Final answer:
Nicole can make a maximum of 28/3 mini pies, but since we cannot have a fraction of a mini pie, the greatest number of mini pies she can make is 9.
Step-by-step explanation:
To find the greatest number of mini pies that Nicole can make, we need to find out how many mini pies she can make with 2/3 of the required butter for 14 mini pies. 2/3 of the butter is equal to (2/3) * 14 = 28/3. Since each mini pie requires 1 unit of butter, Nicole can make a maximum of 28/3 mini pies.
However, we cannot have a fraction of a mini pie, so the greatest number of mini pies Nicole can make with the butter she has is 9 mini pies.