document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25804>Question 25804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem:<BR>\n" );
document.write( "Find the two-digit number whose tens digit is 3 less than the units digit. The original number is 6 more than 4 times the sum of the digits.<BR>\n" );
document.write( "I could REALLY use your HELP! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13890 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "You can solve this with algebra if you want, but I don't think it's worth the effort. We know the number must be two digits, and that the tens digit is 3 less than the units digit. So that means the number must be one of\r<BR>\n" );
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document.write( "14<BR>\n" );
document.write( "25<BR>\n" );
document.write( "36<BR>\n" );
document.write( "47<BR>\n" );
document.write( "58<BR>\n" );
document.write( "69\r<BR>\n" );
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document.write( "The number also has to be 6 more than 4 times the sum of it's digits, so lets work out 4*(sum digits)+6 for each of these numbers\r<BR>\n" );
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document.write( "14 : 26<BR>\n" );
document.write( "25 : 34<BR>\n" );
document.write( "36 : 42<BR>\n" );
document.write( "47 : 50<BR>\n" );
document.write( "58 : 58 - Ah Ha!<BR>\n" );
document.write( "69 : 66\r<BR>\n" );
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document.write( "As you can see 58 is the answer. If you are interested in the algebraic solution then let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the tens digit, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the units digit. The the first condition says <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=u-3 ALIGN=MIDDLE  ALT=\"t=u-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the second condition says <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t%2Bu=4%28t%2Bu%29%2B6 ALIGN=MIDDLE  ALT=\"10t%2Bu=4%28t%2Bu%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substitute the first equation into the second and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11u-30=8u-6 ALIGN=MIDDLE  ALT=\"11u-30=8u-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3u=24 ALIGN=MIDDLE  ALT=\"3u=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=8 ALIGN=MIDDLE  ALT=\"u=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=u-3 ALIGN=MIDDLE  ALT=\"t=u-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5 ALIGN=MIDDLE  ALT=\"t=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope that helps.\r<BR>\n" );
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document.write( "Kev </SPAN>\n" );
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