document.write( "Question 621351: Dmitri needs 7 liters of a 24% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 28% solution and the other an unlimited supply of of the 14% solution. How many liters of each solution should Dmitri use? \n" ); document.write( "

Algebra.Com's Answer #390694 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = liters of 28% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 14% solution needed
\n" ); document.write( " $\"+.28a+\"$ = liters of sulfuric acid in 28% solution
\n" ); document.write( " $\"+.14b+\"$ = liters of sulfuric acid in 14% solution
\n" ); document.write( "-------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+7+\"$
\n" ); document.write( "(2) $\"+%28+.28a+%2B+.14b+%29+%2F+7+=+.24+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(2) $\"+.28a+%2B+.14b+=+1.68+\"$
\n" ); document.write( "(2) $\"+28a+%2B+14b+=+168+\"$
\n" ); document.write( "(2) $\"+2a+%2B+b+=+12+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+2a+%2B+b+=+12+\"$
\n" ); document.write( "(1) $\"+-a+-+b+=+-7+\"$
\n" ); document.write( " $\"+a+=+5+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+7+\"$
\n" ); document.write( "(1) $\"+5+%2B+b+=+7+\"$
\n" ); document.write( "(1) $\"+b+=+2+\"$
\n" ); document.write( "5 liters of 28% solution are needed
\n" ); document.write( "2 liters of 14% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.28a+%2B+.14b+%29+%2F+7+=+.24+\"$
\n" ); document.write( "(2) $\"+%28+.28%2A5+%2B+.14%2A2+%29+%2F+7+=+.24+\"$
\n" ); document.write( "(2) $\"+%28+1.4+%2B+.28+%29+%2F+7+=+.24+\"$
\n" ); document.write( "(2) $\"+1.68%2F7+=+.24+\"$
\n" ); document.write( "(2) $\"+1.68+=+1.68+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );