Question

Brian is creating a collage on a piece of cardboard that has an area of 120r3 square centimeters. The collage is covered entirely by pieces of paper that do not overlap. Each piece has an area of the square root of r to the fifth power square centimeters. Use the given information to determine an expression for the total number of pieces of paper used.

Answer 1

This is a floor tile problem where the area of the floor and the area of the tiles have really weird representations.

To find out how many tiles, divide the area of the floor by the area of the tile.

Let area of tile be a = sqrt(r^5).

Let area of cardboard be A = 120r^3.

A/a = (120r^3)/sqrt(r^5)

Now to resolve those powers of r.

1/sqrt(r^5) = r^(- 5/2)

A/a = 120(r^3)r^(- 5/2)

A/a = 120r^(3 - 5/2)

A/a = 120r^(1/2)

A/a = 120sqrt(r)