My Math Forum Mixture Problem

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 April 4th, 2012, 03:39 PM #1 Newbie   Joined: Apr 2012 Posts: 14 Thanks: 0 Mixture Problem What would my equation(s) be to solve this mixture story problem? How much 12% Na2SO4 and pure water must be mixed to produce 22.8 gallons of a mixture that is 7% sodium sulfate? I started with: Let x = the # of gallons of 12% Na2SO4 And Let y = the # of gallons of 100% water or should it be Let 22.8-x = the # of gallons of 100% water needed?
 April 4th, 2012, 03:49 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Mixture Problem I would start by finding the amount in gallons of pure sodium sulfate we need: $0.07\cdot22.8=1.596$ Now we want to find how many gallons x of the 12% mixture contains that amount: $0.12\cdot x=1.596$ $x=13.3$ So, we need 13.3 gallons of the 12% sodium sulfate and 22.8 - 13.3 = 9.5 gallons of water. We could also simply the process somewhat (combine the two steps into one) and state: $0.12x=0.07\cdot22.8$ $x=13.3$ and then the amount of water is 22.8 - 13.3 = 9.5.
April 4th, 2012, 07:38 PM   #3
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Re: Mixture Problem

Hello, Kimmysmiles0!

Quote:
 $\text{How much 12\% Na}_2\text{SO}_4\text{ and pure water must be mixed} \text{to produce 22.8 gallons of a mixture that is 7\% Na}_2\text{SO}_4\,?$

Since we are adding pure water, we will consider the amount of water at each stage.

$\text{W\!e will use }x\text{ gallons of the 12\% solution (which is 88\% water).}
\;\;\;\text{This contains: }\,0.88x\text{ gallons of water.}$

$\text{W\!e will add }22.8\,-\,x\text{ gallons of pure water.}
\;\;\;\text{This contains: }\,22.8\,-\,x\text{ gallons of water.}$

$\text{The mixture will contain: }\,0.88x\,+\,22.8\,-\,x \:=\:22.8\,-\,0.12x\text{ gallons of water. }\;[1]$

$\text{But we know that the mixture will be 22.8 gallons which is 93\% water.}
\;\;\;\text{It contains: }\,(0.93)(22.8)\,=\,21.204\text{ gallons of water. }\;[2]$

$\text{W\!e just described the final amount of water in }two\:ways.$

$\text{There is our equation! }\:\text{ . . . }\:22.8\,-\,0.12x \:=\:21.204$

$\text{Got it?}$

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