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?

 Apr 18, 2024

Let x be the maximum weight each of my neighbor's small trucks can carry. Then my truck can carry at most x+500 pounds.

The total amount her four trucks can carry is 4x pounds. Since my truck's maximum load is at most 41​ of the total her trucks can carry, we know x+500≤41​⋅4x=x.

Simplifying the inequality on the right gives x+500≤x, which means 500≤0. Since this is not possible, there must be no value of x that satisfies both of our original inequalities. Therefore, there is no upper bound on the amount my truck can carry, so the greatest load it can carry is infinite​ pounds. However this makes no sense in the real world, so we can determine that there is an error in the original problem statement.

 Apr 18, 2024

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