MA100 Quantitative Reasoning

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:

· Dimensions: Front Yard is 30’x20’, Back Yard is 40’x35’, Side Yard is 5’x40’, House is 20’x40’

· 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?

Detail all your assumptions and calculations, and clearly write out your final conclusions.

Please read the rubric attached to see what is needed to successfully complete this project. SHOW ALL OF YOUR WORK IN DETAIL.

Round answers to 2 decimal places when necessary.

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:

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

8) Discuss in at least 3 sentences the best choice for getting topsoil. Discuss what “best” in this case means.

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