To solve this problem, we can use algebra. Let's represent the total number of eggs at the beginning as "E" and the number of eggs used as "U".
We know that after using 30% of the total number of eggs, the cook still had 14 eggs left. This can be expressed as:
E - 0.3E = 14
0.7E = 14
E = 14 / 0.7
E = 20
So, the total number of eggs at the beginning was 20.
To find the number of eggs used:
U = 0.3E
U = 0.3 * 20
U = 6
Therefore, the cook used 6 eggs.