document.write( "Question 1133016: You are a chemist and you have a supply of a brine solution that is 40% salt and a brine that is 20% salt. You are performing a experiment that requires you to have 12 liters of a 25% brine solution. How much of the 40% solution and 20% solution do you need to add together to get the required solution? \n" ); document.write( "

Algebra.Com's Answer #750199 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Most people who write math problems are not chemists... so let's treat this as a mixture problem and ignore the fact that the stated concentrations are physically impossible.

\n" ); document.write( "Here is the easiest way to solve a \"mixture\" problem like this involving two ingredients....

\n" ); document.write( "(1) The desired concentration, 25%, is 1/4 of the way from 20% to 40%. (25-20 = 5; 40-20 = 20; 5/20 = 1/4)

\n" ); document.write( "(2) That means 1/4 of the mixture is the 40% solution; 1/4 of 12 liters is 3 liters.

\n" ); document.write( "ANSWER: 9 liters of the 20% solution and 3 liters of the 40% solution.

\n" ); document.write( "For comparison, here is the traditional algebraic approach, using an equation that says the amount of salt in the two ingredients has to be equal to the amount in the mixture:

\n" ); document.write( " $\".20%28x%29%2B.40%2812-x%29+=+.25%2812%29\"$
\n" ); document.write( " $\"20%28x%29+%2B+40%2812-x%29+=+25%2812%29\"$
\n" ); document.write( " $\"20x%2B480-40x+=+300\"$
\n" ); document.write( " $\"180+=+20x\"$
\n" ); document.write( " $\"x+=+9\"$

\n" ); document.write( "So x = 9 liters of 20% and (12-x) = 3 liters of 40%.

\n" ); document.write( "The first method gets you to the answer faster and with far less work than the second.... \n" ); document.write( "

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