document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174113>Question 174113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the four oldest people in Golden City lived a total of 384 years put together. The difference in ages for the youngest and the second oldest is 14. The second youngest is 3 years older than the youngest. The oldest is 20 years older than the average of the second and youngest. What are their ages?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129020 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=129020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> youngest = a<BR>\n" );
document.write( "second youngest = b<BR>\n" );
document.write( "second oldest = c<BR>\n" );
document.write( "oldest = d<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "all four lived a total of 384 years.:<BR>\n" );
document.write( "a + b + c + d = 384<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "difference in ages for the youngest and the second oldest is 14:<BR>\n" );
document.write( "c - a = 14<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the second youngest is 3 years older than the youngest.<BR>\n" );
document.write( "b = a + 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The oldest is 20 years older than the average of the second and youngest.<BR>\n" );
document.write( "*****<BR>\n" );
document.write( "question here is second what?<BR>\n" );
document.write( "second youngest or second oldest.<BR>\n" );
document.write( "i'll have to solve for both to see.<BR>\n" );
document.write( "if second oldest, then:<BR>\n" );
document.write( "d = (c+a)/2 + 20<BR>\n" );
document.write( "if second youngest, then:<BR>\n" );
document.write( "d = (b+a)/2 + 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equations you have to work with are:<BR>\n" );
document.write( "a + b + c + d = 384<BR>\n" );
document.write( "c = a + 14 (derived from c-a = 14)<BR>\n" );
document.write( "b = a + 3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "before we go any further, we will substitute:<BR>\n" );
document.write( "a + 14 for c, and:<BR>\n" );
document.write( "a + 3 for b<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a + b + c + d becomes:<BR>\n" );
document.write( "a + a + 3 + a + 14 + d = 384<BR>\n" );
document.write( "if we combine like terms, this equation becomes:<BR>\n" );
document.write( "3*a + 17 + d = 384<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we have also:<BR>\n" );
document.write( "d = (c+a)/2 + 20<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "d = (b+a)/2 + 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we'll look at d = (b+a)/2 + 20 first.<BR>\n" );
document.write( "we start with:<BR>\n" );
document.write( "d = (b+a)/2 + 20<BR>\n" );
document.write( "we substitute a+3 for b:<BR>\n" );
document.write( "d = (a + 3 + a)/2 + 20<BR>\n" );
document.write( "we combine like terms:<BR>\n" );
document.write( "d = (2*a + 3)/2 + 20<BR>\n" );
document.write( "we substitute for d in the total equation:<BR>\n" );
document.write( "3*a + 17 + d = 384<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "3*a + 17 + (2*a+3)/2 + 20 = 384<BR>\n" );
document.write( "we combine like terms:<BR>\n" );
document.write( "3*a + 37 + (2*a+3)/2 = 384<BR>\n" );
document.write( "we multiply by 2 to remove fractions:<BR>\n" );
document.write( "6*a + 74 + 2*a + 3 = 768<BR>\n" );
document.write( "we combine like terms:<BR>\n" );
document.write( "8*a + 77 = 768<BR>\n" );
document.write( "we subtract 77 from both sides:<BR>\n" );
document.write( "8*a = 768 - 77<BR>\n" );
document.write( "we combine like terms:<BR>\n" );
document.write( "8*a = 691<BR>\n" );
document.write( "a = 86.375<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i was looking for an integer.<BR>\n" );
document.write( "before going further, i'll try the second option.<BR>\n" );
document.write( "that was:<BR>\n" );
document.write( "d = (c+a)/2 + 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we start with:<BR>\n" );
document.write( "d = (c+a)/2 + 20<BR>\n" );
document.write( "we substitute for c:<BR>\n" );
document.write( "d = (a + 14 + a)/2 + 20<BR>\n" );
document.write( "we substitute for d in the total equation:<BR>\n" );
