problem: Robert wants to fence a rectangular plot of land of at least 500 square feet while using the least amount of fencing possible. He wants the width of the plot to be 5 ft longer than the length. What is the width of the plot?
solution: We set the length to be $l$ and the width to $l+5$. We can write the problem as the inequality $l(l+5)\ge500$. Distributing on the left-hand side, subtracting 500 from both sides, and factoring, we get \begin{align*}
  l(l+5)&\ge500 \quad \Rightarrow \\
  l^2+5l-500&\ge 0 \quad \Rightarrow \\
  (l+25)(l-20)&\ge 0.
  \end{align*}The area is at least 500 square feet when the $l \le -25 \text{ or } l \ge 20$. The dimensions can't be negative, so the smallest length possible while still having an area of at least 500 square ft is $20$ ft. Therefore, the width of the plot is $20+5=\boxed{25 \text{ ft}}$.