee to just show up, and then they charge per hr.<BR>\n" );
document.write( "In cases like these, where we're asked to project to a new data point (in this case an 8-hr job), you should immediately think of a graph. The x-axis would be the hours worked. The y-axis would be the charge for the work (the cost of the job).<BR>\n" );
document.write( "We're given two pairs of values:<BR>\n" );
document.write( "(3,110) and (5,160).<BR>\n" );
document.write( "The next step is to fit a line to them.<BR>\n" );
document.write( "y = mx+b is the general equation for a line.<BR>\n" );
document.write( "m = the slope = rise/run = change in y / change in x <BR>\n" );
document.write( "Call the change in y, dy (for delta y).<BR>\n" );
document.write( "Call the change in x, dx (for delta x).<BR>\n" );
document.write( "m = dy/dx = 50/2 = 25<BR>\n" );
document.write( "The slope is thus 25, which means for each hour, the price goes up by $25. That means the plumber charges $25/hr.<BR>\n" );
document.write( "We also know the plumber charges $110 for a 3-hr job. 3*25 = $75. So the base charge would be $110-75 = $35.<BR>\n" );
document.write( "y = 25x + 35<BR>\n" );
document.write( "Checking this formula at x=3, we know it is 110.<BR>\n" );
document.write( "Checking it at x=5, we obtain:<BR>\n" );
document.write( "y = 25*5 + 35 = 125 + 35 = 160.<BR>\n" );
document.write( "That checks.<BR>\n" );
document.write( "Now to figure an 8-hr job, set x=8 and use the equation\"<BR>\n" );
document.write( "y = 25*8 + 35.<BR>\n" );
document.write( "y = 200 + 35.<BR>\n" );
document.write( "y = 235.<BR>\n" );
document.write( "That means an 8-hr job costs $235. </SPAN>\n" );
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