document.write( "Question 579474: Assef wants to create 50 oz of isopropyl solution of strength 78%.he has on hand some isopropyl solution of strengths 50% and 90%. how much of each solution should be used \n" ); document.write( "

Algebra.Com's Answer #371012 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ounces of 50% solution needed
\n" ); document.write( "Let $\"+b+\"$ = ounces of 90% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$ ounces
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.9b+%29+%2F+50+=+.78+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "(2) $\"+.5a+%2B+.9b+=+.78%2A50+\"$
\n" ); document.write( "(2) $\"+.5a+%2B+.9b+=+39+\"$
\n" ); document.write( "(2) $\"+5a+%2B+9b+=+390+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+5+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+5a+%2B+9b+=+390+\"$
\n" ); document.write( "(1) $\"+-5a+-+5b+=+-250+\"$
\n" ); document.write( " $\"+4b+=+140+\"$
\n" ); document.write( " $\"+b+=+35+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+a+%2B+35+=+50+\"$
\n" ); document.write( "(1) $\"+a+=+50+-+35+\"$
\n" ); document.write( "(1) $\"+a+=+15+\"$
\n" ); document.write( "15 ounces of 50% solution is needed
\n" ); document.write( "35 ounces of 90% solution is needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+.5%2A15+%2B+.9%2A35+%29+%2F+50+=+.78+\"$
\n" ); document.write( "(2) $\"+%28+7.5+%2B+31.5+%29+%2F+50+=+.78+\"$
\n" ); document.write( "(2) $\"+39%2F50+=+.78+\"$
\n" ); document.write( "(2) $\"+39+=+.78%2A50+\"$
\n" ); document.write( "(2) $\"+39+=+39+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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