document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123651>Question 123651</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534404693/algebrahomeworkh>algebra and trigonometry with analiytic geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> When a popular brand of CD player is priced at $320 per unit, a store sells 12 units per week. Each time the price is reduced by $11, however, the sales increase by 2 per week. What selling price will result in weekly revenues of $5166?\r<BR>\n" );
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document.write( "Please enter your answer as a number without the units. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90708 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=90708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> price * # of units = revenues.<BR>\n" );
document.write( "Let x= # of price reductions<BR>\n" );
document.write( "(320-11x)*(12+2x)=5166<BR>\n" );
document.write( "-22x^2+508x+3840=5166<BR>\n" );
document.write( "-22x^2+508x-1326=0<BR>\n" );
document.write( "-11x^2+254x-663=0<BR>\n" );
document.write( "x=3, x=20.091<BR>\n" );
document.write( "320-11*3= $287. Ans.<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "(320-11*3)*(12+2*3)<BR>\n" );
document.write( "=287*18<BR>\n" );
document.write( "=5166<BR>\n" );
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document.write( "The other answer is also correct but the number of price reductions is not even.<BR>\n" );
document.write( "The sales price would be $99.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11x%5E2%2B254x%2B-663+=+0 ALIGN=MIDDLE  ALT=\"-11x%5E2%2B254x%2B-663+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28254%29%5E2-4%2A-11%2A-663=35344 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28254%29%5E2-4%2A-11%2A-663=35344\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=35344 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-254%2B-sqrt%28+35344+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-254%2B-sqrt%28+35344+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28254%29%2Bsqrt%28+35344+%29%29%2F2%5C-11+=+3 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28254%29%2Bsqrt%28+35344+%29%29%2F2%5C-11+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28254%29-sqrt%28+35344+%29%29%2F2%5C-11+=+20.0909090909091 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28254%29-sqrt%28+35344+%29%29%2F2%5C-11+=+20.0909090909091\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11x%5E2%2B254x%2B-663 ALIGN=MIDDLE  ALT=\"-11x%5E2%2B254x%2B-663\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11x%5E2%2B254x%2B-663+=+%28x-3%29%2A%28x-20.0909090909091%29 ALIGN=MIDDLE  ALT=\"-11x%5E2%2B254x%2B-663+=+%28x-3%29%2A%28x-20.0909090909091%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, 20.0909090909091.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-11%2Ax%5E2%2B254%2Ax%2B-663+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-11%2Ax%5E2%2B254%2Ax%2B-663+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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