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House, Yard and Topsoil

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A neighbor has a lawn that isn't looking very good. The picture below shows an overhead image of his house and yard.

He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this.
Here is some of the information you need:
• He's redoing the whole yard.
• What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
• How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
• How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
• How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
• How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
• What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
• What is the current gas cost?
Assume it's $3.79/gallon.

Using this information, figure out whether my neighbor will save money by picking up the soil himself.
Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery?

1. Measure the yard area.

2. Measure the area where soil is not needed.

3. How many cubic feet of soil is needed?

4. How many dump truck trips are needed?

5. Total cost of delivered soil:

6. How many trips will be needed?

7. How many cubic feet can the pickup truck hold?

8. Total cost of using the pickup truck:

9. What other factors need to be considered? List at least 3.

10. Discuss in at least 3 sentences the best choice for getting topsoil. Discuss what "best" in this case means.

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Solution Summary

Step-by-step calculations are shown for the problems. An image showing the measurements used for the calculations is provided.

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#1
Please refer to the file attached for the measurements for each calculation.
The scale provided has been used to measure the distances shown.

Bottom length of yard (ending at the tree in the lower right corner) = 102 ft
Side length of yard = 72 ft
Area of entire plot = 102 ft * 72 ft = 7344 sq ft

Bottom length of house = 39 ft
Left side length of house (that is protruding) = 24 ft
Area of bottom part of house = 39 ft * 24 ft = 936 sq ft

Top length of house = 27 ft
Left side length of house (that is not protruding) = 27 ft
Area of top part of house = 27 ft* 27 ft = 729 sq ft

Area of driveway = 30 ft * 21 ft = 630 sq ft

Yard area = Area of entire plot - Area of bottom part of house - Area of top part of house - Area of driveway
= (7344 - 936 - 729 - 630) sq ft
= 5049 sq ft

#2
I assume #2 is asking us to measure the area of the yard where soil is not needed. Although the instructions say he's redoing the whole yard, some areas of the yard appear not to need soil.

Soil is not needed at the trunk and roots of the big tree in the top right corner of the yard. I will assume the trunk and roots of the tree occupy a circular area that is 3 ft in radius.
Area of roots of big tree = pi * (3 ft)^2 = 28 sq ft

There is a square box on the bottom right corner of the yard. I assume that the box will not need soil. The box measures 10 ft by 10 ft
Area of ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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