document.write( "3*a + 17 + d = 384<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "3*a + 17 + (2*a + 14)/2 + 20 = 384<BR>\n" );
document.write( "we remove parentheses:<BR>\n" );
document.write( "3*a + 17 + 2*a/2 + 14/2 + 20 = 384<BR>\n" );
document.write( "we simplify:<BR>\n" );
document.write( "3*a + 17 + a + 7 + 20 = 384<BR>\n" );
document.write( "we combine like terms:<BR>\n" );
document.write( "4*a + 44 = 384<BR>\n" );
document.write( "we subtract 44 from both sides:<BR>\n" );
document.write( "4*a = 384 - 44<BR>\n" );
document.write( "we simplify:<BR>\n" );
document.write( "4*a = 340<BR>\n" );
document.write( "we divide both sides by 4<BR>\n" );
document.write( "a = 340/4 = 85<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this option looks more promising so we'll pursue further.<BR>\n" );
document.write( "we used the equation for:<BR>\n" );
document.write( "The oldest is 20 years older than the average of the second OLDEST and youngest.<BR>\n" );
document.write( "to solve for d:<BR>\n" );
document.write( "d = (c+a)/2 + 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we have a = 85<BR>\n" );
document.write( "c = a + 14 = 85 + 14 = 99<BR>\n" );
document.write( "c = 99<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b = a + 3 = 85 + 3 = 88<BR>\n" );
document.write( "b = 88<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "d = (c+a)/2 + 20 = (99 + 85)/2 + 20 = 184/2 + 20 = 92 + 20 = 112<BR>\n" );
document.write( "d = 112<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a = 85<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a + b + c + d = 85 + 88 + 99 + 112 = 384<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the equation appears to be satisfied.<BR>\n" );
document.write( "youngest is 85<BR>\n" );
document.write( "second youngest is 88<BR>\n" );
document.write( "second oldest is 99<BR>\n" );
document.write( "oldest is 112<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i also solved for:<BR>\n" );
document.write( "d = (a+b)/2 + 20<BR>\n" );
document.write( "which was:<BR>\n" );
document.write( "The oldest is 20 years older than the average of the second YOUNGEST and youngest.<BR>\n" );
document.write( "the answer came out different but i was still able to solve it and got an answer that also makes sense except that the ages are not in whole integers.<BR>\n" );
document.write( "here's how that worked:<BR>\n" );
document.write( "d = (a+b)/2 + 20<BR>\n" );
document.write( "we substitute for b:<BR>\n" );
document.write( "d = (a + a + 3)/2 + 20<BR>\n" );
document.write( "we substitute for d in the total equation:<BR>\n" );
document.write( "3*a + 17 + d = 384<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "3*a + 17 + (2*a + 3)/2 + 20 = 384<BR>\n" );
document.write( "we combine like terms:<BR>\n" );
document.write( "3*a + 37 + (2*a + 3)/2 = 384<BR>\n" );
document.write( "we subtract 37 from both sides:<BR>\n" );
document.write( "3*a + (2*a + 3)/2 = 347<BR>\n" );
document.write( "we multiply both sides by 2 to get:<BR>\n" );
document.write( "6*a + 2*a + 3 = 2*347<BR>\n" );
document.write( "we combine like terms and simplify:<BR>\n" );
document.write( "8*a + 3 = 694<BR>\n" );
document.write( "we subtract 3 from both sides:<BR>\n" );
document.write( "8*a = 691<BR>\n" );
document.write( "we divide both sides by 8:<BR>\n" );
document.write( "a = 691/8 = 86.375<BR>\n" );
document.write( "b = a + 3 = 89.375<BR>\n" );
document.write( "c = a + 14 = 100.375<BR>\n" );
document.write( "d = (a+b)/2 + 20 = (86.375 + 89.375)/2 + 20 = 175.75/2 + 20 =87.875 + 20 = 107.875<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we have:<BR>\n" );
document.write( "a = 86.375<BR>\n" );
document.write( "b = 89.375<BR>\n" );
document.write( "c = 100.375<BR>\n" );
document.write( "d = 107.875<BR>\n" );
document.write( "add them all up together and we get:<BR>\n" );
document.write( "384<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "whether we used second oldest or second youngest in solving for d, we had a solution either way.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "choose the one that applies to your problem.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );