document.write( "Question 758245: A metallurgist has one alloy containing 34% copper and another containing 55% copper. How many pounds of each alloy must he use to make 49 pounds of a third alloy containing 40% copper? \n" ); document.write( "

Algebra.Com's Answer #461322 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = pounds of 34% alloy needed
\n" ); document.write( "Let $\"+b+\"$ = pounds of 55% alloy needed
\n" ); document.write( " $\"+.34a+\"$ = pounds of copper in $\"+a+\"$
\n" ); document.write( " $\"+.55b+\"$ = pounds of copper in $\"+b+\"$
\n" ); document.write( "----------------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+49+\"$
\n" ); document.write( "(2) $\"+%28+.34a+%2B+.55b+%29+%2F+49+=+.4+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+.34a+%2B+.55b+=+.4%2A49+\"$
\n" ); document.write( "(2) $\"+.34a+%2B+.55b+=+19.6+\"$
\n" ); document.write( "(2) $\"+34a+%2B+55b+=+1960+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+34+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+34a+%2B+55b+=+1960+\"$
\n" ); document.write( "(1) $\"+-34a+-+34b+=+-1666+\"$
\n" ); document.write( " $\"+21b+=+294+\"$
\n" ); document.write( " $\"+b+=+14+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+49+\"$
\n" ); document.write( "(1) $\"+a+%2B+14+=+49+\"$
\n" ); document.write( "(1) $\"+a+=+35+\"$
\n" ); document.write( "35 pounds of 34% alloy are needed
\n" ); document.write( "14 pounds of 55% alloy are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.34a+%2B+.55b+%29+%2F+49+=+.4+\"$
\n" ); document.write( "(2) $\"+%28+.34%2A35+%2B+.55%2A14+%29+%2F+49+=+.4+\"$
\n" ); document.write( "(2) $\"++11.9+%2B+7.7+=+.4%2A49+\"$
\n" ); document.write( "(2) $\"+19.6+=+19.6+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );