document.write( "Question 214085: Some 5% alcohol Solution is mixed with another 20% alcohol solution to get a mixture of 25 liters of 14% solution. Find the amount of each alcohol solution before mixing. \n" ); document.write( "

Algebra.Com's Answer #161698 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = liters of 5% solution
\n" ); document.write( "Let $\"b\"$ = liters of 20% solution
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+%2B+b+=+25\"$
\n" ); document.write( "Alcohol in 5% solution = $\".05a\"$
\n" ); document.write( "Alcohol in 20% solution = $\".2b\"$
\n" ); document.write( "-------------------------------------
\n" ); document.write( " $\"%28.05a+%2B+.2b%29%2F25+=+.14\"$
\n" ); document.write( " $\".05a+%2B+.2b+=+3.5\"$
\n" ); document.write( "(2) $\"5a+%2B+20b+=+350\"$
\n" ); document.write( "Multiply both sides of (1) by $\"5\"$ and subtract from (2)
\n" ); document.write( "(2) $\"5a+%2B+20b+=+350\"$
\n" ); document.write( "(1) $\"-5a+-+5b+=+-125\"$
\n" ); document.write( " $\"15b+=+225\"$
\n" ); document.write( " $\"b+=+15\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"a+%2B+b+=+25\"$
\n" ); document.write( " $\"a+%2B+15+=+25\"$
\n" ); document.write( " $\"a+=+10\"$
\n" ); document.write( "15 liters of 5% solution and 10 liters of 20% solution are needed
\n" ); document.write( "check:
\n" ); document.write( " $\".05a+%2B+.2b+=+3.5\"$
\n" ); document.write( " $\".05%2A10+%2B+.2%2A15+=+3.5\"$
\n" ); document.write( " $\".5+%2B+3+=+3.5\"$
\n" ); document.write( " $\"3.5+=+3.5\"$
\n" ); document.write( "OK \n" ); document.write( "

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