document.write( "Question 711417: A coffee shop decides to make a house blend. She mixes coffee costing 3.00 per pound with coffee costing 5.50 per pound. How many pounds of each coffee does she need to make 40 pounds of the blend costing 4.00 per pound. \n" ); document.write( "

Algebra.Com's Answer #437404 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = pounds of $3/lb coffee needed
\n" ); document.write( "Let $\"+b+\"$ = pounds of $5.50/lb coffee needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=++40+\"$
\n" ); document.write( "(2) $\"+%28+3a+%2B+5.5b+%29+%2F+40+=+4+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+3a+%2B+5.5b+=+160+\"$
\n" ); document.write( "(2) $\"+6a+%2B+11b+=+320+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"6\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+6a+%2B+11b+=+320+\"$
\n" ); document.write( "(1) $\"+-6a+-6b+=+-240+\"$
\n" ); document.write( " $\"+5b+=+80+\"$
\n" ); document.write( " $\"+b+=+16+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=++40+\"$
\n" ); document.write( "(1) $\"+a+=+24+\"$
\n" ); document.write( "24 pounds of $3/lb coffee are needed
\n" ); document.write( "16 pounds of $5.50/lb coffee are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+3%2A24+%2B+5.5%2A16+%29+%2F+40+=+4+\"$
\n" ); document.write( "(2) $\"+%28+72+%2B+88+%29+%2F+40+=+4+\"$
\n" ); document.write( "(2) $\"+160+=+4%2A40+\"$
\n" ); document.write( "(20 $\"+160+=+160+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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