September 2018
Problem of the Month

MOD Pizza

Mr. P's favorite pizza place is MOD Pizza, which serves thin crust and lets you choose any toppings that you want for one price.

When Mr. and Mrs. P go to MOD Pizza, Mr. P orders an eleven inch radius pizza and Mrs. P orders the six inch pizza.

They decide to share the pizzas equally, but Mrs. P eats all of her pizza.   What fractional part of Mr. P's pizza should she get so that they each have the same number of square inches of pizza?

Solution to the Problem:

Mrs. P should should eat 7/20 of Mr. P's pizza.

Use the area formula for a circle to determine the areas of each pizza:
Eleven inch pizza:
A = 3.14 x (11)² = 379.94 sq in
Six inch pizza:
A = 3.14 x (6)² =113.04 sq in

The total area of the two pizzas is 492.98 sq in, so each person should receive 246.49 sq in of pizza.   Since Mrs. P ate 113.04 sq in, she should get 133.45 sq in of Mr. P's pizza.

So, the fractional part of Mr. P's pizza would be 133.45 / 379.94 ≈ .3512 ≈ 7/20.

Both Bryce Villanueva and Rob Miles noted that I must be a hearty eater to consume an 11 inch radius pizza!   The 6 inch pizza and the 11 inch pizza that MOD Pizza sells must be DIAMETERS and not radii.   Thank you for catching that error.

Here are the answers using six inch diameter and eleven inch diameter pizzas:

Eleven inch pizza:
A = 3.14 x (5.5)² = 95.03 sq in
Six inch pizza:
A = 3.14 x (3)² =28.27 sq in

The total area of the two pizzas is 123.30 sq in, so each person should receive 61.65 sq in of pizza.   Since Mrs. P ate 28.27 sq in, she should get 33.38 sq in of Mr. P's pizza.

So, the fractional part of Mr. P's pizza would be 33.38 / 95.03 ≈ .3512 ≈ 7/20.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Bryce Villanueva	University of Central Florida, Orlando, Florida
3. Maura Flake	Mountain View High School, Mountain View, Wyoming
4. Kelly Stubblefield	Mobile, Alabama
5. Rob Miles	Northbrook, Illinois
6. Caleb Frazier	Delta High School, Delta, Colorado
7. GAGAN S.	Bangalore, Karnataka, India
8. Carlota Pombar Rodriguez	Mountain View High School, Mountain View, Wyoming
9. Brijesh Dave	Mumbai City, Maharashtra, India
10. Ivy Joseph	Pune, Maharashtra, India
11. Alexis Barajas	Delta High School, Delta, Colorado
12. Travis Harmon	Mountain View High School, Mountain View, Wyoming
13. Alex Thomas	Mountain View High School, Mountain View, Wyoming
14. Katelyn Tims	Mountain View High School, Mountain View, Wyoming
15. Makayla Kortz	Delta High School, Delta, Colorado

Send any comments or questions to: David Pleacher