document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825679>Question 825679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 50 cm by 75 cm, how wide should the matte be?\r<BR>\n" );
document.write( "\n" );
document.write( "I got an answer that doesn't look right. Please provide me a solution so I can see where I went wrong. Thank you in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497528 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+ ALIGN=MIDDLE  ALT=\"+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the width of the matte in cm<BR>\n" );
document.write( "On one side, the matte plus print =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+%2B+2w+ ALIGN=MIDDLE  ALT=\"+50+%2B+2w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "On the other side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+75+%2B+2w+ ALIGN=MIDDLE  ALT=\"+75+%2B+2w+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "The area of matte plus print is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+50+%2B+2w+%29%2A%28+75+%2B+2w+%29+ ALIGN=MIDDLE  ALT=\"+A+=+%28+50+%2B+2w+%29%2A%28+75+%2B+2w+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+3750+%2B+150w+%2B+100w+%2B+4w%5E2+ ALIGN=MIDDLE  ALT=\"+A+=+3750+%2B+150w+%2B+100w+%2B+4w%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "This area minus the area of the print plus <BR>\n" );
document.write( "the area of the matte which also equals <BR>\n" );
document.write( "the area of the print<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3750+%2B+150w+%2B+100w+%2B+4w%5E2+=+2%2A50%2A75+ ALIGN=MIDDLE  ALT=\"+3750+%2B+150w+%2B+100w+%2B+4w%5E2+=+2%2A50%2A75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3750+%2B+150w+%2B+100w+%2B+4w%5E2+=+7500+ ALIGN=MIDDLE  ALT=\"+3750+%2B+150w+%2B+100w+%2B+4w%5E2+=+7500+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4w%5E2+%2B+250w+-+3750+=+0+ ALIGN=MIDDLE  ALT=\"+4w%5E2+%2B+250w+-+3750+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2w%5E2+%2B+125w+-+1875+=+0+ ALIGN=MIDDLE  ALT=\"+2w%5E2+%2B+125w+-+1875+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+w+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2+ ALIGN=MIDDLE  ALT=\"+a+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+125+ ALIGN=MIDDLE  ALT=\"+b+=+125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-1875+ ALIGN=MIDDLE  ALT=\"+c+=+-1875+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28+-125+%2B-+sqrt%28+125%5E2+-+4%2A2%2A%28-1875%29+%29%29+%2F+%282%2A2%29+ ALIGN=MIDDLE  ALT=\"+w+=+%28+-125+%2B-+sqrt%28+125%5E2+-+4%2A2%2A%28-1875%29+%29%29+%2F+%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28+-125+%2B-+sqrt%28+15625+%2B+15000+%29%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+w+=+%28+-125+%2B-+sqrt%28+15625+%2B+15000+%29%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28+-125+%2B-+sqrt%28+30625+%29%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+w+=+%28+-125+%2B-+sqrt%28+30625+%29%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28+-125+%2B+175%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+w+=+%28+-125+%2B+175%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( I can't use the (-) square root )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+50%2F4+ ALIGN=MIDDLE  ALT=\"+w+=+50%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+12.5+ ALIGN=MIDDLE  ALT=\"+w+=+12.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50%2A75+=+3750+ ALIGN=MIDDLE  ALT=\"+50%2A75+=+3750+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "The area of matte plus print is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+50+%2B+2w+%29%2A%28+75+%2B+2w+%29+ ALIGN=MIDDLE  ALT=\"+A+=+%28+50+%2B+2w+%29%2A%28+75+%2B+2w+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+50+%2B+2%2A12.5+%29%2A%28+75+%2B+2%2A12.5+%29+ ALIGN=MIDDLE  ALT=\"+A+=+%28+50+%2B+2%2A12.5+%29%2A%28+75+%2B+2%2A12.5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+50+%2B+25+%29%2A%28+75+%2B+25+%29+ ALIGN=MIDDLE  ALT=\"+A+=+%28+50+%2B+25+%29%2A%28+75+%2B+25+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+75%2A100+ ALIGN=MIDDLE  ALT=\"+A+=+75%2A100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+7500+ ALIGN=MIDDLE  ALT=\"+A+=+7500+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%2F2+=+7500%2F2+ ALIGN=MIDDLE  ALT=\"+A%2F2+=+7500%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%2F2+=+3750+ ALIGN=MIDDLE  ALT=\"+A%2F2+=+3750+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "The area of the matte or the print\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );