document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185501>Question 185501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The original problem was:<BR>\n" );
document.write( "[A photo is 4 inches longer than it is wide. A 3-inch border is placed around the photo making the total area of the photo and border 165 square inches. What are the dimensions of the photo? ]<BR>\n" );
document.write( "So the initial question was…what was the dimensions of the photo. Since the total area of the photo AND border was 165 square inches, logically the<BR>\n" );
document.write( "Total Area of Border and Photo (R3) = 165 square inches or the sum of the Area of the Border (R2) and Photo (R1).  <BR>\n" );
document.write( "So if I want to find the area of the  photo the equation should read R3 - R1 = R2  since the total area of 165 subtracting the area of the photo should allow us to solve for the border and then substitute for w.<BR>\n" );
document.write( "Let w = width of photo and w + 4 = length of photo so that the dimensions will equal (w)(w+4) = R1\r<BR>\n" );
document.write( "\n" );
document.write( "The area of the border can be seen as the added areas of smaller rectangles surrounding the photo. So that :<BR>\n" );
document.write( "       x +4 + 6 (3)                Each long rectangle = (3x + 30) x 2<BR>\n" );
document.write( "   3x   (x)(x+4)   3x              Each smaller rectangle =  (3x) x 2<BR>\n" );
document.write( "      x + 4 + 6 (3)<BR>\n" );
document.write( "Therefore the area of the border is represented by 6x + 60 + 6x or 12x + 60<BR>\n" );
document.write( "The whole equation can be seen as:<BR>\n" );
document.write( "165 – area of photo = area of border or<BR>\n" );
document.write( "165 – (x2  + 4x) = 12x + 60, using addition principle combine like terms<BR>\n" );
document.write( "165 – x2 -  4x = 12x + 60 becomes 0 = x2 +16x -105<BR>\n" );
document.write( "And this is where I get stuck because I cant find the factors of 16 and 105 that make this equation solvable? <BR>\n" );
document.write( "Can you please show me the solution to this problem so that I understand.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139163 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=139163\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L = length of photo and W = width of photo.<BR>\n" );
document.write( "From the problem...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+W%2B4 ALIGN=MIDDLE  ALT=\"L+=+W%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"A photo is 4 inches longer than it is wide\"<BR>\n" );
document.write( "A 3-inch border is placed around the photo making the total area 165 sq.ins.<BR>\n" );
document.write( "The total area of the photo plus 3-inch border can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28L%2B6%29%28W%2B6%29 ALIGN=MIDDLE  ALT=\"A+=+%28L%2B6%29%28W%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the addition of the 3-inch border adds a total of 6 inches to the length and 6 inches to the width.<BR>\n" );
document.write( "Now Substitute A = 165 and L = W+4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28W%2B4%29%2B6%29%28W%2B6%29+=+165 ALIGN=MIDDLE  ALT=\"%28%28W%2B4%29%2B6%29%28W%2B6%29+=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2%2B16W%2B60+=+165 ALIGN=MIDDLE  ALT=\"W%5E2%2B16W%2B60+=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 165 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2%2B16W-105+=+0 ALIGN=MIDDLE  ALT=\"W%5E2%2B16W-105+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor this quadratic equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W-5%29%28W%2B21%29+=+0 ALIGN=MIDDLE  ALT=\"%28W-5%29%28W%2B21%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+5 ALIGN=MIDDLE  ALT=\"W+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+-21 ALIGN=MIDDLE  ALT=\"W+=+-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Discard the negative solution as lengths are positive quantities.<BR>\n" );
document.write( "The width is 5 inches and the length is 9 inches. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );