document.write( "Question 1092323: A 16-ounce mixed nut product containing 13.5% peanuts is to be packaged. The
\n" ); document.write( "packager has a three-mixed nut product containing 6%, 10%, and 50% peanut
\n" ); document.write( "concentrations in stock. If the amount of 50% peanut product is to be onequarter
\n" ); document.write( "that of the 10% peanut product, then how much of each will be needed
\n" ); document.write( "to produce the desired peanut concentration? \n" ); document.write( "

Algebra.Com's Answer #706940 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = ounces of 6% peanuts needed
\n" ); document.write( "Let $\"+b+\"$ = ounces of 10% peanuts needed
\n" ); document.write( "Let $\"+c+\"$ = ounces of 50% peanuts needed
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+16+\"$
\n" ); document.write( "(2) $\"+%28+.06a+%2B+.1b+%2B+.5c+%29+%2F+16+=+.135+\"$
\n" ); document.write( "(3) $\"+c+=+%281%2F4%29%2Ab+\"$
\n" ); document.write( "-------------------------------------
\n" ); document.write( "There are 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "(2) $\"+.06a+%2B+.1b+%2B+.5c+=+2.16+\"$
\n" ); document.write( "(2) $\"+6a+%2B+10b+%2B+50c+=+216+\"$
\n" ); document.write( "(2) $\"+3a+%2B+5b+%2B+25c+=+108+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( "Multiply both sides of (1) by $\"3%7D+and%0D%0Asubtract+%281%29+from+%282%29%0D%0A%282%29+%7B%7B%7B+3a+%2B+5b+%2B+25c+=+108+\"$
\n" ); document.write( "(1) $\"+-3a+-+3b+-+3c+=+-48+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( " $\"+2b+%2B+22c+=+60+\"$
\n" ); document.write( " $\"+b+%2B+11c+=+30+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+b+=+4c+\"$
\n" ); document.write( " $\"+4c+%2B+11c+=+30+\"$
\n" ); document.write( " $\"+15c+=+30+\"$
\n" ); document.write( " $\"+c+=+2+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+b+=+4c+\"$
\n" ); document.write( " $\"+b+=+4%2A2+\"$
\n" ); document.write( " $\"+b+=+8+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+16+\"$
\n" ); document.write( "(1) $\"+a+%2B+8+%2B+2+=+16+\"$
\n" ); document.write( "(1) $\"+a+=+16+-+10+\"$
\n" ); document.write( "(1) $\"+a+=+6+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "6 ounces of 6% peanuts are needed
\n" ); document.write( "8 ounces of 10% peanuts are needed
\n" ); document.write( "2 ounces of 50% peanuts are needed
\n" ); document.write( "----------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.06a+%2B+.1b+%2B+.5c+%29+%2F+16+=+.135+\"$
\n" ); document.write( "(2) $\"+%28+.06%2A6+%2B+.1%2A8+%2B+.5%2A2+%29+%2F+16+=+.135+\"$
\n" ); document.write( "(2) $\"+%28+.36+%2B+.8+%2B+1+%29+%2F+16+=+.135+\"$
\n" ); document.write( "(2) $\"+2.16+%2F+16+=+.135+\"$
\n" ); document.write( "(2) $\"+2.16+=+2.16+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );