document.write( "Question 630935: By weight,one fertilizer is 10% potassium, 40% nitrogen and 50% phosphorous. A second fertilizer has percents 10, 20 & 70, respectively and a third fertilizer has percents of 0, 40, and 60 respectively. How much of each must be mixed to get 200 lbs of fertilizer with percents of 8, 30 & 62, respectively?\r
\n" ); document.write( "\n" ); document.write( "___ lbs of first mixture
\n" ); document.write( "___ lbs of second mixture
\n" ); document.write( "___ lbs of third mixture \n" ); document.write( "

Algebra.Com's Answer #397225 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+.08%2A200+=+16+\"$ pounds of potassium total
\n" ); document.write( " $\"+.3%2A200+=+60+\"$ pounds of nitrogen total
\n" ); document.write( " $\"+.62%2A200+=+124+\"$ pounds of phosphorus total
\n" ); document.write( "----------------
\n" ); document.write( "Let $\"+a+\"$ = weight in pounds of 1st fertilizer
\n" ); document.write( "Let $\"+b+\"$ = weight in pounds of 2nd fertilizer
\n" ); document.write( "Let $\"+c+\"$ = weight in pounds of 3rd fertilizer
\n" ); document.write( "----------------
\n" ); document.write( " $\"+.1a+%2B+.1b+%2B+0%2Ac+=+16+\"$
\n" ); document.write( " $\"+.4a+%2B+.2b+%2B+.4c+=+60+\"$
\n" ); document.write( " $\"+.5a+%2B+.7b+%2B+.6c+=+124+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+160+\"$
\n" ); document.write( "(2) $\"+4a+%2B+2b+%2B+4c+=+600+\"$
\n" ); document.write( "(3) $\"+5a+%2B+7b+%2B+6c+=+1240+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "(1) $\"+a+=+160+-+b+\"$
\n" ); document.write( "Substitute this into (2)
\n" ); document.write( "(2) $\"+4%2A%28+160+-+b+%29+%2B+2b+%2B+4c+=+600+\"$
\n" ); document.write( "(2) $\"+640+-+4b+%2B+2b+%2B+4c+=+600+\"$
\n" ); document.write( "(2) $\"+-2b+%2B+4c+=+600+-+640+\"$
\n" ); document.write( "(2) $\"+4c+=+2b+-+40+\"$
\n" ); document.write( "(2) $\"+c+=+b%2F2+-+10+\"$
\n" ); document.write( "Substitute (1) and (2) into (3)
\n" ); document.write( "(3) $\"+5%2A%28+160+-+b+%29+%2B+7b+%2B+6%2A%28+b%2F2+-+10+%29+=+1240+\"$
\n" ); document.write( "(3) $\"+800+-+5b+%2B+7b+%2B+3b+-+60+=+1240+\"$
\n" ); document.write( "(3) $\"+5b+=+1240+-+800+%2B+60+\"$
\n" ); document.write( "(3) $\"+5b+=+500+\"$
\n" ); document.write( "(3) $\"+b+=+100+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+=+160+-+b+\"$
\n" ); document.write( "(1) $\"+a+=+160+-+100+\"$
\n" ); document.write( "(1) $\"+a+=+60+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+c+=+b%2F2+-+10+\"$
\n" ); document.write( "(2) $\"+c+=+100%2F2+-+10+\"$
\n" ); document.write( "(2) $\"+c+=+40+\"$
\n" ); document.write( "60 pounds of 1st fertilizer are needed
\n" ); document.write( "100 pounds of 2nd fertilizer are needed
\n" ); document.write( "40 pounds of 3rd fertilizer are needed
\n" ); document.write( "----------------
\n" ); document.write( "You can check like this:
\n" ); document.write( " $\"+.1a+%2B+.1b+%2B+0%2Ac+=+16+\"$
\n" ); document.write( " $\"+.1%2A60+%2B+.1%2A100+=+16+\"$
\n" ); document.write( " $\"+6+%2B+10+=+16+\"$
\n" ); document.write( " $\"+16++=+16+\"$
\n" ); document.write( "OK- you can check (2) and (3) \n" ); document.write( "

\n" );