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Clint's Cowboy Shop buys horse feed for $10  per cubic meter (\(m^3\) ). Clint's customers don't like the metric system, so they'll only buy horse feed by the cubic foot. How many cents should Clint charge for a cubic foot (\(ft^3\)) in order to double his money? (Assume 1 meter equals 3.28 feet and answer as a whole number of cents.)

tertre  Oct 10, 2017
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 #2
avatar+91235 
+1

Hi Tertre, 

 

Clint's Cowboy Shop buys horse feed for $10  per cubic meter ( ). Clint's customers don't like the metric system, so they'll only buy horse feed by the cubic foot. How many cents should Clint charge for a cubic foot () in order to double his money? (Assume 1 meter equals 3.28 feet and answer as a whole number of cents.)

 

if 1 metre = 3.28 feet then    1 metre cubed = 3.28^3  cubed feet

 

\(\frac{10 dollars }{1\not{m^3}}\times \frac{1\not{m^3}}{3.28^3feet^3}=\frac{10}{3.28^3}\;\frac{dollars}{feet^3}\\ =28c/cubic foot\)

 

It is actually a little more than that so he might get a good deal :)

 

See how I have used the units to help me?  Units can be cancelled out just like numbers can be.

In this case I cancelled out so the m^3 cancelled out.

 

----------------------

There is another way of looking at it that I probably should have showed you first.

Many people do not understand the full implications of what division means.

In this case you want  to convert dollars per metre to dollars per square foot.

 

You know is its $10 per cubic metre so it Must be $10 per 3.28^3 cubic feet.

per is divide!  It is just a division.

 

Or to put it another way.

If $10 is divided into 3.28^3 bits, how big is each bit?

10 divided by 3.28^3

Melody  Oct 10, 2017
 #3
avatar+79827 
+2

Well....doubling his money would have the same effect as charging $20 per cubic meter

 

So  a cubic meter =  [3.28 ft ]^3  ≈ 35.29 cubic feet

 

So.....   price [ in cents] / 35.29  cubic feet  =

 

2000 / 35.29  ≈  57 cents per cubic foot

 

 

cool cool cool

CPhill  Oct 10, 2017
 #4
avatar+91235 
+1

Thanks Chris,

Silly me, I did not see the doubling his money bit of the question!

Of course my answer has to be doubled to get that profit! 

Melody  Oct 11, 2017

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