Math CentralQuandaries & Queries


Question from Jean:

Need to know how to feed about 162 people 70 square inches of pizza at the lowest price.

22" Pizza is $9.95
16" Pizza is $5.25
12" Pizza is $2.99

Thanks for your help. Jean

Hi Jean,

I assume that's 70 square inches each so you need 70 × 162 = 11,340 square inches.

The area of a circle of radius r inches is π r2 square inches so the area of a 22 inch diameter pizza is

π r2 = π 112 = 380 square inches.

Hence the 22 inch pizza costs $9.95/380 = $0.026 per square inch or 2.6 cents per square inch.

Determine the area and cost per square inch for the other two sizes.

Start with the size that costs the least per square inch. What is the largest number of these pizzas you can buy and stay below 11,340 square inches? How many square inches remain? Move to the pizza size that is the next least expensive in cents per square inch. How many of these will you need? How many of the most expensive pizza will you now need to complete the order? What is the total cost?

Now go back to the least expensive pizza per square inch. What would be the cost if you purchased one more to complete the entire order with the least expensive per square inch? How does that compare with the total cost in the previous paragraph?

One last option. Buy the largest number of the cheapest pizza per square inch and then complete the order using only the next cheapest pizza? How does the cost compare to the other options?

I hope this helps,

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