I have a large truck and my neighbor has four identical small trucks. My truck can carry at least 800 pounds more than each of her trucks, but no more than one-third what all four of her trucks combined can carry. Knowing only these facts, what is the largest number of pounds that I can be assured of being able to carry in my truck?
Please show work because I am confused on how to do this.
Here's the way I interpret the second question
Let your truck be capable of carrying x lbs
Let the total number of pounds that your neighbor can carry in 4 identical trucks = y
So each of your neighbor's trucks can carry y / 4 lbs
"My truck can carry at least 800 pounds more than each of her trucks" translates to
x ≥ 800 + y / 4
"...but no more than one-third what all four of her trucks combined can carry" translates to
x ≤ y/3
Look at the intersection point of these two inequalities : https://www.desmos.com/calculator/xggshl0aos
Your truck can carry 3200 lbs .....
Your neighbor's trucks can carry 9600 lbs
So each of her trucks can carry 9600/ 4 = 2400 lbs
And your truck carries at least 800 lbs more than each of her trucks [ 3200 - 2400 ]
Plus your truck can carry no more than 1/3 of what all 4 of her trucks can carry.....9600/3 = 3200 lbs