Question 1154226
.
I own a large truck, and my neighbor owns four small trucks that are all identical. 
My truck can carry a load of at least 800 pounds more than each of her trucks, 
but no more than 1/3 of the total load her four trucks combined can carry. 
Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?
~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The condition tells us these two facts

    M >= H + 800       (1)

    M <= {{{(4/3)H}}}.        (2)

where M is "my" truck and H is "her" truck.


Or, in compound form

    H + 800 <= M <= {{{(4/3)H}}}.


It implies

    H + 800 <= {{{(4/3)H}}}.


Simplify by multiplying by 3 (both sides)

    3H + 2400 <= 4H

Hence,

    H >= 2400


Then from (1)

    M >= H + 800 = 2400 + 800 = 3200 pounds.    <U>ANSWER</U>


<U>ANSWER</U>.  3200 pounds is that greatest load "I" can be sure . . . 
</pre>

Solved.