how to find cost of a rectangle with a depth of 3 inches at $29 per cubic yard

Question

A gardener has a rose garden that measures 30 by 20 feet. He wants to put a uniform border of pine bark around the outside of the garden.Write an equation for the cost, C, in dollars as a function of the width x, of the border in feet. Assume again that the border is to be covered to a depth of 3 inches and that pine bark costs $29.

Answer 1

area av holw rektangel=20ft * 30 ft=600 ft

if kuver all av it, vol=(1/4)ft*600=150 ft^3

=150/27=5.5555yd^3

at 29$ per kubik yard=161.11$

##### put bark chips in area around the edjes...

size av inside rektangel=(20-2x)*(30-2x), x=how wide the band av bark

bark area=600-(20-2x)*(30-2x)=600-[600-60x-40x+4x^2]

bark area=100x-4x^2

volume=(1/4)*area=25x-x*x (kubik ft)

or(25x-x*x)/27 kubik yard

kost=29$ per kubik yard=(29/27)*(25x -x*x)...x=path wide in ft