document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340849>Question 340849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hundred's digit of of a number of three figures is 1/2 of the ten's digit and is less than the unit's digit by 3. If the number be divided by the sum of its digits, the quotient is 22.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 #244198 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=244198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There seems to be something wrong but here goes:\r<BR>\n" );
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document.write( "Let x=hundred's digit<BR>\n" );
document.write( "Then 2x=ten's digit<BR>\n" );
document.write( "And x+3=unit's digit\r<BR>\n" );
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document.write( "Sum of the number's digits:x+2x+x+3=4x+3<BR>\n" );
document.write( "So our equation to solve is:<BR>\n" );
document.write( "(100x+20x+x+3)/(4x+3)=22  multiply each side by 4x+3 and simplify<BR>\n" );
document.write( "121x+3=88x+66 subtract 88x and 3 from each side<BR>\n" );
document.write( "121x-88x+3-3=88x-88x+66-3  collect like terms<BR>\n" );
document.write( "33x=63<BR>\n" );
document.write( "x=1.909 which rounds off to 2<BR>\n" );
document.write( "so x=2<BR>\n" );
document.write( "2x=4<BR>\n" );
document.write( "x+3=5\r<BR>\n" );
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document.write( "The number is 245<BR>\n" );
document.write( "ck<BR>\n" );
document.write( "245/11=22.2 which rounds off to 22\r<BR>\n" );
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document.write( "Another way to look at this problem:<BR>\n" );
document.write( "Clearly the 100's digit cannot be greater than 4.  If it was, then the 10's digit would itself be a 2-digit number which is not allowed\r<BR>\n" );
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document.write( "So we only have 4 possibilities for the 100's digit:<BR>\n" );
document.write( "if the 100's digit is 1<BR>\n" );
document.write( "the 10's digit is 2 and the unit's digit is 4<BR>\n" );
document.write( "the number would be 124<BR>\n" );
document.write( "if the 100's digit is 2<BR>\n" );
document.write( "the 10's digit is 4 and the units digit is 5<BR>\n" );
document.write( "the number would be 245<BR>\n" );
document.write( "if the 100's digit is 3<BR>\n" );
document.write( "the 10's digit is 6 and the unit's digit is 6<BR>\n" );
document.write( "the number would be 366<BR>\n" );
document.write( "if the 100's digit is 4<BR>\n" );
document.write( "the 10's digit is 8 and the unit's digit is 7<BR>\n" );
document.write( "the number would be 487\r<BR>\n" );
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document.write( "The number 245, although not an exact solution, comes closer than any of the others\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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