Math : Which pizza offer is the better deal?

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Dominos offers 2 12" medium pizzas with one topping for $12.98

The large is $7.99 for a 14" large one topping.

Which is the better value (i.e. price per inch)? Is two 12" pizza the same as one 24" pizza?

It seems the answer is 2 medium.

Yes the unit price [inch] is slightly more expensive with the 14" pizza.
However, the topping coverage may vary between deals so it's not worth worrying about.

2 x 12" pizzas is equal to 1 x 17" pizza in area, but ften it depends on hhow hungry you are to which is really good value. 1 x 12" might be the best value if you end up wasting some!

It also depends on how much of it you will eat. It doesn't do much good to buy quantity for the cheaper prices if you don't use that extra quantity.

In my case, the $7.99 would be the better deal. I don't eat cheese and so I would throw it away. Might as well get nothing for $7.99 instead of getting nothing for $12.98

Well if 2 x 12" = 1 x 17" is correct, than the $7.99 14" pizza is clearly the better value I believe.

$7.99 14" at the same rate for a 17" would come to $9.70



Someone correct my math if incorrect.

Would a person asking for an addition topping be charged twice for the 2 pizzas?

No.

I can order pizza online for my local shop.
If I use the 'Construct your Own" I get charged £16-99 for a 14" plus 2 toppings but I have found I can cheat the programme [and I can't remember how I do it] and get the same pizza for just £9-99.

I hope they don't read this.

It's time to do the math.

One question, though. Is the 12" and 14" the radius or the diameter? Having never bought a pizza, I'm not sure. I'm assuming it is the diameter.

If so, then 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 $12.98 for two 12 inch pizzas, that is $6.49 for each 12 inch pizza and the 14 inch pizza is $7.98.

The 14 inch pizza costs $1.49 more than the 12 inch pizza, or 1.23 times as much.

Thus, with the 14 inch pizza, you get 1.36 times as much food for 1.23 times the price of the single 12 inch pizza price.

This assumes that the pizza diameters are accurate and that the outside crust without toppings is minimal. Not knowing much about pizzas, I did a google search for pictures of pizzas. From what I can see, some pizzas do have a fairly wide rim around them and some other pizzas don't have much of a rim but the toppings stop as much as an inch from the edge.

So if you assume that the non rim diameters of the pizzas are 12" and 10", then you get an area of 36 π square inches of prime pizza (if there is such a thing) for the 14 inch pizza and 25 π square inches of prime pizza for the 12 inch pizza. This means that the 14 inch pizza would have 1.44 times as much food rather than 1.36 times as much food as the 12 inch pizza but would still only cost 1.23 times as much. To be the same, the 14 inch pizza would have to cost 1.44 * $6.49 = $9.35 instead of $7.99.

So assuming a one inch toping free rim around the pizzas, buying the 12 inch pizzas would cost the same per unit area of topping as paying $9.35 for the 14 inch pizza.

(Note: I did this quickly and may have made one or more mistakes in the calculations. I'd check my arithmetic, but I have to go buy some Christmas gifts for my nephews and nieces kids.)

The answer is correct, but with pizza it is on area, so it on the radius squared (7^2/8.5^2=0.678). This gives a price of 11.78. Not adding much to the conversation, but the maths geek in me thought he'd put the full explanation in.

I should add I concur with Eric, showing you can get the same conclusion looking at a problem from a totally different angle. Isn't maths fun!! !

Not really math related, but whenever I get fast food, I get like 5 dollar menu sandwiches and water instead of a combo meal.

Pizzas of the same style dont get thicker with the size grade. So you dont have to worry about the third dimension of volume, so its about inches squared.

The actual area would pi times the radius squared, but for simplicity's sake lets pretend that pizzas are square (the ratios between the sizes would be the same for pizzas of the same geometric shape).

So the medium,or 12 inch, would be 12 squared.
if they are offering two for 12.98. So that would be two times 144 (288) over 12.98. Which would be four and half cents per square inch for the pair of mediums.

The large, or 14 inch, would be 196 over 799.

About four cents a square inch.

So the single large is the better deal than two mediums. Four is slightly cheaper than four and half!

Actually, I was using the square of the radius multiplied by π. Of course, since I was looking at ratios, the value of π was be factored out.

I was comparing the 14 inch pizza to a single 12 inch pizza. The 12 inch pizza is more expensive per square inch than the 14 inch pizza. Thus, the 14 inch pizza is the better price.

Is pizza measured by diameter or radius?

Like I said, I don't eat cheese at all and have never eaten a pizza. My math above assumed that the 12 inch pizza has a diameter of 12 inches rather than a radius of 12 inches and likewize for the 14 inch pizza.

yikes some smart mathematicians here....and this is simple stuff to you guys...anyway if im eating alone, a large is a better deal, if im eating with my dad (2 6'2 210 plus guys) a medium for each of us for slightly more money wins. I also dont understand how 2 mediums equals 17?

It doesn't equal exactly, but it is reasonably close.

Assuming that the 12 and 17 are the diameters, than the area of a 12 inch pizza is 6*6*π or 36 π. Two of them will have an are of 72 π. For a 17 inch pizza, the area is 8.5*8.5*π or 72.25 π. Thus, they are within π/4 square inches of each other.

If the 12 and 17 are the radii, then the area of a 12 inch pizza is 12*12*π or 144 π and two 12 inch pizzas will have a total area of 288 π. A 17 inch pizza is 17*17*π or 289 π.
Thus, they are within π square inches of each other.