document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110052>Question 110052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find four consecutive odd integers whose sum is 196 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80175 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=80175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the first odd integer ... x<BR>\n" );
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document.write( "then the next odd integer is x + 2<BR>\n" );
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document.write( "the third consecutive odd integer is x + 4<BR>\n" );
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document.write( "the fourth consecutive odd integer is x + 6<BR>\n" );
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document.write( "Note that these show that the difference between consecutive odd integers is 2 ... think in<BR>\n" );
document.write( "terms of 3, 5, 7, and 9 being consecutive odd integers and note that each is 2 away from<BR>\n" );
document.write( "its predecessor.<BR>\n" );
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document.write( "If you add our 4 consecutive odd integers you get:<BR>\n" );
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document.write( "x + (x + 2) + (x + 4) + (x + 6) = 4x + 12<BR>\n" );
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document.write( "but you are told that this sum is 196. So set the sum equal to 196 and write it in the form<BR>\n" );
document.write( "of an equation to get:<BR>\n" );
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document.write( "4x + 12 = 196<BR>\n" );
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document.write( "Get rid of the 12 on the left side by subtracting 12 from both sides to convert the equation to:<BR>\n" );
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document.write( "4x = 196 - 12 = 184<BR>\n" );
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document.write( "Then solve for x by dividing both sides by 4 to get:<BR>\n" );
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document.write( "x = 184/4 = 46 <BR>\n" );
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document.write( "What does this tell us? This cannot be an answer because the first number in the series is<BR>\n" );
document.write( "an even number. Add up the 4 consecutive even integers ... that is add up 46 + 48 + 50 + 52<BR>\n" );
document.write( "and you get 196 as the sum. <BR>\n" );
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document.write( "Try nearby odd numbers ... the sum of 45 + 47 + 49 + 51 equals 192. This is too small so the<BR>\n" );
document.write( "series has to be \"upped.\" Find the sum of 47 + 49 + 51 + 53 = 200. This is too big. So there<BR>\n" );
document.write( "is no series of four consecutive odd numbers that will add to 196.<BR>\n" );
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document.write( "The conclusion is that this problem has no solution.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work on it.<BR>\n" );
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