Answer:
[tex]1:4[/tex]
Step-by-step explanation:
Without loss of generality, let there be 5 star shaped cookies. Following the proportions given, there will be 6 circular cookies. We can set up the following proportion to find out how many triangular cookies there would be:
[tex]\frac{3}{10}=\frac{6}{x},\\3x=60,\\x=20[/tex].
Therefore, for every 5 star shaped cookies there will be 20 triangular cookies.
Simplifying this ratio we have [tex]5:20 \implies \boxed{1:4}[/tex].