Dog Food Mixture

Date: 10/23/2002 at 13:31:10
From: Stacy Brasseaux
Subject: How would I set this up?

How would I set this problem up?

A grocer wishes to mix 6 pounds of Chippy dog food worth $3 per pound 
with Hippy dog food, worth $4 per pound. How much of the Hippy dog 
food should be mixed if the dog food mixture is to sell for $3.20?

Date: 10/23/2002 at 14:38:40
From: Doctor Schwa
Subject: Re: How would I set this up?

Hi Stacy,

My procedure goes something like this:

1. What is known?
We know there are 6 pounds of Chippy, at $3 per pound, so thus $18
spent total. We know Hippy costs $4 per pound. We know the mixture 
sells for $3.20 per pound.

2. What is unknown?
The question asks how much of the Hippy should be mixed. So let h 
stand for the number of pounds of Hippy.

3. How do they relate?
The total cost of the two separate foods equals the total cost of the
combined food.

The cost of Chippy is 6 * 3 dollars.
The cost of Hippy is h * 4 dollars.

What's the cost of the mixture?  (how many pounds) * (3.2 dollars per 
pound)

4. Now you should have an equation you can solve...

5. Check! Does the answer make sense?

You might also find some answers from the Dr. Math archives useful.  I 
found them at http://mathforum.org/mathgrepform.html by searching for 
the keyword mixture. There are other useful ones there too, but I 
didn't want to burden you with too many choices.

   Blending Seed
   http://mathforum.org/library/drmath/view/57266.html 

   Mixing Peanuts and Cashews
   http://mathforum.org/library/drmath/view/57487.html 

   Weighted Averages
   http://mathforum.org/library/drmath/view/57530.html 

   Tea Blend: Price of Inferior Tea
   http://mathforum.org/library/drmath/view/58647.html 

- Doctor Schwa, The Math Forum
  http://mathforum.org/dr.math/