ratio of the shaded area to the unshaded area

Let $2r$ be the diameter of the green circle, then the diameter of the red circle is $4r$ and the diameter of the blue circle is $8r$ .

$\text{unshaded area = area of the two green circles + area of the red circle} = 2\pi r^2 + \pi (2r)^2=2\pi r^2+4\pi r^2=6\pi r^2$

$\text{shaded area = area of the blue circle - unshaded area} = \pi (4r)^2 - 6\pi r^2= 10 \pi r^2$

$\text{ratio} = \dfrac{10 \pi r^2}{6\pi r^2}=\dfrac{5}{3}$