document.write( "Question 755849: A coffee merchant combines coffee costing $6 per pound with coffee cost $3.50 per pound. How many pounds of each should be used to make 50lb of a blend costing $4.20 per pound? \n" ); document.write( "

Algebra.Com's Answer #459859 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = pounds of $6/pound coffee needed
\n" ); document.write( "Let $\"+b+\"$ = pounds of $3.50/pound coffee needed
\n" ); document.write( " $\"+6a+\"$ = cost of $6/pound coffee in blend
\n" ); document.write( " $\"+3.5b+\"$ = cost of $3.50/pound coffee in blend
\n" ); document.write( "----------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(2) $\"+%28+6a+%2B+3.5b+%29+%2F+50+=+4.2+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"++6a+%2B+3.5b+=+4.2%2A50+\"$
\n" ); document.write( "(2) $\"++60a+%2B+35b+=+2100+\"$
\n" ); document.write( "Multiply both sides of (1) by
\n" ); document.write( " $\"+35+\"$ and subtract (1) from (2)
\n" ); document.write( "(2) $\"++60a+%2B+35b+=+2100+\"$
\n" ); document.write( "(1) $\"+-35a+-+35b+=+-1750+\"$
\n" ); document.write( " $\"+25a+=+350+\"$
\n" ); document.write( " $\"+a+=+14+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+14+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+b+=+36+\"$
\n" ); document.write( "14 pounds of $6/pound coffee are needed
\n" ); document.write( "36 pounds of $3.50/pound coffee are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+6a+%2B+3.5b+%29+%2F+50+=+4.2+\"$
\n" ); document.write( "(2) $\"+%28+6%2A14+%2B+3.5%2A36+%29+%2F+50+=+4.2+\"$
\n" ); document.write( "(2) $\"+%28+84+%2B+126+%29+%2F+50+=+4.2+\"$
\n" ); document.write( "(2) $\"+210+=+4.2%2A50+\"$
\n" ); document.write( "(2) $\"+210+=+210+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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