document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129060>Question 129060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manager of an 80 unit apartment complex is trying to deceide what rent to charge. Experience has shown that at a rent of $200.00 all the units will be full but with one additional unit will remain vacant f0r each $20.00increase. Find the # of occupied unit if the total revenue is $20,020.\r<BR>\n" );
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document.write( "This is the problem I am trying to solve, however I am not clear on how or where to start it. If you could possibly show me the steps I would greatly appericate it. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94355 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the number of occupied units.  Then 80 - x is the number of unoccupied units.\r<BR>\n" );
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document.write( "The rental fee is 200 plus 20 times the number of unoccupied units, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2B20%2880-x%29 ALIGN=MIDDLE  ALT=\"200%2B20%2880-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which simplifies to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2B1600-20x ALIGN=MIDDLE  ALT=\"200%2B1600-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800-20x ALIGN=MIDDLE  ALT=\"1800-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is the amount charged per apartment, and there are x occupied apartments, so the total revenue is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281800-20x%29 ALIGN=MIDDLE  ALT=\"x%281800-20x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that is equal to $20,020.\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281800-20x%29=20020 ALIGN=MIDDLE  ALT=\"x%281800-20x%29=20020\"   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=1800x-20x%5E2-20020=0 ALIGN=MIDDLE  ALT=\"1800x-20x%5E2-20020=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by -20:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-90x%2Bx%5E2%2B1001=0 ALIGN=MIDDLE  ALT=\"-90x%2Bx%5E2%2B1001=0\"   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=x%5E2-90x%2B1001=0 ALIGN=MIDDLE  ALT=\"x%5E2-90x%2B1001=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can factor this (the prime factors of 1001 are 7, 11, and 13), or use the quadratic formula, whichever you prefer, but the roots come out to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=77 ALIGN=MIDDLE  ALT=\"x=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "So, if the rental fee is 200 + 20(3) = 260 (3 unoccupied units), then the total revenue is 77 * 260 = 20020.\r<BR>\n" );
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document.write( "But if the rental fee is 200 + 20(67) = 1540, then the total revenue is 13 * 1540, also = 20020.\r<BR>\n" );
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document.write( "The second root presumes that the relationship of rent to unoccupied units is linear across the entire range of possibilities, which I suspect is not the case in real life. </SPAN>\n" );
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