+479 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?
+1768 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.
