document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143781>Question 143781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were:\r<BR>\n" );
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document.write( "The fifth number plus the third number equals fourteen.\r<BR>\n" );
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document.write( "The fourth number is one more than the second number.\r<BR>\n" );
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document.write( "The first number is one less than twice the second number.\r<BR>\n" );
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document.write( "The second number plus the third number equals ten.\r<BR>\n" );
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document.write( "The sum of all five numbers is 30.\r<BR>\n" );
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document.write( "What were the five numbers and in what order?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104645 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=104645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
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document.write( "Let code (in order) = a,b,c,d,e<BR>\n" );
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document.write( "Try to get everything in terms of c, seems like a good approach<BR>\n" );
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document.write( "Write an equation for all five statements:<BR>\n" );
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document.write( "1.\"The fifth number plus the third number equals fourteen.\"<BR>\n" );
document.write( "e + c = 14<BR>\n" );
document.write( "or<BR>\n" );
document.write( "e = (14-c)<BR>\n" );
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document.write( "2.\"The fourth number is one more than the second number.\"<BR>\n" );
document.write( "d = b + 1<BR>\n" );
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document.write( "3.\"The first number is one less than twice the second number.\"<BR>\n" );
document.write( "a = 2b - 1<BR>\n" );
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document.write( "4.\"The second number plus the third number equals ten.\"<BR>\n" );
document.write( "b + c = 10<BR>\n" );
document.write( "or<BR>\n" );
document.write( "b = (10-c)<BR>\n" );
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document.write( "5.\"The sum of all five numbers is 30.\"<BR>\n" );
document.write( "a + b + c + d + e = 30<BR>\n" );
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document.write( "Using Statements 2 and 4 we can substitute (10-c) for b<BR>\n" );
document.write( "d = b + 1<BR>\n" );
document.write( "d = (10-c) + 1<BR>\n" );
document.write( "d = (11-c)<BR>\n" );
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document.write( "Using equations from statements 3 & 4, we can substitute (10-c) for b again:<BR>\n" );
document.write( "a = 2b -1<BR>\n" );
document.write( "a = 2(10-c) - 1<BR>\n" );
document.write( "a = 20 - 2c - 1<BR>\n" );
document.write( "a = (19-2c)<BR>\n" );
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document.write( "We got a, b, d, and e in terms of c, substitute in equation 5<BR>\n" );
document.write( "a + b + c + d + e = 30<BR>\n" );
document.write( "(19-2c) + (10-c) + c + (11-c + (14-c) = 30<BR>\n" );
document.write( "simplify<BR>\n" );
document.write( "-2c - c + c - c - c + 19 + 10 + 14 + 11 = 30<BR>\n" );
document.write( "-4c + 54 = 30<BR>\n" );
document.write( "-4c = 30 - 54<BR>\n" );
document.write( "-4c = -24<BR>\n" );
document.write( "4c = 24; multiplied equation by -1<BR>\n" );
document.write( "c = 24/4<BR>\n" );
document.write( "c = +6<BR>\n" );
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document.write( "What were the five numbers and in what order<BR>\n" );
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document.write( "Using the equations find the other numbers:<BR>\n" );
document.write( "a = 19 - 2(6)<BR>\n" );
document.write( "a = 7<BR>\n" );
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document.write( "b = 10 - 6<BR>\n" );
document.write( "b = 4<BR>\n" );
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document.write( "c = 6<BR>\n" );
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document.write( "d = 11-6<BR>\n" );
document.write( "d = 5<BR>\n" );
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document.write( "e = 14 - 6<BR>\n" );
document.write( "e = 8<BR>\n" );
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document.write( "See if they satisfy statement 5<BR>\n" );
document.write( "7 + 4 + 6 + 5 + 8 = 30<BR>\n" );
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document.write( "His code number should be 74658 </SPAN>\n" );
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