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?

let a large truck be {{{x}}} and   small trucks {{{y}}}

if your truck can carry a load of at least {{{800}}} pounds {{{more}}} than each of her trucks, we have

{{{x=y+800}}}........eq.1 ( = sign means assuming the greatest load you can be sure that my large truck can carry, in pounds)

if your truck can carry  no more than {{{(1/3)}}}  of the total load her {{{four}}} trucks, we have
{{{x=(1/3)4y}}}........eq.2

substitute {{{x}}} from eq.1 

{{{y+800=(1/3)4y}}}

{{{800=(1/3)4y-y}}}

{{{800=4y/3-3y/3}}}


{{{800=y/3}}}

{{{y=800*3}}}

{{{y=2400}}}

go to

{{{x=y+800}}}........eq.1, substitute {{{y}}}

{{{x=2400+800}}}

{{{x=3200}}}->the greatest load you can be sure that my large truck can carry

so, your truck can carry {{{3200}}} pounds and each of her trucks can carry 
 {{{2400}}}