Question

Paolo’s Pizza Pricing

Paolo has just started working at his Uncle Antonio’s pizza parlor. He is trying to figure out which size
meat lover’s pizza provides the best value.
Meat Lover’s Special
9-inch round pizza………………$10.50
12-inch round pizza…….……….$15.00
18-inch round pizza……………..$19.00
Which pizza listed on the menu provides the best value? Write a few sentences
that explain your reasoning

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