document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202378>Question 202378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find 4 consecutive even integers where the product of the two smaller numbers is 56 less than the product of the two larger numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152603 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> smallest number is x<BR>\n" );
document.write( "next larger number is x + 2<BR>\n" );
document.write( "then x + 4<BR>\n" );
document.write( "then x + 6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "they go up by 2 because they are even integers.<BR>\n" );
document.write( "if they were odd integers they would still go up by 2.<BR>\n" );
document.write( "your answer, in this case, however, should be an even integer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "problem states that product of 2 smaller numbers = product of 2 larger numbers minus 56.<BR>\n" );
document.write( "x * (x+2) = (x+4)*(x+6) - 56<BR>\n" );
document.write( "expanding this makes it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2%2Ax ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10%2Ax+%2B+24+-+56 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10%2Ax+%2B+24+-+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2%2Ax ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of the equation to get:<BR>\n" );
document.write( "0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10%2Ax+%2B+24+-+56+-+x%5E2+-+2%2Ax ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10%2Ax+%2B+24+-+56+-+x%5E2+-+2%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax+%2B+24+-+56 ALIGN=MIDDLE  ALT=\"8%2Ax+%2B+24+-+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 56 and subtract 24 from both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56+-+24+=+8%2Ax ALIGN=MIDDLE  ALT=\"56+-+24+=+8%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+8%2Ax ALIGN=MIDDLE  ALT=\"32+=+8%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides of the equation by 8 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "smallest number is 4.<BR>\n" );
document.write( "next largest number is 6<BR>\n" );
document.write( "then 8 <BR>\n" );
document.write( "then 10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "4*6 = 24<BR>\n" );
document.write( "8*10 = 80 - 56 = 24<BR>\n" );
document.write( "product of the smallest numbers = product of the largest numbers - 56 so your answer is good.<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "the 4 consecutive even numbers are:  4,6,8,10<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );