document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=474939>Question 474939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane has a total mass at take-off of 94 000 kg. The fuel and crew are 1/4 of the mass of the unloaded plane and the passengers and luggage are 1/3 of the mass of the fuel and crew. What is the mass of the unloaded plane. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325687 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=325687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mass at takeoff is 94,000 kg.<BR>\n" );
document.write( "this includes fuel and crew and passengers and luggage<BR>\n" );
document.write( "the fuel and crew are 1/4 of the mass of the unloaded plane.<BR>\n" );
document.write( "the passengers and luggage are 1/3of the mass of the fuel and crew.<BR>\n" );
document.write( "let a = mass of unloaded plane.<BR>\n" );
document.write( "let b = mass of fuel and crew.<BR>\n" );
document.write( "let c = mass of passenters and luggage.<BR>\n" );
document.write( "mass of the plane at takeoff is equal to a + b + c.<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "a + b + c = 94,000 kg.<BR>\n" );
document.write( "b is equal to 1/4 * a.<BR>\n" );
document.write( "c is equal to 1/3 * b.<BR>\n" );
document.write( "substituting for c in the equation gets:<BR>\n" );
document.write( "a + b + (b/3) = 94,000 kg<BR>\n" );
document.write( "substituting for b in the equation gets:<BR>\n" );
document.write( "a + (a/4) + ((a/4)/3) = 94,000 kg<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "a + (a/4) + (a/12) = 94,000 kg<BR>\n" );
document.write( "convert all denominators on the left hand side of this equation to 12 to get:<BR>\n" );
document.write( "12a/12 + 3a/12 + a/12 = 94,000 kg.<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "16a/12 = 94,000 kg<BR>\n" );
document.write( "multiply both sides of this equation by (12/16) to get:<BR>\n" );
document.write( "a = (94,000 * 12)/16 = 70,500 kg.<BR>\n" );
document.write( "since b = a/4, this means that b = 70,500 / 4 = 17,625 kg.<BR>\n" );
document.write( "since c = b/3, this means that c = 5,875 kg.<BR>\n" );
document.write( "the sum of a + b + c = 70,500 + 17625 + 5,875 = 94,000.<BR>\n" );
document.write( "the numbers look good.<BR>\n" );
document.write( "we'll confirm by tracing back to the original requirements using them.<BR>\n" );
document.write( "the load of the plan at takeoff is 94,000 kg.<BR>\n" );
document.write( "the weight of the empty plane is equal to 70,500 kg.<BR>\n" );
document.write( "the weight of the fuel and crew is equal to 1/4 of that (70,500 / 4 = 17,625 kg).<BR>\n" );
document.write( "the weight of the passengers and luggage is equal to 1/3 of the weight of the fuel and crew (17,625 / 3 = 5,875).<BR>\n" );
document.write( "the weight of the plane at takeoff is the weight of the unloaded plan plus the weight of the fuel and crew plus the weight of the passengers and luggage.<BR>\n" );
document.write( "the weight of the plane at takeoff is equal to 70,500 + 17,625 + 5,875 which is equal to 94,000 kg.<BR>\n" );
document.write( "numbers are good.<BR>\n" );
document.write( "problem is solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );