To find the ratio of the number of donuts without frosting to the number of donuts with frosting, we first need to determine how many donuts do not have frosting.
The total number of donuts made is 93, and the number of donuts with frosting is 55. Therefore, the number of donuts without frosting is:
\[ 93 - 55 = 38 \]
Now, we have:
- Number of donuts without frosting = 38
- Number of donuts with frosting = 55
Next, we can write the ratio of donuts without frosting to donuts with frosting:
\[ \text{Ratio} = \text{Donuts without frosting} : \text{Donuts with frosting} = 38 : 55 \]
Thus, the ratio of the number of donuts without frosting to the number of donuts with frosting is:
\[ \boxed{38:55} \]