To determine how many cakes to order for a party that could have as few as 50 people and as many as 100 people, we first need to define how many people each cake can serve. This information wasn't provided, so for illustrative purposes, let's assume each cake serves 12 people.
To find out how many cakes are needed for 50 and 100 people, we can calculate as follows:
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For 50 people: \[ \text{Number of cakes} = \frac{50}{12} \approx 4.17 \] Since you cannot order a fraction of a cake, you would need to round up to 5 cakes.
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For 100 people: \[ \text{Number of cakes} = \frac{100}{12} \approx 8.33 \] Again, rounding up, you would need 9 cakes.
Thus, depending on the number of attendees, you would need to order between 5 and 9 cakes.
If you'd like me to consider a different number of servings per cake or if there's additional context for using pi, please let me know!