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Topic: Systems of Linear Equations
Replies: 6   Last Post: Jan 29, 2011 10:13 PM

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Alexandros Bantis

Posts: 4
Registered: 1/29/11
Re: Systems of Linear Equations
Posted: Jan 29, 2011 10:13 PM
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On 01/28/2011 12:33 PM, mathematicsstudent wrote:
> Hello,
>
> I have to solve this problem:
>
> The manager of a bulk foods establishment sells a trail mix for $8
> per pound and premium cashews for $15 per pound. The manager wishes
> to make a 105-pound trail mix-cashew mixture that will sell for $12
> per pound. How many pounds of each should be used?
>
> I figured out that the first equation should be: X + Y = 105
>
> How do I write the other equation? I tried this, but it didn't work:
> 08x + .15Y = 12
>
> If you can guide me along, I would greatly appreciate it!
>
> Thank you.


There are a couple of questions that have to be answered. First, is how
to express the two variables in terms of a single variable.

Pounds(trailmix) + Pounds(cashews) = 105
Therefore P(cashews) = 105 - P(trailmix)
Thus, we have our two variables:

P = pounds of trailmix
105 - P = pounds of cashews

Next we have to determine the weighted average. The basic formula would
be Average price = $/pounds.

Using dimensional analysis, we can arrive at the weighted average as
follows:

Average Price = ($/lb) / Total Pounds

This is because the 'pounds' cancel each other out, and you are left
with price.

hope this helps,

alex



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