document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71159>Question 71159</A>: <I><SPAN STYLE=\"word-break: break-all;\">  six painters can paint 10 homes in 9 weeks. because of time constraints, the homes need to be finished in 2 weeks. how many ADDITIONAL painters must be hired to finish painting the 10 homes in only two weeks? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50883 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=50883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=number of ADDITIONAL painters needed to finish painting the 10 homes in 2 weeks<BR>\n" );
document.write( "Now we know that:<BR>\n" );
document.write( "If six painters can paint 10 homes in 9 weeks, then<BR>\n" );
document.write( "six painters can paint 10/9 homes per week and, in two weeks, six painters can paint 20/9 homes leaving only (90/9-20/9=70/9) homes to paint by the ADDITIONAL painters.<BR>\n" );
document.write( "Also, one painter can paint (10/9)(1/6) or 10/54 homes per week and in two weeks, one painter can paint 20/54 or 10/27 homes.  So our equation to solve is\r<BR>\n" );
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document.write( "(10/27)(x)=70/9  multiply both sides by the LCM (27)\r<BR>\n" );
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document.write( "10x=210 divide both sides by 10\r<BR>\n" );
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document.write( "x=21---------------ADDITIONAL painters needed to finish the job in 2 weeks\r<BR>\n" );
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document.write( "Another way to look at this problem:<BR>\n" );
document.write( "If six painters can paint 10 homes in 9 weeks, then one painter can paint 10 homes in (6)(9) or 54 weeks and x painters can paint 10 homes in 54/x weeks.\r<BR>\n" );
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document.write( "So our equation to solve is:\r<BR>\n" );
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document.write( "54/x=2 multiply both sides by x\r<BR>\n" );
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document.write( "54=2x  divide both sides by 2\r<BR>\n" );
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document.write( "x=27---------------------total required to finish in 2 weeks\r<BR>\n" );
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document.write( "27-6=21--------------------ADDITIONAL painters required\r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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