document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112957>Question 112957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> number problem.  if one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3.  what are the two integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82282 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=82282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the first integer is x, then the next consecutive integer is x+1.<BR>\n" );
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document.write( "The problem tells you to find one-half of the first integer and subtract it from three-fifths <BR>\n" );
document.write( "of the second integer.<BR>\n" );
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document.write( "Since the first integer is x, one-half of that integer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "And since the second integer is x+1, then three fifths of that integer is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29%2A%28x+%2B+1%29 ALIGN=MIDDLE  ALT=\"%283%2F5%29%2A%28x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A%28x%2B1%29%29%2F5 ALIGN=MIDDLE  ALT=\"%283%2A%28x%2B1%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract the first from the second and you have a difference of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A%28x%2B1%29%29%2F5+-+x%2F2 ALIGN=MIDDLE  ALT=\"%283%2A%28x%2B1%29%29%2F5+-+x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, the problem tells you that this difference is equal to 3. So you can write this<BR>\n" );
document.write( "in equation form as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A%28x%2B1%29%29%2F5+-+x%2F2+=+3 ALIGN=MIDDLE  ALT=\"%283%2A%28x%2B1%29%29%2F5+-+x%2F2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can get rid of the denominator 5 by multiplying all terms on both sides of this equation<BR>\n" );
document.write( "by 5 and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28x%2B1%29+-%285x%29%2F2+=+15 ALIGN=MIDDLE  ALT=\"3%2A%28x%2B1%29+-%285x%29%2F2+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next you can get rid of the denominator 2 by multiplying all terms on both sides of this<BR>\n" );
document.write( "equation by 2 and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A3%2A%28x%2B1%29+-+5x+=+30 ALIGN=MIDDLE  ALT=\"2%2A3%2A%28x%2B1%29+-+5x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply the 2 times 3 and the equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%28x%2B1%29+-+5x+=+30 ALIGN=MIDDLE  ALT=\"6%2A%28x%2B1%29+-+5x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now do the distributed multiplication on the left side by multiplying 6 times both of the<BR>\n" );
document.write( "terms in the parentheses to make the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B+6+-+5x+=+30 ALIGN=MIDDLE  ALT=\"6x+%2B+6+-+5x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the 6x and -5x and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+6+=+30 ALIGN=MIDDLE  ALT=\"x+%2B+6+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 6 on the left side by subtracting 6 from both sides to reduce the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24 ALIGN=MIDDLE  ALT=\"x+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This tells you that one of the integers is 24. Then next consecutive integer must be 25.<BR>\n" );
document.write( "So the two numbers you were looking for are 24 and 25.<BR>\n" );
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document.write( "Check. Half of 24 is 12. And three-fifths of 25 is 15. Subtract 12 from 15 and the answer<BR>\n" );
document.write( "is 3 ... just as the problem said it should be. Therefore, the answer is correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how you can solve it.<BR>\n" );
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