document.write( "Question 493024: What weight of an alloy containing 10% silver must be melted with an alloy containing 60% silver to obtain 10 lb of an
\n" ); document.write( "alloy containing 40% silver? \n" ); document.write( "

Algebra.Com's Answer #335272 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = pounds of 10% silver alloy to be added
\n" ); document.write( "Let $\"b\"$ = pounds of 60% silver alloy to be added
\n" ); document.write( "given:
\n" ); document.write( " $\"+.1a+\"$ = pounds of silver in 10% alloy
\n" ); document.write( " $\"+.6b+\"$ = pounds of silver in 60% alloy
\n" ); document.write( " $\"+.4%2A10+=+4+\"$ = pounds of silver in final alloy
\n" ); document.write( "-------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(2) $\"+.1a+%2B+.6b+=+4+\"$
\n" ); document.write( "----------------
\n" ); document.write( "(2) $\"+a+%2B+6b+=+40+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+a+%2B+6b+=+40+\"$
\n" ); document.write( "(1) $\"+-a+-+b+=+-10+\"$
\n" ); document.write( " $\"+5b+=+30+\"$
\n" ); document.write( " $\"+b+=+6+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(1) $\"+a+%2B+6+=+10+\"$
\n" ); document.write( "(1) $\"+a+=+4+\"$
\n" ); document.write( "4 pounds of 10% silver alloy need to be added
\n" ); document.write( "6 pounds of 60% silver alloy need to be added
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+.1a+%2B+.6b+=+4+\"$
\n" ); document.write( "(2) $\"+.1%2A4+%2B+.6%2A6+=+4+\"$
\n" ); document.write( "(2) $\"+.4+%2B+3.6+=+4+\"$
\n" ); document.write( "(2) $\"+4+=+4+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );