document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27695>Question 27695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what are three consecutive even intergers whose sum is 114? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15076 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what are three consecutive even intergers whose sum is 114?<BR>\n" );
document.write( "Any two consecutive even integers differ by 2<BR>\n" );
document.write( "Let the required 3 consecutive even integers be<BR>\n" );
document.write( "(a-2), a and (a+2)<BR>\n" );
document.write( "By data the sum of the 3 numbers is 114<BR>\n" );
document.write( "Therefore we have<BR>\n" );
document.write( "[(a-2) + a + (a+2)] = 114<BR>\n" );
document.write( "(a-2+a+a+2)=114<BR>\n" );
document.write( "which implies (a+a+a) = 114 <BR>\n" );
document.write( "(using additive commutativity and associativity <BR>\n" );
document.write( "and the additive inverse law:-2+2=0)<BR>\n" );
document.write( "That is 3a = 114 <BR>\n" );
document.write( "Therefore  a = 114/3 = 38.<BR>\n" );
document.write( "Hence the three consecutive even integers are (38-2), 38 and (38+2)<BR>\n" );
document.write( "Answer:  36,38 and 40<BR>\n" );
document.write( "Verification:<BR>\n" );
document.write( "Of course 36,38 and 40 are all even (as each is a multiple of 2)<BR>\n" );
document.write( "And their sum = 36 + 38 +40 = 114 which is correct.<BR>\n" );
document.write( "One question? Why should we consider the required numbers in the above fashion?<BR>\n" );
document.write( "Why not of the form   a, (a+2), (a+4) ?<BR>\n" );
document.write( "This form is ofcourse right and that is what we normally tend to proceed with.<BR>\n" );
document.write( "There is nothing wrong with it.<BR>\n" );
document.write( "The sum here is [a +(a+2) +(a+4)] = 114<BR>\n" );
document.write( "After applying additive commutativity and associativity,we get<BR>\n" );
document.write( "  3a + 6 = 114<BR>\n" );
document.write( " 3a = 114-6<BR>\n" );
document.write( "3a = 108<BR>\n" );
document.write( "a = 108/3 = (36X3)/3 = 36<BR>\n" );
document.write( "And here the numbers are 36, 36+2, 36+4 that is 36,38 and 40 of course<BR>\n" );
document.write( "What is the advantage of the first method?<BR>\n" );
document.write( "If we consider in the fashion:<BR>\n" );
document.write( "(a-2), a and (a+2)<BR>\n" );
document.write( "then the sum can be visualised mentally and the answer 3a= 114 flashes ina jiffy as a result and we immediately get the answer a =36. Cool! is n't it? That is the advantage.<BR>\n" );
document.write( " </SPAN>\n" );
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