document.write( "Question 529855: A 25% and a 40% salt solution are combined to make 10 gallons of 35% salt solution. How much of each strength solution is required? \n" ); document.write( "

Algebra.Com's Answer #349773 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = gallons of 25% solution needed
\n" ); document.write( "Let $\"b\"$ = gallons of 40% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( " $\"+%28+.25a+%2B+.4b+%29+%2F+10+=+.35+\"$
\n" ); document.write( " $\"+.25a+%2B+.4b+=+3.5+\"$
\n" ); document.write( "(2) $\"+25a+%2B+40b+=+350+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+25+\"$ ,
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+25a+%2B+40b+=+350+\"$
\n" ); document.write( "(1) $\"+-25a+-+25b+=+-250+\"$
\n" ); document.write( " $\"+15b+=+100+\"$
\n" ); document.write( " $\"+b+=+6.667+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(1) $\"+a+%2B+6.667+=+10+\"$
\n" ); document.write( "(1) $\"+b+=+3.333+\"$
\n" ); document.write( "3.333 gallons of 25% solution are needed
\n" ); document.write( "6.666 gallons of 40% solution are needed
\n" ); document.write( "check:
\n" ); document.write( " $\"+%28+.25%2A3.333+%2B+.4%2A6.666+%29+%2F+10+=+.35+\"$
\n" ); document.write( " $\"+%28.8333+%2B+2.666%29+%2F+10+=+.35+\"$
\n" ); document.write( " $\"+3.4999+=+3.5+\"$
\n" ); document.write( "close enough
\n" ); document.write( "OK \n" ); document.write( "

\n" );