document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=301267>Question 301267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A picture 19 inches by 24 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 188 square inches?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #215999 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=215999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     A picture 19 inches by 24 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 188 square inches? <BR>\n" );
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document.write( "Let w = width of border<BR>\n" );
document.write( "then<BR>\n" );
document.write( "\"area of border\" = \"area of mat\" - \"area of picture\"<BR>\n" );
document.write( "188 = (19+2w)(24+2w) - 19(24)<BR>\n" );
document.write( "188 = 456+38w+48w+4w^2 - 456<BR>\n" );
document.write( "188 = 38w+48w+4w^2<BR>\n" );
document.write( "188 = 4w^2+86w<BR>\n" );
document.write( "0 = 4w^2+86w-188<BR>\n" );
document.write( "0 = 2w^2+43w-94<BR>\n" );
document.write( "Solve using the quadratic formula.  Doing so yields:<BR>\n" );
document.write( "w = {2, -23.5}<BR>\n" );
document.write( "Of course, we can toss out the negative solution leaving:<BR>\n" );
document.write( "w = 2 inches<BR>\n" );
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document.write( "Details of quadratic:<BR>\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=quadratic.solver>SOLVE quadratic equation with variable</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=2x%5E2%2B43x%2B-94+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B43x%2B-94+=+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=%2843%29%5E2-4%2A2%2A-94=2601 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2843%29%5E2-4%2A2%2A-94=2601\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2601 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+=+%28-43%2B-sqrt%28+2601+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-43%2B-sqrt%28+2601+%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-%2843%29%2Bsqrt%28+2601+%29%29%2F2%5C2+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2843%29%2Bsqrt%28+2601+%29%29%2F2%5C2+=+2\"   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-%2843%29-sqrt%28+2601+%29%29%2F2%5C2+=+-23.5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2843%29-sqrt%28+2601+%29%29%2F2%5C2+=+-23.5\"   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=2x%5E2%2B43x%2B-94 ALIGN=MIDDLE  ALT=\"2x%5E2%2B43x%2B-94\"   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=2x%5E2%2B43x%2B-94+=+2%28x-2%29%2A%28x--23.5%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B43x%2B-94+=+2%28x-2%29%2A%28x--23.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2, -23.5.\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+2%2Ax%5E2%2B43%2Ax%2B-94+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B43%2Ax%2B-94+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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