Question

Paolo’s Pizza Pricing

Answer 1

The area of the pizza is πr² or in terms of the diameter,

A =  π(d/2)² = (π/4)d²

All our diameters are multiples of three, d=3k, so A=(9π/4)k²

The 9π/4 is just a constant, it won't affect the relative value.  

We can say little a is the amount of pizza in some units, such that

a = k²

We want to compare unit costs, cost per amount for the three pies, lower ratio means better value.   Let's call p the price of a pie in cents.

u = cents/values = p/k²

9 inch, k=3, p=1050, u=1050/3² = 116.666... cents per unit

12 inch, k=4, p=1500, u=1500/4² = 93.75  cents per unit

18 inch, k=6, p=1900, u=1900/6² = 52.777...  cents per unit

Clearly the 18 inch pizza is the best value.

Answer: 18-inch round pizza