document.write( "Question 705073: i need help with this. A 45% salt solution was mixed with a 75% salt solution to produce 15 kilograms of solution that was 67% salt. how much of each solution was used? \n" ); document.write( "

Algebra.Com's Answer #434406 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = kg of 45% salt solution needed
\n" ); document.write( "Let $\"+b+\"$ = kg of 75% salt solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+15+\"$
\n" ); document.write( "(2) $\"+%28+.45a+%2B+.75b+%29+%2F+15+=+.67+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "(2) $\"+.45a+%2B+.75b+=+.67%2A15+\"$
\n" ); document.write( "(2) $\"+.45a+%2B+.75b+=+10.05+\"$
\n" ); document.write( "(2) $\"+45a+%2B+75b+=+1005+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+45+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+45a+%2B+75b+=+1005+\"$
\n" ); document.write( "(1) $\"+-45a+-+45b+=+-675+\"$
\n" ); document.write( " $\"+30b+=+330+\"$
\n" ); document.write( " $\"+b+=+11+\"$
\n" ); document.write( "and,, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+15+\"$
\n" ); document.write( "(1) $\"+a+%2B+11+=+15+\"$
\n" ); document.write( "(1) $\"+a+=+4+\"$
\n" ); document.write( "4 kg of 45% salt solution is needed
\n" ); document.write( "11 kg of 75% salt solution is needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.45a+%2B+.75b+%29+%2F+15+=+.67+\"$
\n" ); document.write( "(2) $\"+%28+.45%2A4+%2B+.75%2A11+%29+%2F+15+=+.67+\"$
\n" ); document.write( "(2) $\"+%28+1.8+%2B+8.25+%29+%2F+15+=+.67+\"$
\n" ); document.write( "(2) $\"+10.05+%2F+15+=+.67+\"$
\n" ); document.write( "(2) $\"+10.05+=+.67%2A15+\"$
\n" ); document.write( "(2) $\"+10.05+=+10.05+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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