document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133842>Question 1133842</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive even integers such that the sum of the middle two is 1/4 the product of the second and three integers, write an equation and solve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751089 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume you mean sum of the first two, not \"middle two\".<BR>\n" );
document.write( "Let x = the middle number<BR>\n" );
document.write( "Then the 3 numbers are x-2, x, and x+2<BR>\n" );
document.write( "The sum of the first two is x-2 + x = 2x - 2<BR>\n" );
document.write( "The product of the last two is x(x+2) = x^2 + 2x<BR>\n" );
document.write( "So the equation is:<BR>\n" );
document.write( "2x - 2 = (1/4)(x^2 + 2x)<BR>\n" );
document.write( "Collect terms and solve:<BR>\n" );
document.write( "x^2 - 6x + 8 = 0<BR>\n" );
document.write( "This factors as (x-2)(x-4) = 0<BR>\n" );
document.write( "Thus x = 2 or x = 4<BR>\n" );
document.write( "There are two sequences that meet the conditions:<BR>\n" );
document.write( "0, 2, 4 and 2, 4, 6 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );