document.write( "Question 363416: An amount of 40% acid solution is to be mixed wih enough 10% acid solution to make 25% acid solution. If there are to be 2o liters of the final mixture, how much of each solution should be mixed together? \n" ); document.write( "

Algebra.Com's Answer #259118 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = liters of 40% solution needed
\n" ); document.write( "Let $\"b\"$ = liters of 10% solution needed
\n" ); document.write( "given:
\n" ); document.write( " $\".4a\"$ = liters of alcohol in 40% solution
\n" ); document.write( " $\".1b\"$ = liters of alcohol in 10% solution
\n" ); document.write( " $\".25%2A2+=+.5\"$ = liters of alcohol in final solution
\n" ); document.write( "--------------------
\n" ); document.write( "(1) $\"%28.4a+%2B+.1b%29%2F2+=+.25\"$
\n" ); document.write( "(2) $\"a+%2B+b+=+2\"$
\n" ); document.write( "from (1)
\n" ); document.write( "(1) $\".4a+%2B+.1b+=+.5\"$
\n" ); document.write( "(1) $\"4a+%2B+b+=+5\"$
\n" ); document.write( "Subtract (2) from (1)
\n" ); document.write( " $\"4a+%2B+b+=+5\"$
\n" ); document.write( " $\"-a+-+b+=+-2\"$
\n" ); document.write( " $\"3a+=+3\"$
\n" ); document.write( " $\"a+=+1\"$
\n" ); document.write( "and
\n" ); document.write( " $\"a+%2B+b+=+2\"$
\n" ); document.write( " $\"1+%2B+b+=2\"$
\n" ); document.write( " $\"b+=+1\"$
\n" ); document.write( "1 liter of 40% solution and 1 liter of 10% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"%28.4a+%2B+.1b%29%2F2+=+.25\"$
\n" ); document.write( "(1) $\"%28.4%2A1+%2B+.1%2A1%29%2F2+=+.25\"$
\n" ); document.write( " $\".5%2F2+=+.25\"$
\n" ); document.write( " $\".5+=+.5\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );