document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99332>Question 99332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of 2 consecutive integers is 250.  Identify BOTH of the numbers.  The formula must construct an algebraic equation with a variable. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72264 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=72264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I suspect that you have an error in the way you stated your problem. There are NO two integers<BR>\n" );
document.write( "that are consecutive and add up to 250.<BR>\n" );
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document.write( "The way to express two consecutive integers is to let the smaller one be represented<BR>\n" );
document.write( "by x. The next integer up from it is x + 1.  The problem says that these two<BR>\n" );
document.write( "integers<BR>\n" );
document.write( "are to total 250 when added. In equation form this means that:<BR>\n" );
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document.write( "x + x + 1 = 250<BR>\n" );
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document.write( "Combine the two x's on the left side to make the equation become:<BR>\n" );
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document.write( "2x + 1 = 250<BR>\n" );
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document.write( "Get rid of the +1 on the left side by subtracting +1 from both sides to reduce the equation<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "2x = 249<BR>\n" );
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document.write( "Solve for x by dividing both sides of this equation by 2 ... the multiplier of x to get:<BR>\n" );
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document.write( "x = 249/2 = 124.5<BR>\n" );
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document.write( "This doesn't work out to be a whole number. 124 and 125 are two consecutive integers<BR>\n" );
document.write( "but they add to be 249. And 125 and 126 are the next pair of consecutive integers,<BR>\n" );
document.write( "but they add to 251.  So there is no solution.<BR>\n" );
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document.write( "But if you had said to find two consecutive EVEN integers, then there would be a solution.<BR>\n" );
document.write( "Represent the smaller integer by x. Then the next even integer would be 2 above that so it<BR>\n" );
document.write( "would be x + 2. [Think in terms of 4 as an even integer. The next even integer is 6 and<BR>\n" );
document.write( "it is equal to 4 + 2.]<BR>\n" );
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document.write( "Now when you add the two even integers the equation becomes:<BR>\n" );
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document.write( "x + x + 2 = 250<BR>\n" );
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document.write( "Combine the two x's on the left side to get:<BR>\n" );
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document.write( "2x + 2 = 250<BR>\n" );
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document.write( "Get rid of the +2 on the left side by subtracting 2 from both sides to make the equation:<BR>\n" );
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document.write( "2x = 248<BR>\n" );
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document.write( "Solve for x by dividing both sides by 2 to reduce the equation to:<BR>\n" );
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document.write( "x = 124<BR>\n" );
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document.write( "And, since the next even integer is 2 above that number, it is 126. This works because<BR>\n" );
document.write( "124 plus 126 does equal 250.<BR>\n" );
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document.write( "Hope this discussion helps you to find your mistake in the problem and shows you the process<BR>\n" );
document.write( "that you use to solve problems such as these.<BR>\n" );
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