document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=597021>Question 597021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. Can someone please teach me how to solve this question? It's quite easy but I want to know how. It would mean a lot. Thanks!\r<BR>\n" );
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document.write( "How many integers between 197 and 303 are divisible by 4 or 10? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377988 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A GENERAL APPROACH TO THIS TYPE OF PROBLEM:<BR>\n" );
document.write( "Numbers divisible by 4 (also called multiples of 4) can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2An ALIGN=MIDDLE  ALT=\"4%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > in meant to be an integer.<BR>\n" );
document.write( "The first one is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=4%2A1 ALIGN=MIDDLE  ALT=\"4=4%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Multiple number 49 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=196=4%2A49 ALIGN=MIDDLE  ALT=\"196=4%2A49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Counting all between multiple number 50, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200=4%2A50 ALIGN=MIDDLE  ALT=\"200=4%2A50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "multiple number 75, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300=4%2A75 ALIGN=MIDDLE  ALT=\"300=4%2A75\"   DISABLED_style= \"max-width:90%; height:auto;\" > , there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75-49=26 ALIGN=MIDDLE  ALT=\"75-49=26\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Numbers divisible by 10 (also called multiples of 10) can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Am ALIGN=MIDDLE  ALT=\"10%2Am\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > in meant to be an integer.<BR>\n" );
document.write( "The first one is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=10%2A1 ALIGN=MIDDLE  ALT=\"10=10%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Multiple number 19 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=190=10%2A19 ALIGN=MIDDLE  ALT=\"190=10%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Counting all between multiple number 20, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200=10%2A20 ALIGN=MIDDLE  ALT=\"200=10%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "multiple number 30, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300=10%2A30 ALIGN=MIDDLE  ALT=\"300=10%2A30\"   DISABLED_style= \"max-width:90%; height:auto;\" > , there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30-19=11 ALIGN=MIDDLE  ALT=\"30-19=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Numbers that are divisible by 4 and by 10, are also divisible by their least common multiple, 20, and we should be careful not to count them twice.<BR>\n" );
document.write( "Since there are only a few between 197 and 300, I'll just count them. It's just 200, 220, 240, 260, 280, and 300, just 6 of them.\r<BR>\n" );
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document.write( "The numbers between 197 and 303 that are divisible by 4 or by 10 are the 26 that are divisible by 4, plus the 11 divisible by 10, minus the 6 that are divisible by both, so it is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2B11-6=highlight%2831%29 ALIGN=MIDDLE  ALT=\"26%2B11-6=highlight%2831%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "ALTERNATE APPROACH (for when there are not too many numbers to count):<BR>\n" );
document.write( "In this case, we could also had carefully listed and counted the numbers.<BR>\n" );
document.write( "200, 204, 208, 210, 212,<BR>\n" );
document.write( "216, 220, 224, 228, 230,<BR>\n" );
document.write( "232, 236, 240, 244, 248,<BR>\n" );
document.write( "250, 252, 256, 260, 264,<BR>\n" );
document.write( "268, 270, 272, 276, 280,<BR>\n" );
document.write( "284, 288, 290, 292, 296, and<BR>\n" );
document.write( "300.<BR>\n" );
document.write( " </SPAN>\n" );
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