document.write( "Question 625725: How Much Tin and how much lead must be added to 700 pounds of an alloy containing 50% tin and 25% lead to make an alloy which is 60% tin and 20% lead? \n" ); document.write( "

Algebra.Com's Answer #393743 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = pounds of tin to be added
\n" ); document.write( "Let $\"+b+\"$ = pounds of lead to be added
\n" ); document.write( " $\"+.5%2A700+=+350+\"$ pounds of tin in original alloy
\n" ); document.write( " $\"+.25%2A700+=+175+\"$ pounds of lead in original alloy
\n" ); document.write( "----------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+%28+a+%2B+350+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.6+\"$
\n" ); document.write( "(2) $\"+%28+b+%2B+175+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.2+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(1) $\"+a+%2B+350+=+.6%2A%28+a+%2B+b+%2B+700+%29+\"$
\n" ); document.write( "(1) $\"+a+%2B+350+=+.6a+%2B+.6b+%2B+420+\"$
\n" ); document.write( "(1) $\"+.4a+-+.6b+=+420+-+350+\"$
\n" ); document.write( "(1) $\"+.4a+-+.6b+=+70+\"$
\n" ); document.write( "(1) $\"+4a+-+6b+=+700+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+%28+b+%2B+175+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.2+\"$
\n" ); document.write( "(2) $\"+b+%2B+175+=+.2%2A%28+a+%2B+b+%2B+700+%29+\"$
\n" ); document.write( "(2) $\"+b+%2B+175+=+.2a+%2B+.2b+%2B+140+\"$
\n" ); document.write( "(2) $\"+.8b+-+.2a++=+140+-+175+\"$
\n" ); document.write( "(2) $\"+.8b+-+.2a+=+-35+\"$
\n" ); document.write( "(2) $\"+2a+-+8b+=+350+\"$
\n" ); document.write( "Multiply both sides of (2) by $\"2\"$
\n" ); document.write( "and subtract (2) from (1)
\n" ); document.write( "(1) $\"+4a+-+6b+=+700+\"$
\n" ); document.write( "(2) $\"+-4a+%2B+16b+=+-700+\"$
\n" ); document.write( " $\"+10b+=+0+\"$
\n" ); document.write( " $\"+b+=+0+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+2a+-+8b+=+350+\"$
\n" ); document.write( "(2) $\"+2a+-+8%2A0+=+350+\"$
\n" ); document.write( "(2) $\"+2a+=+350+\"$
\n" ); document.write( "(2) $\"+a+=+175+\"$
\n" ); document.write( "175 pounds of tin should be added and
\n" ); document.write( "no lead should be added
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+%28+a+%2B+350+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.6+\"$
\n" ); document.write( "(1) $\"+%28+175+%2B+350+%29+%2F+%28+175+%2B+0+%2B+700+%29+=+.6+\"$
\n" ); document.write( "(1) $\"+525+%2F+875+=+.6+\"$
\n" ); document.write( "(1) $\"+21%2F35+=+.6+\"$
\n" ); document.write( "(1) $\"+21+=+21+\"$
\n" ); document.write( "OK
\n" ); document.write( "(2) $\"+%28+b+%2B+175+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.2+\"$
\n" ); document.write( "(2) $\"+%28+0+%2B+175+%29+%2F+%28+175+%2B+0+%2B+700+%29+=+.2+\"$
\n" ); document.write( "(2) $\"+175+%2F+875+=+.2+\"$
\n" ); document.write( "(2( $\"+175+=+175+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );