document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5278>Question 5278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr.Ranger is a plumber. He bills his clients for the cost of the call plus the number of hours he works. He earns $470 for a job that takes him 12 hours, whereas he recieves $225 for a 5 hour job.<BR>\n" );
document.write( "a) what is his hourly rate?<BR>\n" );
document.write( "b)what does he charge for the call?<BR>\n" );
document.write( "c)Give an equation that represents his earnings.<BR>\n" );
document.write( "d)Mr.Ranger has jsut finished a contract for which he will be paid $295. How many hours did he work?<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 #2681 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=2681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since you are looking for two unknowns (x = cost of call and y = hourly rate), it seems reasonable to expect to require two equations to solve the problem.<BR>\n" );
document.write( "Let's set up the required equations from the given information:\r<BR>\n" );
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document.write( "1) x + 12y = $470   The cost of the call (x) + 12 hrs @ $y per hour is $470.<BR>\n" );
document.write( "2) x +  5y = $225   The cost of the call (x) +  5 hrs @ $y per hour is $225.\r<BR>\n" );
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document.write( "Rewrite equation 1):  x = $470 - 12y and substitute into equation 2).\r<BR>\n" );
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document.write( "2a) ($470 - 12y) + 5y = $225  Simplify and solve for y, the hourly rate.\r<BR>\n" );
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document.write( "$470 - 7y = $225 Subtract $225 from both sides.<BR>\n" );
document.write( "$245 - 7y = 0  Add 7y to both sides.<BR>\n" );
document.write( "$245 = 7y Divide both sides by 7.<BR>\n" );
document.write( "$35 = y  This is Mr. Ranger's hourly rate.\r<BR>\n" );
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document.write( "To find the cost of the call, x:\r<BR>\n" );
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document.write( "x = $470 - 12y<BR>\n" );
document.write( "x = $470 - 12($35)<BR>\n" );
document.write( "x = $470 - $420<BR>\n" );
document.write( "x = $50 This is Mr. Ranger's cost of the call.\r<BR>\n" );
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document.write( "The equation that represents his earnings can now be written as:\r<BR>\n" );
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document.write( "E = $50 + $35(y)  Where: y is the number of hours spent doing the job.\r<BR>\n" );
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document.write( "Verification is left as an exercise for the student.<BR>\n" );
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