document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=873914>Question 873914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit numeral is 10. The number named by the numeral is 18 more than the number named when the digits are reversed. What is the original numeral?<BR>\n" );
document.write( "Equation & answer please.. Thank You! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527212 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=527212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= tens digit.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ones/units digit.<BR>\n" );
document.write( " <BR>\n" );
document.write( "One of the statements in the problem says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Bu=10 ALIGN=MIDDLE  ALT=\"t%2Bu=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t%2Bu ALIGN=MIDDLE  ALT=\"10t%2Bu\"   DISABLED_style= \"max-width:90%; height:auto;\" >= value of the two-digit numeral.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10u%2Bt ALIGN=MIDDLE  ALT=\"10u%2Bt\"   DISABLED_style= \"max-width:90%; height:auto;\" >= value of the number named when the digits are reversed.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Another statement in the problem says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t%2Bu ALIGN=MIDDLE  ALT=\"10t%2Bu\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10u%2Bt ALIGN=MIDDLE  ALT=\"10u%2Bt\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That can be written as the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t%2Bu=10u%2Bt%2B18 ALIGN=MIDDLE  ALT=\"10t%2Bu=10u%2Bt%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Subtracting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t-t%2Bu-u=10u-u%2Bt-t%2B18 ALIGN=MIDDLE  ALT=\"10t-t%2Bu-u=10u-u%2Bt-t%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9t=9u%2B18 ALIGN=MIDDLE  ALT=\"9t=9u%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, dividing both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9t%2F9=%289u%2B18%29%2F9 ALIGN=MIDDLE  ALT=\"9t%2F9=%289u%2B18%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=9u%2F9%2B18%2F9 ALIGN=MIDDLE  ALT=\"t=9u%2F9%2B18%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=u%2B2 ALIGN=MIDDLE  ALT=\"t=u%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Take the equation above, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Bu=10 ALIGN=MIDDLE  ALT=\"t%2Bu=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > written at the beginning,<BR>\n" );
document.write( "we have the system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28t%2Bu=10%2Ct=u%2B2%29 ALIGN=MIDDLE  ALT=\"system%28t%2Bu=10%2Ct=u%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which we call \"a system of linear equations.\"<BR>\n" );
document.write( "We can solve it \"by substitution,\"<BR>\n" );
document.write( "meaning that we take an expression that is equal to one variable from one equation,<BR>\n" );
document.write( "and substitute that expression for the variable in the other equation.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2B2 ALIGN=MIDDLE  ALT=\"u%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Bu=10 ALIGN=MIDDLE  ALT=\"t%2Bu=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2B2%2Bu=10 ALIGN=MIDDLE  ALT=\"u%2B2%2Bu=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2Bu%2B2=10 ALIGN=MIDDLE  ALT=\"u%2Bu%2B2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2u%2B2=10 ALIGN=MIDDLE  ALT=\"2u%2B2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2u=10-2 ALIGN=MIDDLE  ALT=\"2u=10-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2u=8 ALIGN=MIDDLE  ALT=\"2u=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=8%2F2 ALIGN=MIDDLE  ALT=\"u=8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28u=4%29 ALIGN=MIDDLE  ALT=\"highlight%28u=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Now, we substitute the value found for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=u%2B2 ALIGN=MIDDLE  ALT=\"t=u%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=u%2B2 ALIGN=MIDDLE  ALT=\"t=u%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4%2B2 ALIGN=MIDDLE  ALT=\"t=4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=6%29 ALIGN=MIDDLE  ALT=\"highlight%28t=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "So, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6 ALIGN=MIDDLE  ALT=\"t=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=4 ALIGN=MIDDLE  ALT=\"u=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the two-digit numeral is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2864%29 ALIGN=MIDDLE  ALT=\"highlight%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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