document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173635>Question 173635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four numbers have a total of 92. The first number is twice the second number and the third number is 4 more than the sum of the first two. The fourth number is 3 less than the difference of the first two numbers. What are the numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128489 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=128489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a,b,c,d = the numbers.<BR>\n" );
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document.write( "a + b + c + d = 92<BR>\n" );
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document.write( "first number is twice the second number:<BR>\n" );
document.write( "a = 2b<BR>\n" );
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document.write( "third number is 4 more than the sum of the first two:<BR>\n" );
document.write( "c = a + b + 4<BR>\n" );
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document.write( "fourth number is 3 less than the difference of the first two numbers.<BR>\n" );
document.write( "d = a - b - 3<BR>\n" );
document.write( "since a > b this would be positive.<BR>\n" );
document.write( "it works this way.<BR>\n" );
document.write( "if we chose b - a, the difference would be negative and the result would not work out.  <BR>\n" );
document.write( "the assumption here is that we are looking for the absolute value of the difference which makes the difference always positive.<BR>\n" );
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document.write( "the rest is just a substitution for what we know.<BR>\n" );
document.write( "we start with:<BR>\n" );
document.write( "a + b + c + d = 92<BR>\n" );
document.write( "since a = 2b, we substitute 2b for a to get:<BR>\n" );
document.write( "2b + b + c + d = 92<BR>\n" );
document.write( "since c = a + b + 4, we substitute a + b + 4 to get:<BR>\n" );
document.write( "2b + b + a + b + 4 + d = 92<BR>\n" );
document.write( "since a = 2b, we again substitute 2b for a to get:<BR>\n" );
document.write( "2b + b + 2b + b + 4 + d = 92<BR>\n" );
document.write( "since d = a - b - 3, e substitute a - b - 3 for d to get:<BR>\n" );
document.write( "2b + b + 2b + b + 4 + (a - b - 3) = 92<BR>\n" );
document.write( "since a = 2b, we again substitute 2b for a to get:<BR>\n" );
document.write( "2b + b + 2b + b + 4 + (2b - b - 3) = 92<BR>\n" );
document.write( "we remove parentheses to get:<BR>\n" );
document.write( "2b + b + 2b + b + 4 + 2b - b - 3 = 92<BR>\n" );
document.write( "we combine likes to get:<BR>\n" );
document.write( "7b + 1 = 92<BR>\n" );
document.write( "we subtract 1 from both sides of the equation to get:<BR>\n" );
document.write( "7b = 91<BR>\n" );
document.write( "we divide both sides of the equation by 7 to get:<BR>\n" );
document.write( "b = 13<BR>\n" );
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document.write( "since b = 13, then<BR>\n" );
document.write( "a = 2b = 26<BR>\n" );
document.write( "c = a + b + 4 = 26 + 13 + 4 = 43<BR>\n" );
document.write( "d = a - b - 3 = 26 - 13 - 3 = 10<BR>\n" );
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document.write( "all variables are:<BR>\n" );
document.write( "a = 26<BR>\n" );
document.write( "b = 13<BR>\n" );
document.write( "c = 43<BR>\n" );
document.write( "d = 10<BR>\n" );
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document.write( "sum of these is 92 satisfying the equation a + b + c + d = 92<BR>\n" );
document.write( "a = 2b is good since 26 is 2 * 13<BR>\n" );
document.write( "c = a + b + 4 = 43 is good since 26 + 13 + 4 = 43<BR>\n" );
document.write( "d = a - b - 3 is good since 26 - 13 - 3 = 10<BR>\n" );
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document.write( "your answer is:<BR>\n" );
document.write( "a = 26<BR>\n" );
document.write( "b = 13<BR>\n" );
document.write( "c = 43<BR>\n" );
document.write( "d = 10 </SPAN>\n" );
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