document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186725>Question 186725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the height of a photo is 4 inches more than its width. After enlargement the height will increase by 18 inches and the width by 12 inches. If the ratio of the area of the original photo to the area of the enlarged photo is 4:25, then what will the new dimensions of the pgoto become? thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139978 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=139978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the height of a photo is 4 inches more than its width. After enlargement the<BR>\n" );
document.write( "height will increase by 18 inches and the width by 12 inches.<BR>\n" );
document.write( " If the ratio of the area of the original photo to the area of the enlarged<BR>\n" );
document.write( " photo is 4:25, then what will the new dimensions of the photo become? <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = the width of the photo<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(x+4) = the height<BR>\n" );
document.write( "then<BR>\n" );
document.write( "Area = x(x+4) = (x^2 + 4x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"After enlargement the height will increase by 18 inches and the width by 12 inches.\"<BR>\n" );
document.write( "(x+4+18) = (x + 22) is the height after enlargement<BR>\n" );
document.write( "and <BR>\n" );
document.write( "(x+12) = width after enlargement<BR>\n" );
document.write( "then<BR>\n" );
document.write( "Area = (x+22) * (x+12) = (x^2 + 34x + 264)<BR>\n" );
document.write( ";<BR>\n" );
document.write( "If the ratio of the area of the original photo to the area of the enlarged photo is 4:25,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+4x%29%2F%28x%5E2+%2B+34x+%2B+264%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+4x%29%2F%28x%5E2+%2B+34x+%2B+264%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F25 ALIGN=MIDDLE  ALT=\"4%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "25(x^2 + 4x) = 4(x^2 + 34x + 264)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "25x^2 + 100x = 4x^2 + 136x + 1056<BR>\n" );
document.write( ":<BR>\n" );
document.write( "25x^2 - 4x^2 + 100x - 136x - 1056 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "21x^2 - 36x - 1056 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "7x^2 - 12x - 352 = 0 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "use the quadratic formula: a=7, b=-12, c=-352<BR>\n" );
document.write( "You should get a positive solution of x = 8<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The enlarged dimensions:<BR>\n" );
document.write( "8 + 22 = 30\" is the height<BR>\n" );
document.write( "8 + 12 = 20\" is the width<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A8%29%2F%2830%2A20%29 ALIGN=MIDDLE  ALT=\"%2812%2A8%29%2F%2830%2A20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96%2F600 ALIGN=MIDDLE  ALT=\"96%2F600\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F25 ALIGN=MIDDLE  ALT=\"4%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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