According to Bartholomew Cubbins, 20 of his hats had feathers. Twenty of the hats with no feathers were red. 15 were green, and 30 were blue. What is the ratio of hats with feathers to hats with no feathers? (Write as a fraction in lowest terms.)
The number of hats with no feathers is $20+20+15+30 = 85$, so the ratio is $\frac{20}{85}$. This fraction reduces to $\boxed{\frac{4}{17}}.$
To find the ratio of hats with feathers to hats with no feathers, we need to determine the number of hats with feathers and the number of hats with no feathers.
According to Bartholomew Cubbins, 20 of his hats had feathers. This means the number of hats with feathers is 20.
Now, we can determine the number of hats with no feathers. We know that the total number of hats is the sum of the hats with feathers and the hats with no feathers.
The number of red hats (with no feathers) is given as 20. The number of green hats (with no feathers) is given as 15. And the number of blue hats (with no feathers) is given as 30.
Therefore, the total number of hats with no feathers is 20 + 15 + 30 = 65.
So, the ratio of hats with feathers to hats with no feathers is 20/65.
This fraction can be simplified to lowest terms by dividing both the numerator and denominator by their greatest common divisor, which is 5.
Thus, the simplified ratio is 4/13.