Modeling With a Power Function...?

Question

The number of pepperoni slices that Kim puts on a pizza varies directly as the square of the diameter of the pizza. If she puts 15 slices on a 10 inch diameter pizza, how many slices should she put on a 16 inch diameter pizza?

Answer 1

Hi Bon, let x represent the number of slices of pepperoni Kim puts on the 16 inch pizza. Set up a proportion to represent the 10 inch pizza and the 16 inch pizza.

 

Proportion:

 

15 / 10² = x / 16²

 

Cross multiply:

 

10² * x = 15 * 16²

 

100x = 15 * 256

 

100x = 3840

 

Divide both sides by 100:

 

x = 38.4

 

Since we normally use whole slices of pepperoni, round the number of slices up to 39.

 

Check:

 

10² is about 2.5 times smaller than 16².

 

If we multiply the number of slices Kim puts on a 10 inch pizza by 2.5 we get about 38 slices. Therefore, our answer is valid.

 

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