(No trains are involved.)
Which is the better deal:
- 12 six-inch Giordano's Deep Dish Pizzas from Costco for $125?
- Three 10-inch Giordano's Deep Dish Pizzas from Costco for $95?
Hubby and I were faced with this dilemma recently. Notwithstanding there's no way 12 six-inch pizzas would fit in my freezer, we were compelled to figure out which was the better buy. Hence, we set out to conquer the question using math. (And you can, too!)
First, we calculated the total area of the pizzas in inches. The small pizzas were 9π square inches each (area = πr2 where r=3 or half of the diameter of six inches and π =3.14159). Multiply that by 12 pizzas and that's a total of 108π inches. The large pizzas were 25π square inches each x 3 = 75π total square inches.
75π =235.619 (3 large pizzas) $95
108π =339.292 (12 small pizzas) $125
The price of the large pizzas is $0.40 per square inch while the price of the small pizzas is $0.37 per square inch.
Another way to look at it is the total area of the large pizzas is 69.4% of the total square inches of the small pizzas but the price of the large pizzas is 76% of the small pizza price. Either way, that would make the small pizzas the better deal.
But, we only eat half of the large pizza. Half of a large pizza is only 12.5π square inches while a single 6-inch pizza is 9π square inches.
9π =28.274 (1 small pizza)
12.5π =39.27 (1/2 large pizza)
A small pizza is only 72% the size of the amount of pizza we would normally eat. That means, we might need to heat two small pizzas for every half of a large pizza. 12 small pizzas would yield 6 meals at a total of $20.83/meal ($125/6). Three large pizzas would also yield six meals but for a total of $15.83/meal ($95/6). That would make the large pizzas the better deal.
What about the crust to toppings ratio?
The circumference of the pizza (the crust) is calculated as πd where d=the diameter. As discussed before, the pizzas were 6 and 10 inches in diameter. (Their respective radii were 3 and 5.)
Area (the good stuff in the middle) πr2 πrr r
Circumference (crust) πd = π2r = 2
3/2 is the area to circumference ratio of the small pizza while 5/2 is the area to circumference ratio of the large pizza. There's more middle stuff in the larger pizzas while the smaller pizzas have proportionately more crust. Unless you really like a lot of crust, the larger pizza again looks like the better deal.
Ultimately, Costco sold out of all pizzas before we could come up with a solution.
So, if we take a train to Chicago and it leaves at 4 am traveling east at an average rate of 54 miles per hour and the pizzas are shipped to a western destination, where would we have to disembark to eat the pizza?
Just kidding. The best deal right now on Giordano's pizza is from Giordano's Pizza.
But, you have to buy 6 10-inch pizzas for $170 which is ....
