document.write( "Question 517417: ann and nancy use a metal alloy that is 16% copper to make jewerly. How many ounces of a 11% alloy must be mixed with a 24% allot to form 130 ounces of the desired alloy? \n" ); document.write( "

Algebra.Com's Answer #344774 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = ounces of 11% alloy needed
\n" ); document.write( "Let $\"b\"$ = ounces of 24% alloy needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+130+\"$
\n" ); document.write( "(2) $\"+%28+.11a+%2B+.24b+%29+%2F+130+=+.16+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "(2) $\"+.11a+%2B+.24b+=+.16%2A130+\"$
\n" ); document.write( "(2) $\"+.11a+%2B+.24b+=+20.8+\"$
\n" ); document.write( "(2) $\"+11a+%2B+24b+=+2080+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+11+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+11a+%2B+24b+=+2080+\"$
\n" ); document.write( "(1) $\"+-11a+-+11b+=+-1430+\"$
\n" ); document.write( " $\"+13b+=+650+\"$
\n" ); document.write( " $\"+b+=+50+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+130+\"$
\n" ); document.write( "(1) $\"+a+=+130+-+50+\"$
\n" ); document.write( "(1) $\"+a+=+80+\"$
\n" ); document.write( "80 ounces of 11% alloy are needed
\n" ); document.write( "50 ounces of 24% alloy are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.11%2A80+%2B+.24%2A50+%29+%2F+130+=+.16+\"$
\n" ); document.write( "(2) $\"+%28+8.8+%2B+12+%29+%2F+130+=+.16+\"$
\n" ); document.write( "(2) $\"+20.8+=+.16%2A130+\"$
\n" ); document.write( "(2) $\"+20.8+=+20.8+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );