document.write( "Question 845168: one alloy is 50% silver and another is 20% silver. How much of each alloy is needed to make 100 kilograms of alloy which is 45% silver? \n" ); document.write( "

Algebra.Com's Answer #509165 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = kg of 50% silver needed
\n" ); document.write( "Let $\"+b+\"$ = kg of 20% silver needed
\n" ); document.write( "---------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.2b+%29+%2F+100+=+.45+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "(2) $\"+.5a+%2B+.2b+=+45+\"$
\n" ); document.write( "(2) $\"+5a+%2B+2b+=+450+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+5a+%2B+2b+=+450+\"$
\n" ); document.write( "(1) $\"+-2a+-+2b+=+-200+\"$
\n" ); document.write( " $\"+3a+=+250+\"$
\n" ); document.write( " $\"+a+=+83.333+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(1) $\"+b+=+100+-+83.333+\"$
\n" ); document.write( "(1) $\"+b+=+16.667+\"$
\n" ); document.write( "83.333 kg of 50% silver is needed
\n" ); document.write( "16.667 kg of 20% silver is needed
\n" ); document.write( "-------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.2b+%29+%2F+100+=+.45+\"$
\n" ); document.write( "(2) $\"+%28+.5%2A83.333+%2B+.2%2A16.667+%29+%2F+100+=+.45+\"$
\n" ); document.write( "(2) $\"+%28+41.6665+%2B+3.3334+%29+%2F+100+=+.45+\"$
\n" ); document.write( "(2) $\"+45.00005+=+45+\"$
\n" ); document.write( "close enough \n" ); document.write( "

\n" );