SOLUTION: The ABC Shipping Company charges $290 for all packages weighing less than or equal to 5lbs, $520 for packages weighing more than 5lbs and less than 10lbs, and $800 for all packages

Let x = # of packages weighing 101 lbs or more.



Then the number of packages weighting 51 lbs or less is 1.5x,

and the number of packages weighting between 51 lbs and 101 lbs is  (300 - x - 1.5x) = (300-2.5x).



So you have this single equation for x


    290*(1.5x) + 520*(300-2.5x) + 800x = 150800.



The setup is done. The rest is just technique.



Solve for x and then find the number of packages in each category.

    the problem is to be solved using only one equation for one single unknown - 

    not two equations for 2 unknowns and not 3 equations for 3 unknowns.


    Your major task in solving such problems is to "catch" this fact and then to choose the leading unknown 
    and to build an equation around it.