document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=567574>Question 567574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two digit number is 9. If the digits are reversed, the number formed bears the ratio 3:8 to the original number. Find the original number (Ans. 77) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366616 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=366616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the tens digit = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let the units digit = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The actual number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10a+%2B+b+ ALIGN=MIDDLE  ALT=\"+10a+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The number with the digits reversed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10b+%2B+a+ ALIGN=MIDDLE  ALT=\"+10b+%2B+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+=+9+ ALIGN=MIDDLE  ALT=\"+a+%2B+b+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+10b+%2B+a+%29+%2F+%28+10a+%2B+b+%29+=+3%2F8+ ALIGN=MIDDLE  ALT=\"+%28+10b+%2B+a+%29+%2F+%28+10a+%2B+b+%29+=+3%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8%2A%28+10a+%2B+b+%29+ ALIGN=MIDDLE  ALT=\"+8%2A%28+10a+%2B+b+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8%2A%2810b+%2B+a%29+=+3%2A%28+10a+%2B+b+%29+ ALIGN=MIDDLE  ALT=\"+8%2A%2810b+%2B+a%29+=+3%2A%28+10a+%2B+b+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80b+%2B+8a+=+30a+%2B+3b+ ALIGN=MIDDLE  ALT=\"+80b+%2B+8a+=+30a+%2B+3b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+22a+-+77b+=+0+ ALIGN=MIDDLE  ALT=\"+22a+-+77b+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+22a+=+77b+ ALIGN=MIDDLE  ALT=\"+22a+=+77b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+%2877%2F22%29%2Ab+ ALIGN=MIDDLE  ALT=\"+a+=+%2877%2F22%29%2Ab+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+%287%2F2%29%2Ab+ ALIGN=MIDDLE  ALT=\"+a+=+%287%2F2%29%2Ab+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute (2) into (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287%2F2%29%2Ab+%2B+b+=+9+ ALIGN=MIDDLE  ALT=\"+%287%2F2%29%2Ab+%2B+b+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7b+%2B+2b+=+18+ ALIGN=MIDDLE  ALT=\"+7b+%2B+2b+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9b+=+18+ ALIGN=MIDDLE  ALT=\"+9b+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+2+ ALIGN=MIDDLE  ALT=\"+b+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2B+b+=+9+ ALIGN=MIDDLE  ALT=\"+a%2B+b+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+2+=+9+ ALIGN=MIDDLE  ALT=\"+a+%2B+2+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+7+ ALIGN=MIDDLE  ALT=\"+a+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The original number is 72<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+10b+%2B+a+%29+%2F+%28+10a+%2B+b+%29+=+3%2F8+ ALIGN=MIDDLE  ALT=\"+%28+10b+%2B+a+%29+%2F+%28+10a+%2B+b+%29+=+3%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+10%2A2+%2B+7+%29+%2F+%28+10%2A7+%2B+2+%29+=+3%2F8+ ALIGN=MIDDLE  ALT=\"+%28+10%2A2+%2B+7+%29+%2F+%28+10%2A7+%2B+2+%29+=+3%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27+%2F+72+=+3%2F8+ ALIGN=MIDDLE  ALT=\"+27+%2F+72+=+3%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+72+ ALIGN=MIDDLE  ALT=\"+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27+=+3%2A9+ ALIGN=MIDDLE  ALT=\"+27+=+3%2A9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27+=+27+ ALIGN=MIDDLE  ALT=\"+27+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Note that the answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+77+ ALIGN=MIDDLE  ALT=\"+77+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is impossible,<BR>\n" );
document.write( "since the digits have to add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );