document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472691>Question 472691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if one half of an integer is added to one fifth the next consecutive integers,the sum is 17.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 #324049 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=324049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's call the integer N. Then the next consecutive integer is one more than N or it is N+1.<BR>\n" );
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document.write( "Now you are told to add 1/2 of the integer N (which is N/2) to 1/5 of the next consecutive integer. And 1/5 of the next consecutive integer is (1/5)*(N+1).  This sum is to equal 17.  In equation form this relationship is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2F2+%2B+%281%2F5%29%2A%28N%2B1%29+=+17 ALIGN=MIDDLE  ALT=\"N%2F2+%2B+%281%2F5%29%2A%28N%2B1%29+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the denominators by multiplying all terms in this equation by 10, a common denominator of 2 and 5, to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2AN%2F2+%2B+%2810%2F5%29%2A%28N%2B1%29+=+10%2A17 ALIGN=MIDDLE  ALT=\"10%2AN%2F2+%2B+%2810%2F5%29%2A%28N%2B1%29+=+10%2A17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide the integer in each denominator into the integer in the corresponding numerator and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2AN+%2B+2%2A%28N%2B1%29+=+10%2A17 ALIGN=MIDDLE  ALT=\"5%2AN+%2B+2%2A%28N%2B1%29+=+10%2A17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the distributed multiplication on the left side and the multiplication on the right side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2AN+%2B+2%2AN+%2B+2+=+170 ALIGN=MIDDLE  ALT=\"5%2AN+%2B+2%2AN+%2B+2+=+170\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the two terms containing N:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2AN+%2B+2+=+170 ALIGN=MIDDLE  ALT=\"7%2AN+%2B+2+=+170\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 2 on the left side by subtracting 2 from both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2AN+=+168 ALIGN=MIDDLE  ALT=\"7%2AN+=+168\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for N by dividing both sides by 7:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+24 ALIGN=MIDDLE  ALT=\"N+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then if N is 24, the next consecutive integer is 25, and those are the two integers asked for in the problem ... namely 24 and 25.<BR>\n" );
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document.write( "Check: 1/2 of N is 12, and 1/5 of N+1 is 5. If you add those two integers together, you do get 17 as is specified in the problem. <BR>\n" );
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document.write( "Hope that helps you to understand this problem. </SPAN>\n" );
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