Abigail orders a large 2 topping pizza for $14 and a medium 1 topping pizza for $10. If all costs of a medium pizza are 80% of a similar large pizza, find the price of a large plain cheese pizza and the cost of each large pizza topping.

Question

retireed · Answer

Okay, kind of confusing to me.  Lots of data and I am having trouble with an equation.

Let's see what we know....

Large 2 top      = 14
Medium 1 top  = 10
Medium X top   = 0.80 Large X top

What is the price of a Large No top?   What is price of a large 1 top?

Correct?

anonymous · Answer

Yes! I am having a problem coming up with an equation.

retireed · Answer

We know a Medium 2 Top will equal 80% of a Large 2 Top...

Medium 2 Top = 0.08 (14) = 11.2   Correct ?

From here if we subtract Medium 2 Top from Medium 1 top we can determine the price of and medium single topping.

anonymous · Answer

Looks right. So what do I subtract from 11.20?

retireed · Answer

Medium 1 topping.

It is given in the question.

anonymous · Answer

Ok so thats 1.20 per topping! So that helps us find the cost of a medium topping. So to find the cost of a large I would have to subtract 0.80?

retireed · Answer

Correct, $1.20 is the cost of a medium topping.

I am confused as to how you came up subtracting $0.80 to find the cost of a large, since the cost of a large topping would be greater than $1.20. Can you clarify your reasoning?

anonymous · Answer

Sorry I mean adding. So the price of a large topping would be 2.00 and the cost of a large cheese pizza would be $10?

retireed · Answer

I'm checking your math.  

How did you get $2 for the cost of a large topping?  

I'm getting something else, but I could be wrong.

anonymous · Answer

If a medium topping is 1.20, a medium topping is .80 of a large topping so a large topping would be $2?

retireed · Answer

Okay, great that is the same reasoning I used, but I think our math is incorrect.

This is what I did and see if you agree....

        MT1 is 1 medium topping    LT1 is one large topping

     MT1 = 0.8 LT1      the original ratio of medium to large and we know MT1 is $1.20

So   LT1 =  MT1 / 0.8      = 1.2 / 0.8  ????

What do you get ?

retireed · Answer

Here is a quasi equation form of my reasoning

L2 =14                 cost of a large 2 topping pizza
M1=10                 cost of a medium 1 topping pizza

M = 0.8L              ratio between medium and large

0.8L2 -M1 = MT1     cost of one medium topping

MT1  =  0.8 LT1      going back to the original ratio

MT1 / 0.8  = LT1     cost of one large topping

LT1 is a critical value if you know the cost of a large topping you should be able to find the price or cost of a L1 and a large no topping cheese pizza