document.write( "Question 1092040: 40 liters of a 50% salt solution are reduced to a 40% salt solution. How much of salt solution must be drained off and replaced with distilled water so that the resulting solution contains only 40% solution? \n" ); document.write( "
Algebra.Com's Answer #706543 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!

First a traditional algebraic solution; and then I will show you the unorthodox method I use to solve mixture problems. If you understand my method, it will get you to the answer much faster and with far less work.

\n" ); document.write( "You are draining x liters of the 50% salt solution and replacing it with distilled water (0% salt) to obtain 40 liters of 40% salt solution. Don't get confused with the \"draining and replacing\"; in the end you are simply mixing two ingredients.

\n" ); document.write( " let x = liters of distilled water (0% salt)
\n" ); document.write( " then 40-x = liters of 50% salt solution

\n" ); document.write( "You want the 40 liters you end up with to be 40% salt. Equating the amounts of salt in the two ingredients to the amount in the final mixture gives you the algebraic equation:

\n" ); document.write( "\"%280%29x%2B.50%2840-x%29+=+.40%2840%29\"
\n" ); document.write( "\"20-.5x+=+16\"
\n" ); document.write( "\"4+=+.5x\"
\n" ); document.write( "\"x+=+8\"

\n" ); document.write( "You need to drain 8 liters of the 50% salt solution and replace it with distilled water to get 40 liters of 40% salt solution.

\n" ); document.write( "Now my method, based on the ratios in which the two ingredients are mixed.

\n" ); document.write( "The difference between the percentages of salt in the original salt solution and in the desired mixture is 50-40=10; the difference between the percentages of salt in the desired mixture and in the distilled water is 40-0 = 0.

\n" ); document.write( "Those differences of 40 and 10 mean the two ingredients must be mixed in the ratio 40:10, or 4:1. And since 40% is closer to 50% than to 0%, the larger portion must be the 50% salt solution.

\n" ); document.write( "But 40 liters in the ratio 4:1 means 32 liters of one ingredient and 8 of the other.

\n" ); document.write( "So you need 32 liters of the original 50% salt solution and 8 liters of distilled water.

\n" ); document.write( "No equations to solve; just a couple of subtractions and finding a ratio....
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