document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=522973>Question 522973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the difference of digits of two digit number is 1.five times the sum of the number plus one is equal to the number. 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 #347160 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=347160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the difference of digits of two digit number is 1.<BR>\n" );
document.write( "five times the sum of the number plus one is equal to the number.<BR>\n" );
document.write( " find the number<BR>\n" );
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document.write( "Two digits, a, b<BR>\n" );
document.write( "then<BR>\n" );
document.write( "10a + b = the number<BR>\n" );
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document.write( "\"the difference of digits of two digit number is 1.\"<BR>\n" );
document.write( "a - b = 1<BR>\n" );
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document.write( "\"five times the sum of the number plus one is equal to the number.\"<BR>\n" );
document.write( "5(a+b) + 1 = 10a + b<BR>\n" );
document.write( "5a + 5b + 1 = 10a + b<BR>\n" );
document.write( "5a - 10a + 5b - b = -1<BR>\n" );
document.write( "-5a + 4b = -1<BR>\n" );
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document.write( "Use substitution here, multiply the 1st equation by 4, add to the 2nd eq<BR>\n" );
document.write( "+4a - 4b = 4<BR>\n" );
document.write( "-5a + 4b = -1<BR>\n" );
document.write( "--------------addition eliminates b, find a<BR>\n" );
document.write( "-a = 3<BR>\n" );
document.write( "a = -3<BR>\n" );
document.write( "find b<BR>\n" );
document.write( "-3 - b = 1<BR>\n" );
document.write( "-b = 1 + 3<BR>\n" );
document.write( "-b = 4<BR>\n" );
document.write( "b = -4<BR>\n" );
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document.write( "The number<BR>\n" );
document.write( "-3(10) + (-4) = -34 is the number<BR>\n" );
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document.write( "Usually not a neg answer in these problems, see if this works in the statement:<BR>\n" );
document.write( "\"five times the sum of the number plus one is equal to the number.\"<BR>\n" );
document.write( "5(-3 + (-4)) + 1 = -34<BR>\n" );
document.write( "5(-7) + 1 = -34<BR>\n" );
document.write( "-35 + 1 = -34; confirms our solution of -34\r<BR>\n" );
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document.write( " </SPAN>\n" );
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