document.write( "Question 871590: How many ounces of a 31% alcohol solution and a 41% alcohol solution must be combined to form 40 ounces of a 40% alcohol solution? \n" ); document.write( "

Algebra.Com's Answer #525636 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ounces of 31% solution needed
\n" ); document.write( "Let $\"+b+\"$ = ounces of 41% solution needed
\n" ); document.write( "--------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b=+40+\"$
\n" ); document.write( "(2) $\"+%28+.31a+%2B+.41b+%29+%2F+40++=+.4+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "(2) $\"+.31a+%2B+.41b+=+16+\"$
\n" ); document.write( "(2) $\"+31a+%2B+41b+=+1600+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+31+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+31a+%2B+41b+=+1600+\"$
\n" ); document.write( "(1) $\"+-31a+-+31b+=+-1240+\"$
\n" ); document.write( " $\"+10b+=+360+\"$
\n" ); document.write( " $\"+b+=+36+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b=+40+\"$
\n" ); document.write( "(1) $\"+a+=+4+\"$
\n" ); document.write( "----------------
\n" ); document.write( "4 ounces of 31% solution are needed
\n" ); document.write( "36 ounces of 41% solution are needed
\n" ); document.write( "---------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.31a+%2B+.41b+%29+%2F+40++=+.4+\"$
\n" ); document.write( "(2) $\"+%28+.31%2A4+%2B+.41%2A36+%29+%2F+40++=+.4+\"$
\n" ); document.write( "(2) $\"+%28+1.24+%2B+14.76+%29+%2F+40+=+.4+\"$
\n" ); document.write( "(2) $\"+16%2F40+=+.4+\"$
\n" ); document.write( "(2) $\"+16+=+16+\"$
\n" ); document.write( "OK
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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