document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278810>Question 278810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student wants to know how many integers between 1 and 1000 are a multiple of 4 or a multiple of 5.  She wonders if it is correct to find the number of those integers that are multiples of 4 and add the number of those that are multiples of 5.  How do you respond? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202801 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202801\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not quite.\r<BR>\n" );
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document.write( "there are certain numbers that are both multiples of 5 and multiples of 4 and those need to be subtracted from the total because they will be counted twice.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume the numbers were from 1 to 100 (we can count those easier.\r<BR>\n" );
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document.write( "100 / 4 = 25<BR>\n" );
document.write( "100 / 5 = 20<BR>\n" );
document.write( "100 / 20 = 5\r<BR>\n" );
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document.write( "The total of numbers should be 25 + 20 - 5 = 40 numbers.\r<BR>\n" );
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document.write( "we would have:\r<BR>\n" );
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document.write( "4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100\r<BR>\n" );
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document.write( "5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100\r<BR>\n" );
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document.write( "20 is counted twice so we have to subtract 1 of them.<BR>\n" );
document.write( "40 is counted twice so we have to subtract 1 of them.<BR>\n" );
document.write( "60, 80, and 100 are counted twice so we have to subtract 1 of them.\r<BR>\n" );
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document.write( "the same principle applies from 1 to 1000.\r<BR>\n" );
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document.write( "number of 4's is 1000/4 = 250<BR>\n" );
document.write( "number of 5's is 1000/5 = 200<BR>\n" );
document.write( "number of 20's (4*5) is 1000/20 = 50<BR>\n" );
document.write( "total is 250 + 200 - 50 = 400\r<BR>\n" );
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document.write( "bottom line is you have to subtract the numbers that are both divisible by 4 and 5 to avoid them from being double counted.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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