document.write( "Question 696133: Ten gallons of 30% acid solution is obtained by mixing a 20% solution with a 50% solutions.How much of each solution must be used? \n" ); document.write( "

Algebra.Com's Answer #428818 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = gallons of 20% solution needed
\n" ); document.write( "Let $\"+b+\"$ = gallons of 50% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(2) $\"+%28+.2a+%2B+.5b+%29+%2F+10+=+.3+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+.2a+%2B+.5b+=+3+\"$
\n" ); document.write( "(2) $\"+2a+%2B+5b+=+30+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+2a+%2B+5b+=+30+\"$
\n" ); document.write( "(1) $\"+-2a+-+2b+=+-20+\"$
\n" ); document.write( " $\"+3b+=+10+\"$
\n" ); document.write( " $\"+b+=+10%2F3+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(1) $\"+a+%2B+10%2F3+=+10+\"$
\n" ); document.write( "(1) $\"+a+=+30%2F3+-+10%2F3+\"$
\n" ); document.write( "(1) $\"+a+=+20%2F3+\"$
\n" ); document.write( "3 and 1/3 gallons of 20% solution are needed
\n" ); document.write( "6 and 2/3 gallons of 50% solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+.2a+%2B+.5b+%29+%2F+10+=+.3+\"$
\n" ); document.write( "(2) $\"+%28+%282%2F10%29%2A%2820%2F3%29+%2B+%281%2F2%29%2A%2810%2F3%29+%29+%2F+10+=+3%2F10+\"$
\n" ); document.write( "(2) $\"+%28+40%2F30+%2B+10%2F6+%29+%2F+10+=+3%2F10+\"$
\n" ); document.write( "(2) $\"+40%2F30+%2B+50%2F30+=+3+\"$
\n" ); document.write( "(2) $\"+90%2F30+=+3+\"$
\n" ); document.write( "(2) $\"+3+=+3+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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