document.write( "Question 1091191: A 50%sulfuric acid solution is to be mixed with a 75% sulfuric acid solution to get 60 liters of a 60% sulfuric acid solution . How many liters of the 50% solution and the 75% solution should be mixed \n" ); document.write( "

Algebra.Com's Answer #705578 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = liters of 50% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 75% solution needed
\n" ); document.write( "----------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+60+\"$
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.75b+%29+%2F+60+=+.6+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( " $\"+.5a+%2B+.75b+=+36+%7D%5D%5D%0D%0A%7B%7B%7B+50a+%2B+75b+=+3600+\"$
\n" ); document.write( "(2) $\"+2a+%2B+3b+=+144+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"2\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+2a+%2B+3b+=+144+\"$
\n" ); document.write( "(1) $\"+-2a+-2b+=+-120+\"$
\n" ); document.write( "------------------------
\n" ); document.write( " $\"+b+=+24+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+24+=+60+\"$
\n" ); document.write( "(1) $\"+a+=+36+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "36 liters of 50% solution are needed
\n" ); document.write( "24 liters of 75% solution are needed
\n" ); document.write( "---------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+.5a+%2B+.75b+=+36+\"$
\n" ); document.write( " $\"+.5%2A36+%2B+.75%2A24+=+36+\"$
\n" ); document.write( " $\"+18+%2B+18+=+36+\"$
\n" ); document.write( " $\"+36+=+36+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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