document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557253>Question 557253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sum of 3 consecutive integers is 21 larger than twice the smallest integer. find integer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362539 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=362539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consecutive integers are each separated from the preceding number by 1. So if we let I represent the first integer, then the next higher integer (the second integer) is I + 1, and I + 2 is the third and final integer.<BR>\n" );
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document.write( "The sum of these 3 consecutive integers is, therefore:<BR>\n" );
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document.write( "I + I + 1 + I + 2<BR>\n" );
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document.write( "Simplify this sum by adding the three I's and adding the two constants to get:<BR>\n" );
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document.write( "3I + 3<BR>\n" );
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document.write( "The problem tells you that this sum is 21 more than twice the smallest integer, which is I. So we multiply the smallest integer by 2 to get 2I and then add 21 to that. It will equal the sum of the 3 integers. In equation form this is:<BR>\n" );
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document.write( "3I + 3 = 21 + 2I<BR>\n" );
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document.write( "Get rid of the 2I on the right side by subtracting 2I from both sides to get:<BR>\n" );
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document.write( "I + 3 = 21<BR>\n" );
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document.write( "Finally get rid of the 3 on the left side by subtracting 3 from both sides and you have:<BR>\n" );
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document.write( "I = 18<BR>\n" );
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document.write( "This means that the 3 consecutive integers are 18, 19, and 20.<BR>\n" );
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document.write( "The sum of these 3 integers is 18 + 19 + 20 = 57<BR>\n" );
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document.write( "Twice the smallest (2 times 18) equals 36 and when you add 21 to that you also get 57.<BR>\n" );
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document.write( "This tells us that our answer is correct, and the 3 consecutive integers are 18, 19, and 20.<BR>\n" );
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document.write( "I hope this helps you to understand how to do this problem that involves consecutive integers.<BR>\n" );
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