document.write( "Question 344176: A 40% salt solution is to be mixed with a 60% salt solution to obtain 100 gallons of a 45% salt solution. How much of each solution must be used? \n" ); document.write( "

Algebra.Com's Answer #246264 by josmiceli(19441) $\"\"$ $\"About$

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In words:
\n" ); document.write( "(amount of salt in final solution)/(total gallons of final solution)
\n" ); document.write( "=45%
\n" ); document.write( "Let $\"a\"$ = gallons of 40% solution
\n" ); document.write( "Let $\"b\"$ = gallons of 60% solution
\n" ); document.write( "given:
\n" ); document.write( "Amount of salt in 40% solution = $\".4a\"$
\n" ); document.write( "Amount of salt in 60% solution = $\".6b\"$
\n" ); document.write( "(1) $\"a+%2B+b+=+100\"$
\n" ); document.write( "(2) $\"%28.4a+%2B+.6b%29%2F+100+=+.45\"$
\n" ); document.write( "(2) $\".4a+%2B+.6b+=+45\"$
\n" ); document.write( "(2) $\"4a+%2B+6b+=+450\"$
\n" ); document.write( "Multiply both sides of (1) by $\"4\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"4a+%2B+6b+=+450\"$
\n" ); document.write( "(1) $\"-4a+-+4b+=+-400\"$
\n" ); document.write( " $\"2b+=+50\"$
\n" ); document.write( " $\"b+=+25\"$ gallons
\n" ); document.write( "And, from (1)
\n" ); document.write( " $\"a+%2B+b+=+100\"$
\n" ); document.write( " $\"a+%2B+25+=+100\"$
\n" ); document.write( " $\"a+=+75\"$
\n" ); document.write( "75 gallons of 40% solution and 25 gallons of 60% solution must be used
\n" ); document.write( "check answer:
\n" ); document.write( " $\"%28.4a+%2B+.6b%29%2F+100+=+.45\"$
\n" ); document.write( " $\"%28.4%2A75+%2B+.6%2A25%29%2F100+-+.45\"$
\n" ); document.write( " $\"%2830+%2B+15%29%2F100+=+.45\"$
\n" ); document.write( " $\"45%2F100+=+.45\"$
\n" ); document.write( " $\".45+=+.45\"$
\n" ); document.write( "OK \n" ); document.write( "

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