document.write( "Question 944272: a chemist needs 120 milliliters of a 30% solution but only has only 14% and 38% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. \n" ); document.write( "

Algebra.Com's Answer #575726 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ml of 14% solution needed
\n" ); document.write( "Let $\"+b+\"$ = ml of 38% solution needed
\n" ); document.write( "-------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+120+\"$
\n" ); document.write( "(2) $\"+%28+.14a+%2B+.38b+%29+%2F+120+=+.3+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( "(2) $\"+.14a+%2B+.38b+=+.3%2A120+\"$
\n" ); document.write( "(2) $\"+.14a+%2B+.38b+=+36+\"$
\n" ); document.write( "(2) $\"+14a+%2B+38b+=+3600+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+14+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+14a+%2B+38b+=+3600+\"$
\n" ); document.write( "(1) $\"+-14a+-+14b+=+-1680+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( " $\"+24b+=+1920+\"$
\n" ); document.write( " $\"+b+=+80+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+120+\"$
\n" ); document.write( "(1) $\"+a+=+40+\"$
\n" ); document.write( "40 ml of 14% solution is needed
\n" ); document.write( "80 ml of 38% solution is needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.14%2A40+%2B+.38%2A80+%29+%2F+120+=+.3+\"$
\n" ); document.write( "(2) $\"+%28+5.6+%2B+30.4+%29+%2F+120+=+.3+\"$
\n" ); document.write( "(2) $\"+36+=+.3%2A120+\"$
\n" ); document.write( "(2) $\"+36+=+36+\"$
\n" ); document.write( "OK \n" ); document.write( "

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