document.write( "Question 752248: How many gallons of a 3.6% salt solution must be mixed with a 7% salt solution to obtain 25 gallons of a 4.5% salt solution \n" ); document.write( "

Algebra.Com's Answer #457649 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = gallons of 3.6% solution needed
\n" ); document.write( "Let $\"+b+\"$ = gallons of 7% solution needed
\n" ); document.write( " $\"+.036a+\"$ = gallons of salt in 3.6% solution
\n" ); document.write( " $\"+.07b+\"$ = gallons of salt in 7% solution
\n" ); document.write( "------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+25+\"$
\n" ); document.write( "(2) $\"+%28+.036a+%2B+.07b+%29+%2F+25+=+.045+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( "(2) $\"+%28+36a+%2B+70b+%29+%2F+25+=+45+\"$
\n" ); document.write( "(2) $\"+36a+%2B+70b+=+1125+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+36+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+36a+%2B+70b+=+1125+\"$
\n" ); document.write( "(1) $\"+-36a+-+36b+=+-900+\"$
\n" ); document.write( " $\"+34b+=+225+\"$
\n" ); document.write( " $\"+b+=+6.618+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+=+25+\"$
\n" ); document.write( "(1) $\"+a+=+18.382+\"$
\n" ); document.write( "18.382 gallons of 3.6% solution are needed
\n" ); document.write( "6.618 gallons of 7% solution are needed
\n" ); document.write( "-----------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.036a+%2B+.07b+%29+%2F+25+=+.045+\"$
\n" ); document.write( "(2) $\"+%28+.036%2A18.382+%2B+.07%2A6.618+%29+%2F+25+=+.045+\"$
\n" ); document.write( "(2) $\"+%28+.6618+%2B+.4633+%29+%2F+25+=+.045+\"$
\n" ); document.write( "(2) $\"+1.1251+=+.045%2A25+\"$
\n" ); document.write( "(2) $\"+1.1251+=+1.125+\"$
\n" ); document.write( "close enough
\n" ); document.write( " \n" ); document.write( "

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