Question

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 $400$ pounds more than each of her trucks, but no more than $\frac{7}{12}$ 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?

Answer 1

Let s be the capacity of each small truck and L the capacity of the large truck. The conditions give
L ≥ s + 400 and L ≤ (7/12)(4s) = (7/3)s.
Combining,
s + 400 ≤ (7/3)s ⇒ 400 ≤ (4/3)s ⇒ s ≥ 300.
Hence L ≥ s + 400 ≥ 300 + 400 = 700.

So the greatest load you can be sure your truck can carry is 700 pounds.