document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129645>Question 129645</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. <BR>\n" );
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 \r<BR>\n" );
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document.write( "1 solutions\r<BR>\n" );
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document.write( "Answer 94355 by solver91311(860)   on 2008-02-25 20:07:28: \r<BR>\n" );
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document.write( "You can put this solution on YOUR website!<BR>\n" );
document.write( "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( ", which simplifies to: \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( " 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( "Divide by -20:<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  and , \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. \r<BR>\n" );
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document.write( "***************This the help that I received and I understand it up to here,however how do you compute this into a quadratic equation? That is what I don't understand. Thank you for your time........................................ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94650 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=94650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The manager of an 80 unit apartment complex is trying to deceide what rent to charge.<BR>\n" );
document.write( "Experience has shown that at a rent of $200.00 all the units will be full but  one additional unit will remain vacant f0r each $20.00 increase.<BR>\n" );
document.write( "Find the # of occupied units if the total revenue is $20,020.<BR>\n" );
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document.write( "Let \"x\" be the number of $20 increases.<BR>\n" );
document.write( "Price per unit will be (200+20x)<BR>\n" );
document.write( "# of units occupied will be (80-x)<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "Revenue = price per unit * # of units occupied:<BR>\n" );
document.write( "20,020  = (200+20x)(80-x)<BR>\n" );
document.write( "-20x^2 +1600x-200x + 16000 = 20,020<BR>\n" );
document.write( "-20x^2+1400x -4020 = 0<BR>\n" );
document.write( "Divide thru by -20 to get:<BR>\n" );
document.write( "x^2-70s+201=0<BR>\n" );
document.write( "Factor to get:<BR>\n" );
document.write( "(x-67)(x+3)=0<BR>\n" );
document.write( "Positive answer:<BR>\n" );
document.write( "x = 67 (The number of $20 raises)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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