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
`(9)/(20)` of the pizza the Hernandez family ate.

Explanation:

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

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

Radius =
`(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 =
`(100\pi)/(15)=(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*(20)/(3)\pi\text{ in.}^2= 80\pi\text{ in.}^2`

Diameter of Mullins family's pizza = 12 inches

Radius =
`(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 =
`(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*18\pi\text{ in.}^2=36\pi\text{ in.}^2`

Since,
`(36\pi)/(80\pi)=(9)/(20)`

Hence, Mullins family eat
`(9)/(20)` of the pizza the Hernandez family ate.