document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=629795>Question 629795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the average of four numbers is 40. the third is 12 more than the second. the second is five times the first. the fourth is 8 less than the first. find 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 #396500 by </B><A HREF=/tutors/aboutme.mpl?userid=Charles3475><B>Charles3475(23)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Charles3475><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=Charles3475><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=396500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the four numbers be a, b, c, d\r<BR>\n" );
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document.write( "(a+b+c+d)/4=40    (Definition of average)\r<BR>\n" );
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document.write( "a+b+c+d = 160   (multiply by 4)\r<BR>\n" );
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document.write( "c = b + 12   (Given)\r<BR>\n" );
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document.write( "b = 5*a      (Given)\r<BR>\n" );
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document.write( "d = a - 8    (Given)\r<BR>\n" );
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document.write( "c = (5*a) + 12   (Substitution)\r<BR>\n" );
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document.write( "Each number has been expressed in terms of \"a\", we may now solve for \"a\" by substituting each expression back into the original equation.\r<BR>\n" );
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document.write( "a+ 5*a + (5*a + 12) + (a-8) = 160  (Substitution)\r<BR>\n" );
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document.write( "a + 5*a + 5*a + 12 + a -8 = 160    (Expansion of terms)\r<BR>\n" );
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document.write( "12*a +4 = 160    (add like terms)\r<BR>\n" );
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document.write( "12*a = 156       (subtract 4 from both sides)\r<BR>\n" );
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document.write( "a = 13   (divide both sides by 4)\r<BR>\n" );
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document.write( "With \"a\" we may solve for each of the other numbers.\r<BR>\n" );
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document.write( "b = 5*a = 5*13 = 65  (Substitution and simplify)\r<BR>\n" );
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document.write( "c = 5*a + 12 = 5*13 + 12 = 77  (Substitution and simplify)\r<BR>\n" );
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document.write( "d = a - 8 = 13 - 8 = 5    (Substitution and simplify)\r<BR>\n" );
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document.write( "13 + 65 + 77 + 5 = 160 (Check)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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