Question:
Daphne has a rope that is 60 meters long. She wants to use it to mark the boundary of a circle whose radius is an integer. What's the largest possible radius for her circle, in meters?

Answer:
The 60-meter rope will mark the circumference of the circle, which is equal to $2\pi r$. So we look for the largest integer $r$ such that the circumference is less than or equal to 60. We have $$2\pi r\le60\qquad\implies r\le\frac{60}{2\pi}\approx \frac{30}{3.14}.$$We know that $\frac{30}{3.14}<\frac{31.4}{3.14}=10$, but greater than $\frac{31.4-3.14}{3.14}=9$, so the largest possible radius is $\boxed{9}$ meters.