document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85407>Question 85407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If one-half of a number is added to one-third of the next consecutive number, the sum is 67. What are the two numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61574 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=61574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If x is the unknown number, then the next consecutive number is x + 1.<BR>\n" );
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document.write( "If one-half of the unknown number (that is (1/2)*x) is added to one-third of the next <BR>\n" );
document.write( "consecutive number (that is (1/3)*(x + 1)) the sum is 67.<BR>\n" );
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document.write( "In equation form this can be written as:<BR>\n" );
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document.write( "(1/2)*x + (1/3)*(x + 1) = 67<BR>\n" );
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document.write( "Multiply out the distributed multiplication on the left side to get:<BR>\n" );
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document.write( "(1/2)*x + (1/3)*x + (1/3) = 67<BR>\n" );
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document.write( "Get rid of the denominators by multiplying everything in this equation by the common <BR>\n" );
document.write( "denominator of 2*3 or 6. If you multiply all the terms by 6 the result is:<BR>\n" );
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document.write( "(6/2)*x + (6/3)*x + (6/3) = 67 * 6<BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "3*x + 2*x + 2 = 402<BR>\n" );
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document.write( "The x terms can be added together to get:<BR>\n" );
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document.write( "5*x + 2 = 402<BR>\n" );
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document.write( "Subtract 2 from both sides:<BR>\n" );
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document.write( "5*x = 400<BR>\n" );
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document.write( "Divide both sides by 5 and you get:<BR>\n" );
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document.write( "x = 80<BR>\n" );
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document.write( "that means that the next consecutive integer is 81. So the two numbers are 80 and 81.<BR>\n" );
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document.write( "Check:<BR>\n" );
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document.write( "Does one-half of 80 when added to one-third of 81 = 67?<BR>\n" );
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document.write( "One-half of 80 is 40 and one-third of 81 is 27.  Adding 40 and 27 does result in 67, so<BR>\n" );
document.write( "the two numbers 80 and 81 do satisfy the problem.<BR>\n" );
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document.write( "Hope this helps. </SPAN>\n" );
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