document.write( "Question 1030124: How many ounces of a 17% alcohol solution and a 40% alcohol solution must be combined to obtain 46 ounces of a 32% solution? \n" ); document.write( "

Algebra.Com's Answer #645037 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ounces of 17% alcohol solution needed
\n" ); document.write( "Let $\"+b+\"$ = ounces of 40% alcohol solution needed
\n" ); document.write( "---------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+46+\"$
\n" ); document.write( "(2) $\"+%28+.17a+%2B+.4b+%29+%2F+46+=+.32+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+.17a+%2B+.4b+=+14.72+\"$
\n" ); document.write( "(2) $\"+17a+%2B+40b+=+1472+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+17+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+17a+%2B+40b+=+1472+\"$
\n" ); document.write( "(1) $\"+-17a+-+17b+=+-782+\"$
\n" ); document.write( "------------------------
\n" ); document.write( " $\"+23b+=+690+\"$
\n" ); document.write( " $\"+b+=+30+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+30+=+46+\"$
\n" ); document.write( "(1) $\"+a+=+16+\"$
\n" ); document.write( "16 ounces of 17% alcohol solution are needed
\n" ); document.write( "30 ounces of 40% alcohol solution are needed
\n" ); document.write( "----------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.17a+%2B+.4b+%29+%2F+46+=+.32+\"$
\n" ); document.write( "(2) $\"+%28+.17%2A16+%2B+.4%2A30+%29+%2F+46+=+.32+\"$
\n" ); document.write( "(2) $\"+%28+2.72+%2B+12+%29+%2F+46+=+.32+\"$
\n" ); document.write( "(2) $\"+14.72+=+.32%2A46+\"$
\n" ); document.write( "(2) $\"+14.72+=+14.72+\"$
\n" ); document.write( "OK \n" ); document.write( "

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