Geometry Question?

Question

To landscape her 70ft-by-60ft rectangular backyared, Sam is planning first to put down a 4in. layer of topsoil. She can buy bags of topsoil at $2.50 per 3-ft^3 bag, with free delivery. Or, she can buy bulk topsoil for $22.00/yd^3, plus a $20 delivery fee. Which option is less expensive? Explain.

Answer 1

Best Answer - Chosen by Asker

first figure out how must topsoil you need. Your dimensions are 70ft by 60 ft with a height of 1/3ft.

70 X 60 X 1/3 = 1400 ft^3 approximately

Then you just figure how much it would cost for each method.

You would need 467 3 ft^3 bags which would be $1167.50

1400/3 = 466.666.. X 2.5 = 1167.50

For the second price you must convert to yards^3.

1 foot cubed = 0.037037037 yards cubed so

1400 x 0.037037037 =51.85 yds^3

51.85 X 22 = 1140.74 + $20 delivery fee = $1160.74


Buying in bulk is cheaper it seems.

Asker's Rating:

Asker's Comment:

I knew most of it but I didn't know to convert to yards^3

Answer 2

70 * 60 * 1/3 = 1400 ft³

This would require 1400/3=467 3 ft³ bags for a total price of 467 * 2.50 = $1,167.50.

Or, since a cubic yard = 27 ft³, it would require 1400/27=52 27 ft³ bags for a total price of $1,144 + $20 = $1,164.00, a slightly better deal.

PS: I would like to point out to bigts... that you can't buy fractions of bags, and 4 inches is *exactly* 1/3 of a foot.