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#1 2013-01-20 22:39:12

kjames
Guest

mixture problem

How much copper and how much magnesium should be added to 200 lbs of an alloy containing 20% copper and 40% magnesium to produce an alloy containing 24%copper and 50% magnesium?

#2 2013-01-20 23:38:33

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,848

Re: mixture problem

Hi kjames,

Sorry, but I'm tied up doing something else for quite a while, and so I can only give a quick answer that isn't exact (it's a decimal approximation), and as I got it with Excel's Goal Seek I can't give the method you probably want, either.

Here's what I got:
Copper: add 33.846153846154 lbs
Magnesium: add 73.846153846154 lbs


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#3 2013-01-20 23:47:42

kjames
Guest

Re: mixture problem

Thanks for giving time in answering my question but can somebody else show me the solution so that I can learn how to do it..thank you!

#4 2013-01-21 00:47:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,730

Re: mixture problem

Hi;

Let c be the amount of copper to be added and m the amount of magnesium to be added

c = 440 / 13, m = 960 / 13


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2013-01-21 11:37:23

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,848

Re: mixture problem

Hi,

Nice and compact, Bobby! smile I didn't think of going that way.

This is how I've done it:

Initially...
Copper      =  20% of 200 lbs  =   40 lbs
Magnesium =  40% of 200 lbs  =   80 lbs
Other         =  40% of 200 lbs  =   80 lbs
Totals        = 100%                 = 200 lbs

When added...
Copper        =   24% of x lbs
Magnesium  =   40% of x lbs
Other          =   26% of x lbs, ∴ x = 80/26% lbs
Total           = 100%

Copper added      = 24% of x = (24*80/26)-40 lbs = (960/13)-40   = 440/13
Magnesium added = 50% of x = (50*80/26)-80 lbs = (2000/13)-80 = 960/13


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#6 2013-01-21 11:49:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,730

Re: mixture problem

Hi;

There are many ways to solve a problem. That should be enough to make the OP happy!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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