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

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Barb Knox

Posts: 577
Registered: 12/6/04
Re: Systems of Linear Equations
Posted: Jan 29, 2011 4:53 PM
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In article
<4d20b9dc-92ad-4525-bcb1-2136548271ca@b8g2000vbi.googlegroups.com>,
The Qurqirish Dragon <qurqirishd@aol.com> wrote:

> On Jan 29, 1:24 am, Barb Knox <s...@sig.below> wrote:
> > In article
> > <1350903580.11101.1296246811610.JavaMail.r...@gallium.mathforum.org>,
> >
> >  mathematicsstudent <mathematicsstud...@hotmail.com> 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?

> >
> > <rant>
> >
> > Yet another wretched attempt to make a mathematics problem seem relevant
> > to the "real world".  In the actual real world, the price a retailer
> > charges for a mixture is NOT determined by the prices charged for the
> > separate ingredients.  In the actual real world, the retailer would be
> > more likely to put in about 20% cashews and charge $11.95 per pound for
> > the New Cashew-Enhanced Trail Mix.
> >
> > The really sad aspect of this is that with a half a minute of thought
> > the problem writer could have come up with a mixture problem that did
> > make sense in the "real world".
> >
> > </rant>
> >

> And similarly the cost of packaging is different, and then you have
> increased cost from buying smaller quantities of the two types before
> mixing, and the shopkeep is greedy, and there is another store across
> the street selling an unknown mixture of these for $11, and...
> I hope you get the point of that. The use of nuts and trail mix is NOT
> to give a real-world example, but rather to make something concrete
> that people who aren't pure math thinkers can hopefully grasp more
> easily.
> Word this problem anyway you want, and I can find something that
> doesn't match the "real world"


I accept your challenge:

Barbara has the job of providing some nibblies for a party, with a
strict budget of $24 for 2 pounds mixed nuts which must include cashews,
since that's the host's favourite. The local bulk food store does have
mixed nuts at $8 per pound (tax inclusive), but these lack cashews.
They also have just cashews at $15 per pound (tax inclusive). What
quantity of each of those two items should she buy in order to make 2
pounds altogether for $24?


> Even if you want to remain reasonable, they don't want to use 3 pages
> in a book for one word problem.


My example is short, and even has a little bit of drama in it.

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| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum videtur.
| BBB aa a r bbb |
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