document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=671>Question 671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An experienced painter made $600 for working on a certain job.  His apprentice, who makes $3 per hour less, also made $600.  However, the apprentice worked 10 hours more then the painter.  How much does the painter make per hour? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244 by </B><A HREF=/tutors/aboutme.mpl?userid=arden42><B>arden42(16)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=arden42><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=244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets call the painter's hourly rate p, the apprentice's hourly rate a, the painter's hours i and the apprentice's hours h.\r<BR>\n" );
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document.write( "This is what we know so far:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+p-3 ALIGN=MIDDLE  ALT=\"a+=+p-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=i%2B10 ALIGN=MIDDLE  ALT=\"h=i%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ha+=+600 ALIGN=MIDDLE  ALT=\"ha+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ip+=+600 ALIGN=MIDDLE  ALT=\"ip+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting the first and second equations into the 3rd gives:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%2B10%29%28p-3%29+=+600 ALIGN=MIDDLE  ALT=\"%28i%2B10%29%28p-3%29+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we know ip also equals 600 (according to the 4th equation above), we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%2B10%29%28p-3%29+=+ip ALIGN=MIDDLE  ALT=\"%28i%2B10%29%28p-3%29+=+ip\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand the brackets:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ip+%2B10p+-3i+-30+=+ip ALIGN=MIDDLE  ALT=\"ip+%2B10p+-3i+-30+=+ip\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we want to find p, we need to express i in terms of p. To do this, we make i the subject:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3i+=+10p+-30 ALIGN=MIDDLE  ALT=\"3i+=+10p+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+10p%2F3+-+10 ALIGN=MIDDLE  ALT=\"i+=+10p%2F3+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, if we substitute this value for i into the 4th of our original equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2810p%2F3+-+10%29+=+600 ALIGN=MIDDLE  ALT=\"p%2810p%2F3+-+10%29+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand the brackets:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810p%5E2%29%2F3+-+10p+=+600 ALIGN=MIDDLE  ALT=\"%2810p%5E2%29%2F3+-+10p+=+600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remove fractions and get everything on one side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10p%5E2+-+30p+-+1800+=+0 ALIGN=MIDDLE  ALT=\"10p%5E2+-+30p+-+1800+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide everything by 10:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2+-+3p+-+180+=+0 ALIGN=MIDDLE  ALT=\"p%5E2+-+3p+-+180+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have a quadratic we can factorise:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-15%29%28p%2B12%29+=+0 ALIGN=MIDDLE  ALT=\"%28p-15%29%28p%2B12%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So p equals either 15 or -12. Since the painter can't be charging a negative rate, he must earn $15 an hour. </SPAN>\n" );
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