document.write( "Question 853076: How many gallons of a 24% saline solution (NaCl) must be mixed with 5 gallons of pure water to make a 9% solution? \n" ); document.write( "

Algebra.Com's Answer #513895 by josgarithmetic(39617) $\"\"$ $\"About$

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The densities may be needed.
\n" ); document.write( "24%, about 1.19 g/ml
\n" ); document.write( "9%, about 1.07 g/ml
\n" ); document.write( "WATER, 1.00 g/ml and 1 gallon = 3.7854 liters\r
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\n" ); document.write( "\n" ); document.write( "5 gallons of water is $\"5%2A3.7854=18.927\"$ liters\r
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\n" ); document.write( "\n" ); document.write( "The question could be restated as , how many liters of 24% w/vol saline must be mixed with 18.927 liters of water to make 9% w/vol. solution?\r
\n" ); document.write( "\n" ); document.write( "Start the solution process assigning variables:
\n" ); document.write( "u = volume liters of the 24% w/vol. saline\r
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\n" ); document.write( "\n" ); document.write( "WRONG--SEE BELOW!___ $\"24%28grams%2F%28100%2Aml%29%29%281000%2Aml%2Fliter%29%2Au%2F%2818.927%2Bu%29=9\"$ -------densities seem not to be needed.\r
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\n" ); document.write( "\n" ); document.write( "Change the result for u back to gallons from the liters.
\n" ); document.write( "-
\n" ); document.write( "The attempt at unit checking was overdone and created confusion. Since densities were not needed, the more typical setup should simply be:
\n" ); document.write( " $\"highlight%28%2824u%29%2F%2818.927%2Bu%29=9%29\"$
\n" ); document.write( "and this will give $\"u=11.356\"$ liters, which converts to 3 gallons.
\n" ); document.write( "RESULT: $\"highlight%283%2Agallons%29\"$ of 24% w/v saline. \n" ); document.write( "

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