SOLUTION: A commercial airplane has a total mass at take off of 102000 kg. The luggage and fuel are 1/3 the mass of the unloaded plane, and the crew and passengers are 1/4 the mass of th

Algebra ->  Equations -> SOLUTION: A commercial airplane has a total mass at take off of 102000 kg. The luggage and fuel are 1/3 the mass of the unloaded plane, and the crew and passengers are 1/4 the mass of th      Log On


   

Question 1151791: A commercial airplane has a total mass at take off of 102000 kg. The luggage and fuel are 1/3
the mass of the unloaded plane, and the crew and passengers are 1/4
the mass of the fuel and luggage. Solve for p, the mass of the unloaded plane.
Answer by ikleyn(52850) About Me  (Show Source):
You can put this solution on YOUR website!
.

If p is the mass of the unloaded plane, then


    - the luggage and fuel mass is  %281%2F3%29%2Ap,   and

    - the mass of the crew and passengers is  %281%2F4%29%2A%281%2F3%29%2Ap.


The total mass equation is then


    p + %281%2F3%29p + %281%2F12%29p = 102000  kilograms.


Simplify and solve for p


    %2817%2F12%29p = 102000

    p = %28102000%2A12%29%2F17 kilograms.


Use your calculator.

Solved.