consider two circles, a smaller one and a larger one. If the larger one has a radius that is 3 feet larger than that of the smaller circle and the ratio of the circumferences is 2:1, what are the radii of the two circles?

Begin by diagramming the two circles just as it states in theproblem

Now determine the circumference of each circle
On the Right, we get 2$\pi$(r+3)
On the Left, we get 2$\pi$r
The ratio of these must be 2:1
$\frac{2}{1}=\frac{2\pi (r+3)}{2\pi r}=\frac{r+3}{r}$
now we can use the first and last fractions and use crossmultiplication to solve for r
$$\begin{gathered} (2)(r)=(1)(r+3) \\ 2r+r+3 \\ r=3 \end{gathered}$$
which is the radius of the smaller circle
r+3=6is the radius of the larger circle