Mario Agnello is opening a new pizza shop in town. He plans to offer a twelve-inch diameter pizza and an eighteen-inch diameter pizza. He has set the price of a twelve-inch cheese pizza at eight dollars, based on the amount of ingredients needed to cover that size crust. If Mario would like to keep the pricing proportional, what should he charge for an eighteen-inch cheese pizza?

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Question

Mario Agnello is opening a new pizza shop in town. He plans to offer a twelve-inch diameter pizza and an eighteen-inch diameter pizza. He has set the price of a twelve-inch cheese pizza at eight dollars, based on the amount of ingredients needed to cover that size crust. If Mario would like to keep the pricing proportional, what should he charge for an eighteen-inch cheese pizza? 

Show and explain your solution

e.mccormick · Answer

Do you know how to find the square are of a circle?

anonymous · Answer

No, I really don't understand.

e.mccormick · Answer

Ever seen $\pi r^2$ before?

anonymous · Answer

Yes I have I think it's Pi*Radius* something I just forgot...

e.mccormick · Answer

Yes.  pi times radius times radius or pi r sqared.   That gives you the area of the circle.  Once you know the surface area of both circles you can set up a ratio between them.

anonymous · Answer

That's the part where I get stuck

e.mccormick · Answer

OK, well, first, they say the pizzas are eighteen-inch and twelve-inch in diameter.  So, what is the radius measure of each pizza?

anonymous · Answer

Um... 12 inches?

e.mccormick · Answer

Well, diameter is twice the radius.  So you need to cut those numbers in half.

anonymous · Answer

So 6...

imstuck · Answer

For the pricing to be proportional, as is any linear function, it can be solved with a ratio.
12"/$8=18"/x
cross multiply and solve for x.  That makes the pricing of the 12" pizza be proportional to the pricing of an 18" pizza.  You don't need to do all that stuff with the area.

anonymous · Answer

Oh wow thanks IMStuck you got straight to the point.

e.mccormick · Answer

So @IMStuck , you are saying that a proportional change in linear will cause the "based on the amount of ingredients needed to cover that size crust" to be proportional for a different area?

imstuck · Answer

I am saying that if a 12" cost $8, it would feasibly cost $12 to cover an $18.  Yes, that's what I am saying.

anonymous · Answer

Can you explain?

anonymous · Answer

I will

e.mccormick · Answer

Take a 1 by 1 square.  Say I need 1 thing to cover it because the square area is 1.  Then I double the size, so a 2 by 2 square.  According to you, I would only need 2 things to cover it because it is 2x the linear size.  But the area is 2 by 2 or 4.  So I would not cover it.  That is why IMStuck  is wrong.

imstuck · Answer

If a 12" costs $8, then you set up the ratio like this:|dw:1409003178296:dw|