document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=710743>Question 710743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am a two-digit number. You can count to me by 4's plus 3 or by 5's plus 3. What is the smallest number I can be? How many different numbers can I be? Explain your answers.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437260 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=437260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I believe the problem means that if you count by 4's for a while and then add 3, you get to the number,<BR>\n" );
document.write( "and if you count by 5's for a while and then add 3, you also get to the number.<BR>\n" );
document.write( "In both cases, before adding 3, you had arrived to a number that was a multiple of 4, and a multiple of 5.<BR>\n" );
document.write( "The smallest such number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A5=20 ALIGN=MIDDLE  ALT=\"4%2A5=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and adding 3 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2B3=highlight%2823%29 ALIGN=MIDDLE  ALT=\"20%2B3=highlight%2823%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the smallest number that you can arrive to by<BR>\n" );
document.write( "counting by 4's and adding 3,<BR>\n" );
document.write( "and also by counting by 5's and adding 3.<BR>\n" );
document.write( "The other larger such numbers are any multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > plus 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A20%2B3=40%2A3=highlight%2843%29 ALIGN=MIDDLE  ALT=\"2%2A20%2B3=40%2A3=highlight%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A20%2B3=60%2A3=highlight%2863%29 ALIGN=MIDDLE  ALT=\"3%2A20%2B3=60%2A3=highlight%2863%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A20%2B3=80%2A3=highlight%2883%29 ALIGN=MIDDLE  ALT=\"4%2A20%2B3=80%2A3=highlight%2883%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The next such number,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A20%2B3=100%2A3=103 ALIGN=MIDDLE  ALT=\"5%2A20%2B3=100%2A3=103\"   DISABLED_style= \"max-width:90%; height:auto;\" > , is not a two-digit number.<BR>\n" );
document.write( "So the number in the problem can be any of those 4 numbers:<BR>\n" );
document.write( "23 (the smallest), or 43, or 63, or 83. </SPAN>\n" );
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