document.write( "Question 683962: Three varieties of coffee-Coffee A, Coffee B, and Coffee C-are combined and roasted, yielding a 55-lb batch of coffee beans. Twice as man pounds of Coffee C, which retails for $10.19 per lb, are needed as Coffee A, which sells for $15.21 per lb. Coffee B retails for $12.99 per lb. How many pounds of each coffee should be used in a blend that sells for $12.61 per lb \n" ); document.write( "

Algebra.Com's Answer #423831 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = pounds of coffee A needed
\n" ); document.write( "Let $\"+b+\"$ = pounds of coffee B needed
\n" ); document.write( "Let $\"+c+\"$ = pounds of coffee C needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+c+=+2a+\"$
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+c+=+55+\"$
\n" ); document.write( "(3) $\"+%28+15.21a+%2B+12.99b+%2B+10.19c+%29+%2F+55+=+12.61+\"$
\n" ); document.write( "--------------------------------------------
\n" ); document.write( "Multiply both sides of (3) by $\"+100+\"$
\n" ); document.write( "(3) $\"+%28+1521a+%2B+1299b+%2B+1019c+%29+%2F+55+=+1261+\"$
\n" ); document.write( "(3) $\"++1521a+%2B+1299b+%2B+1019c++=+69355+\"$
\n" ); document.write( "Multiply both sides of (2) by $\"+1019+\"$ and
\n" ); document.write( "subtract (2) from (3)
\n" ); document.write( "(3) $\"+1521a+%2B+1299b+%2B+1019c+=++69355+\"$
\n" ); document.write( "(2) $\"++-1019a+-+1019b+-+1019c+=+-56045+\"$
\n" ); document.write( " $\"+502a+%2B+280b+=+13310+\"$
\n" ); document.write( " $\"+280b+=+13310+-+502a+\"$
\n" ); document.write( " $\"+b+=+1331%2F28+-+%28+251%2F140+%29%2Aa+\"$
\n" ); document.write( "Plug this into (2)
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+c+=+55+\"$
\n" ); document.write( "(2) $\"+a+%2B+1331%2F28+-+%28+251%2F140+%29%2Aa+%2B+2a+=+55+\"$
\n" ); document.write( "(2) $\"+3a+-+%28+251%2F140+%29%2Aa++=+55+-++1331%2F28+\"$
\n" ); document.write( "(2) $\"+a%2A%28+3+-+1.7929+%29+=+55+-+47.5357+\"$
\n" ); document.write( "(2) $\"+1.2071a+=+7.4643+\"$
\n" ); document.write( "(2) $\"+a+=+6.1837+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+c+=+2a+\"$
\n" ); document.write( "(1) $\"+c+=+2%2A6.1837+\"$
\n" ); document.write( "(1) $\"+c+=+12.3673+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+c+=+55+\"$
\n" ); document.write( "(2) $\"+6.1837+%2B+b+%2B+12.3673+=+55+\"$
\n" ); document.write( "(2) $\"+b+=+55+-+6.1837+-+12.3673+\"$
\n" ); document.write( "(2) $\"+b+=+55+-+18.5510+\"$
\n" ); document.write( "(2) $\"+b+=+36.449+\"$
\n" ); document.write( "6.1837 pounds of coffee A are needed
\n" ); document.write( "36.449 pounds of coffee B are needed
\n" ); document.write( "12.3673 pounds of coffee C are needed
\n" ); document.write( "---------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+c+=+55+\"$
\n" ); document.write( "(2) $\"+6.1837+%2B+36.449+%2B+12.3673+=+55+\"$
\n" ); document.write( "(2) $\"+55+=+55+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+%28+15.21a+%2B+12.99b+%2B+10.19c+%29+%2F+55+=+12.61+\"$
\n" ); document.write( "(3) $\"+%28+15.21%2A6.1837+%2B+12.99%2A36.449+%2B+10.19%2A12.3673+%29+%2F+55+=+12.61+\"$
\n" ); document.write( "(3) $\"++94.0541+%2B+473.4725+%2B+126.0228+=+55%2A12.61+\"$
\n" ); document.write( "(3) $\"+693.5494+=+693.55+\"$
\n" ); document.write( "close enough
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );