document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249475>Question 249475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of 2 consecutive integers is 27 more than 5 times the larger integer find the integers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181706 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=181706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We always seek ways to use the fewest unknowns when solving word problems.  <BR>\n" );
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document.write( "We could call the two integers 'x' and 'y'.  But we are told they are consecutive, so we can say:<BR>\n" );
document.write( "x = x<BR>\n" );
document.write( "y = x+1<BR>\n" );
document.write( "That gives us only one unknown, 'x'.<BR>\n" );
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document.write( "We also are given some relationships:<BR>\n" );
document.write( "the sum of two consecutive integers:  x + x+1<BR>\n" );
document.write( "is 27 more than 5 times the larger integer:  5(x+1) + 27<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "x + x+1 = 5(x+1) + 27<BR>\n" );
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document.write( "Collecting and simplifying terms<BR>\n" );
document.write( "2x + 1 = 5x + 5 + 27<BR>\n" );
document.write( "2x + 1 = 5x + 32<BR>\n" );
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document.write( "Subtracting 1 from both sides<BR>\n" );
document.write( "2x = 5x + 31<BR>\n" );
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document.write( "Subtracting 5x from both sides<BR>\n" );
document.write( "-3x = 31<BR>\n" );
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document.write( "Dividing both sides by -3 shows that 'x' is NOT an integer, so there is no solution...<BR>\n" );
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document.write( "If only the setup had been 26 more instead of 27.  (Or is that a typo?)<BR>\n" );
document.write( "Then we would have had:<BR>\n" );
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document.write( "2x + 1 = 5x + 5 + 26<BR>\n" );
document.write( "2x + 1 = 5x + 31<BR>\n" );
document.write( "2x = 5x + 30<BR>\n" );
document.write( "-3x = 30<BR>\n" );
document.write( "x = -10<BR>\n" );
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document.write( "Then the two consecutive integers would have been:  -10 and -9.<BR>\n" );
document.write( "-10 + (-9) = -19<BR>\n" );
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document.write( "5*(-9) = -45<BR>\n" );
document.write( "-45 + 26 = -19<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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