document.write( "Question 444701: how many gallons of a 5% salt solution must be mixed with 40 gallons of a 9% solution to obtain a 7% solution? \n" ); document.write( "

Algebra.Com's Answer #306478 by oberobic(2304) $\"\"$ $\"About$

You can put this solution on YOUR website!
The key to solution/mixture problems is to figure out how much \"pure\" stuff you need.
\n" ); document.write( "x = unknown gallons of 5% salt solution that you can add
\n" ); document.write( "40 = gallons of 9% salt solution you started with
\n" ); document.write( "40+x = gallons of 7% salt solution that is the final result
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\n" ); document.write( ".07(40+x) = .05x + .09(40)
\n" ); document.write( "Multiply through by 100 to get rid of decimals.
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\n" ); document.write( "7(40+x) = 5x + 9(40)
\n" ); document.write( "280 +7x = 5x +360
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\n" ); document.write( "Subtract 5x from both sides.
\n" ); document.write( "280 +2x = 360
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\n" ); document.write( "Subtract 280 from both sides.
\n" ); document.write( "2x = 80
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\n" ); document.write( "Divide both sides by 2
\n" ); document.write( "x = 40
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\n" ); document.write( "Hmmm. That suggests 40 gallons of 5% solution added to 40 gallons of 9% solution will produce 80 gallons of 7% solution.
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\n" ); document.write( "Always check your answer.
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\n" ); document.write( "80*.07 = 5.6 gallons of salt
\n" ); document.write( "40*.05 = 2.0 gallons of salt
\n" ); document.write( "40*.09 = 3.6 gallons of salt
\n" ); document.write( "5.6 = 2.0 + 3.6
\n" ); document.write( "Checks.
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\n" ); document.write( "Answer: Add 40 gallons of 5% solution to 40 gallons of 9% solution to obtain a 7% solution. \n" ); document.write( "

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