document.write( "Question 644755: two metal alloys, containing 26% copper and 54% copper are to be mixed together to get 210 oz that is 30% copper. How much of each should be used? \n" ); document.write( "

Algebra.Com's Answer #405247 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ounces of 1st alloy needed
\n" ); document.write( "Let $\"+b+\"$ = ounces of 2nd alloy needed
\n" ); document.write( "given:
\n" ); document.write( " $\"+.26a+\"$ = ounces of copper in 1st alloy
\n" ); document.write( " $\"+.54b+\"$ = ounces of copper in 2nd alloy
\n" ); document.write( "(1) $\"+%28+.26a+%2B+.54b+%29+%2F+210+=+.3+\"$
\n" ); document.write( "(2) $\"+a+%2B+b+=+210+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "(1) $\"+.26a+%2B+.54b+=+.3%2A210+\"$
\n" ); document.write( "(1) $\"+.26a+%2B+.54b+=+63+\"$
\n" ); document.write( "(1) $\"+26a+%2B+54b+=+6300+\"$
\n" ); document.write( "Multiply both sides of (2) by $\"+26+\"$
\n" ); document.write( "and subtract (2) from (1)
\n" ); document.write( "(1) $\"+26a+%2B+54b+=+6300+\"$
\n" ); document.write( "(2) $\"+-26a+-+26b+=+-5460+\"$
\n" ); document.write( " $\"+28b+=+840+\"$
\n" ); document.write( " $\"+b+=+30+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+a+%2B+b+=+210+\"$
\n" ); document.write( "(2) $\"+a+=+210+-+30+\"$
\n" ); document.write( "(2) $\"+a+=+180+\"$
\n" ); document.write( "180 ounces of 1st alloy are needed
\n" ); document.write( "30 ounces of 2nd alloy are needed
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+%28+.26a+%2B+.54b+%29+%2F+210+=+.3+\"$
\n" ); document.write( "(1) $\"+%28+.26%2A180+%2B+.54%2A30+%29+%2F+210+=+.3+\"$
\n" ); document.write( "(1) $\"+46.8+%2B+16.2+=+.3%2A210+\"$
\n" ); document.write( "(1) $\"+63+=+63+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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