document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138954>Question 1138954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two numbers whose sum is<BR>\n" );
document.write( "28 and whose product is the maximum possible value.\r<BR>\n" );
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document.write( "What two numbers yield this​ product? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756727 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x, y be the two numbers<BR>\n" );
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document.write( "x + y = 28<BR>\n" );
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document.write( "if the two numbers are 1 and 27, then<BR>\n" );
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document.write( "1) x + y = 28<BR>\n" );
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document.write( "2) xy = 27<BR>\n" );
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document.write( "solve equation 1 for y, then substitute for y in equation 2<BR>\n" );
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document.write( "3) y = 28 -x<BR>\n" );
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document.write( "x(28-x) = 27<BR>\n" );
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document.write( "4) -x^2 +28x -27 = 0<BR>\n" );
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document.write( "the graph of equation 4 is a parabola that curves downward, so the coordinates of the vertex is the maximum values for x and y<BR>\n" );
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document.write( "x coordinate = -b/2a = -28/2(-1) = 14<BR>\n" );
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document.write( "substitute for x in equation 3<BR>\n" );
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document.write( "y = 28 -14 = 14<BR>\n" );
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document.write( "the maximum product occurs when x=14 and y=14<BR>\n" );
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document.write( "Note 14 * 14 = 196<BR>\n" );
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