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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 600 pounds more than each of her trucks, but no more than 1/2 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?

 Sep 19, 2024
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Let the load that the small trucks be equal to a variable, small_load. Let the load that the large truck can carry be large_load.

By the statements:

large_load >= small_load + 600

large_load <= (small_load)*4/2 = 2(small_load)

Thus, 2(small_load) >= large_load >= small_load + 600, so 2(small_load) >= small_load + 600

Thereafter, small_load >= 600.

Plugging it into the upper-bound inequality:

large_load <= 2(small_load) = 2(600) = 1200 pounds.

 Sep 19, 2024

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