document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208625>Question 1208625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A three digit number \"ABC\" is divided by the two digit number \"AC\". The quotient is 16 with no remainder. What is the largest possible number \"ABC\"? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846999 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The value of the 3-digit number ABC is 100A+10B+C.<BR>\n" );
document.write( "The value of the 2-digit number AC is 10A+C.<br><BR>\n" );
document.write( "The 3-digit number is 16 times the 2-digit number:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100A%2B10B%2BC=16%2810A%2BC%29 ALIGN=MIDDLE  ALT=\"100A%2B10B%2BC=16%2810A%2BC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100A%2B10B%2BC=160A%2B16C ALIGN=MIDDLE  ALT=\"100A%2B10B%2BC=160A%2B16C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10B=60A%2B15C ALIGN=MIDDLE  ALT=\"10B=60A%2B15C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=6A%2B1.5C ALIGN=MIDDLE  ALT=\"B=6A%2B1.5C\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "B is a single-digit integer; A is a single-digit integer so 6A is an integer.  That means 1.5C must be an integer, which means C is an even single-digit integer.<br><BR>\n" );
document.write( "Try different values of C in equation [1] to find which ones give single-digit values for B:<br><BR>\n" );
document.write( "C=0: B=6A so A=1 and B=6; ABC is 160.  160/16 = 10 so that solution is good<br><BR>\n" );
document.write( "C=2: B=6A+3 so A is 1 and B is 9; ABC is 192.  192/16 = 12 so that solution is good<br><BR>\n" );
document.write( "For larger values of C, B=6A+1.5C will make B no longer a single-digit integer, so there are no more solutions.<br><BR>\n" );
document.write( "The two numbers ABC that satisfy the given condition are 160 and 192.<br><BR>\n" );
document.write( "ANSWER: 192<br><BR>\n" );
document.write( " </SPAN>\n" );
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