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 $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ 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?

maximum Nov 5, 2023

#1**0 **

Let x be the load that each of the neighbor's small trucks can carry. We know that my large truck can carry a load of at least 500 pounds more than each of her trucks, so my truck can carry at least x+500 pounds.

We also know that my truck can carry no more than 41 of the total load her four trucks combined can carry, so my truck can carry at most 4x.

Therefore, the greatest load I can be sure that my large truck can carry is 3x+500 pounds.

parmen Nov 5, 2023