Question

The Hernandez family ordered one jumbo pizza with a diameter of 20 inches, cut it into 15 equal slices, and had 3 slices left over after dinner. The Mullins family ordered two medium pizzas, each with a diameter of 12 inches, cut them into 8 equal slices each, and had 6 slices left over after dinner. How much pizza did the Mullins family eat as a fraction of the pizza the Hernandez family ate?

Answer 1

Answer: Mullins family eat $\dfrac{9}{20}$ of the pizza the Hernandez family ate.

Step-by-step explanation:

Area of circle = $\pi r^2$ , where r is the radius

Given, Diameter of Hernandez family's pizza = 20 inches

Radius = $\dfrac{20}{2}$ = 10 inches

Area of Hernandez family's pizza  = $\pi (10)^2=100\pi \text{ in.}^2$

Since, they divide pizza into 15 pieces , area of each slice = $\dfrac{100\pi}{15}=\dfrac{20}{3}\pi\text{ in.}^2$

They left with 3 slices i.e. they ate 12 slices, area of all 12 slices = 12 x (area of each slice)

= $12\times\dfrac{20}{3}\pi\text{ in.}^2= 80\pi\text{ in.}^2$

Diameter of Mullins family's pizza = 12 inches

Radius = $\dfrac{12}{2}$ = 6 inches

Area of Mullins family's pizza  = $\pi (12)^2=144\pi \text{ in.}^2$

Since, they divide pizza into 8 pieces , area of each slice = $\dfrac{144\pi}{8}=18\pi\text{ in.}^2$

They left with 6 slices i.e. they ate 2 slices, area of all 2 slices = 2 x (area of each slice)

= $2\times18\pi\text{ in.}^2=36\pi\text{ in.}^2$

Since, $\dfrac{36\pi}{80\pi}=\dfrac{9}{20}$

Hence, Mullins family eat $\dfrac{9}{20}$ of the pizza the Hernandez family ate.