Math : Which pizza offer is the better deal?

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ahh makes sense ... and very interesting

Diameter.

The radius of a 12 inch is six.

But its simpler to just square the diameter and mulitply by 3/4 because the area of a circle is about 3/4 the area of a square with sides the same as the circle's diameter ( ie a pizza has about 3/4 the area of the box it came in).

Two 12 inches would be 108 times two (216). And the one 14 incher would be 152 abouts.

216 into the two for one medium special price of 12.98 is six cents a square inch.
Dividing the the large price over its area would be: Seven ninety nine over 152 which is roughly 5.2 cents a square inch.

So the one big pizza is the better deal than the two mediums to the tune of six to five point two.

If you look at the ratio of area compared to the ratio of cost, you don't have to approximate the area. Multiply by π and then when you look at the ratio, you have a π in the numerator and denominator and so you just factor it out.

in the case of pizza the area is PIE r squared hehe

That joke was sure hidden in plain sight!

Or maybe plain with toppings.

Last edited by naturalplastic on 25 Dec 2012, 11:10 am, edited 1 time in total.

I gave the wrong price for the two mediums.

It is $11.98.

The pizza looks like this. There is no crust on the edge.



How does that change the answer?

11.98 instead of 12.98 ( basically 12 dollars instead of 13)?

The total price would be one 13th less.

So the price per square inch would also be one thirteenth less.

Instead of six cents- its roughly 5 and a half cents per square inch.

Still a little more than the 5.2 for the one large.

The lack of border would make no difference because presumably both sizes lack a border so the ratio of values would be the same.

Good job there isn't a follow up question of sharing the slices as I've never seen a pizza cut into slices that way. Actually looks quite cool, but gives completely random sizes.

Here's a revision of my earlier answer using the corrected price of $11.98 for two twelve inch pizzas.

-----------------------------------

It's time to do the math.

The 14 inch pizza would have a radius of 7" and a surface area of 49 π square inches. The 12 inch pizza would have a surface area of 36 π square inches. Thus, the 14 inch pizza has a surface area of 49/36 of the 12 inch pizza or 1.36 times as large.

At $11.98 for two 12 inch pizzas, that is $5.99 for each 12 inch pizza and the 14 inch pizza is $7.99.

The 14 inch pizza costs $2.00 more than the 12 inch pizza, or 1.33 times as much.

Thus, with the 14 inch pizza, you get 1.36 times as much food for 1.33 times the price of the single 12 inch pizza price.

If the 14 inch pizza was priced the same per square inch as the two 12 inch pizzas, then the 14 inch pizza would be priced at 1.36 times $5.99, of $8.15, only sixteen cents more.

for the 2 12" pizzas:
3.1415926 * 6(r) ^2 = 113.0973336 square inches for 1x 12" pizza.
113.0973336 square inches * 2(pizzas) =226.1946672 square inches which costs $12.98, so each square inch costs $0.0573842

for the single 14" pizza:
3.1415926 * 7 (r) ^2 = 153.9380374 square inches which costs $7.99, so each square inch costs $0.051904001
2*12--- $0.0573842 /inch^2
1*14--- $0.0519040 /inch^2

0.0573842/0.0519040=1.105583368, so the 2*12 inch pizzas are 10.558% more expensive with respect to their entire surface area.

many people are interested mainly in the area occupied by the "topping" rather than the area of the base crust. if one takes this into account, then it would be necessary to to subtract the area of "untopped" crust, from the total area of the pizza.

an average pizza has topping on it until about 1/2 inch short of it's perimeter.
so, with respect to this fact, it is easy to calculate the area of the topping rather than the entire area of the pizza.

if the topping extends to within 1/2 inch of the edge, then "R" is reduced by 1/2 inch, and so the new calculation is:

2x11" pizzas =pi*5.5^2= 95.03317615 square inches x 2 =190.0663523 square inches for the topped area of the 2x 12" complete pizzas.

that is $0.06829194 per square inch of topping.

the single 14" pizza (with a 13" diameter topping) will be recalculated as 132.7322874
square inches of topping.
that is $0.060196356 per square inch of topping.

therefore the 14" one is better value if one wants a maximum value for the topping.

What you says makes some sense. However, so does eric76's answer.

There is a big difference between the two and I can not understand why.

You are making the assumption of a 1/2 edge without toppings which would apply to both pizzas.

Why such a difference in answers?

Eric76 says a large would be 16 cents more. The way you calculate it, it would be $1.07 more.

Both can't be right. We are talking about a math equation.

Note that he was using the original $12.98 for two 12 inch pizzas. In my latest post, I was using the revised $11.98 for two 12 inch pizzas.

Also, from the picture, there appeared to be very little crust without topping.

That's one terrible looking pizza...why is it cut like that? Why is there no border? Why doesnt it look fresh

who knew there was so much work involved in figuring out which sized pizza was the better value. I would have done price divided by inches and been done with it ha.

That wouldve lead you astray to the wrong answer.

Price divided by inches SQUARED is the way to do it.
Thats the real lesson here - Dorothy!
And there is no place like home!

Basically I and several other said the same thing- you take the square of the two sizes (12 squared and 14 squared) and divide by the price to compare price per square inch. The rest of the thread consists different ways of solving the same problem- reinventing the same wheel over and over. Its not that there is so much work. This is mostly make-work.

Comparing SUBS?
Thats simple linear math- a twelve inch has twice the mass of a six inch because a subs hieght and width remain the same after its cleaved in two.

But when comparing pizzas- you have square the inchage.

incorrect. the pizza's were circular, not square. the area inside a circle = pi *r^2.