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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?

 Nov 5, 2023
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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.

 Nov 5, 2023

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