document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205571>Question 1205571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two-digit number is such that its tens digit is greater than its unit digit by 4. The two-digit number is less than 4 times the product of its digits by 11. Find the number  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842483 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=842483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Although the re-wording of the problem as suggested by the other tutor would make the problem easier to read, there is in fact no ambiguity in the given wording.<br><BR>\n" );
document.write( "\"A is less than B by 11\" means exactly the same thing as \"A is 11 less than B\".<br><BR>\n" );
document.write( "To solve the problem as stated....<br><BR>\n" );
document.write( "Let x be the units digit<BR>\n" );
document.write( "Then x+4 is the tens digit<br><BR>\n" );
document.write( "The 2-digit number is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28x%2B4%29%2Bx=11x%2B40 ALIGN=MIDDLE  ALT=\"10%28x%2B4%29%2Bx=11x%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The product of the digits is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B4%29=x%5E2%2B4x ALIGN=MIDDLE  ALT=\"x%28x%2B4%29=x%5E2%2B4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The two-digit number is less than 4 times the product of its digits by 11:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2B40=4%28x%5E2%2B4x%29-11 ALIGN=MIDDLE  ALT=\"11x%2B40=4%28x%5E2%2B4x%29-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2B40=4x%5E2%2B16x-11 ALIGN=MIDDLE  ALT=\"11x%2B40=4x%5E2%2B16x-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B5x-51=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B5x-51=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%284x%2B17%29=0 ALIGN=MIDDLE  ALT=\"%28x-3%29%284x%2B17%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x = 3 or x = -17/4; of course the negative solution makes no sense in the problem.<br><BR>\n" );
document.write( "So the units digit is x=3 and the tens digit is x+4=7.<br><BR>\n" );
document.write( "ANSWER: 73<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "product of digits: 7*3 = 21<BR>\n" );
document.write( "4 times product of digits: 4*21 = 84<BR>\n" );
document.write( "11 less than 4 times product of digits: 84-11 = 73<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );