document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486660>Question 486660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Twelve consecutive integers are arranged in order from least to greatest. If the sum of the first six integers is 381, what is the sum of the last six integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332647 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=332647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The integers are consecutive. Therefore, each integer is obtained by adding 1 to the immediately preceding integer.<BR>\n" );
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document.write( "So if n+0 is the first integer, then n+1 is the second integer and the third integer is n+1+1 or n+2, and so on. The first six of the integers are:<BR>\n" );
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document.write( "n + 0<BR>\n" );
document.write( "n + 1<BR>\n" );
document.write( "n + 2<BR>\n" );
document.write( "n + 3<BR>\n" );
document.write( "n + 4<BR>\n" );
document.write( "n + 5<BR>\n" );
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document.write( "The sum of these 6 numbers is 6n + (0+1+2+3+4+5) which simplifies to 6n + 15.<BR>\n" );
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document.write( "The problem states that the sum of the first 6 numbers is 381. So we can set up the equation:<BR>\n" );
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document.write( "6n + 15 = 381<BR>\n" );
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document.write( "Get rid of the 15 on the left side by subtracting 15 from both sides as follows:<BR>\n" );
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document.write( "6n + 15 - 15 = 381 - 15<BR>\n" );
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document.write( "On the left side the + 15 and the -15 cancel each other out and on the right side 381 - 15 = 366. So the equation simplifies to:<BR>\n" );
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document.write( "6n = 366<BR>\n" );
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document.write( "solve for n by dividing both sides by 6 to get:<BR>\n" );
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document.write( "n = 366/6 = 61<BR>\n" );
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document.write( "We now know that the first number is 61. Therefore, because they are consecutive, the first 6 numbers are 61, 62, 63, 64, 65, and 66. That means that the seventh through twelfth numbers are 67, 68, 69, 70, 71, and 72.  Adding these 6 numbers:<BR>\n" );
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document.write( "67 + 68 + 69 + 70 + 71 + 72<BR>\n" );
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document.write( "results in the total of 417 and that's the answer to this problem.<BR>\n" );
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document.write( "Hope that this helps you to understand the problem.<BR>\n" );
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