document.write( "Question 136617: A wholesaler wants to blend coffee containing 35% caffeine with a coffee containing 15% caffeine to produce a 500 pound blend of coffee containing 18% caffeine. How much of each type of coffee is required? \n" ); document.write( "

Algebra.Com's Answer #100045 by ptaylor(2198) $\"\"$ $\"About$

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Let x=amount of 35% coffee needed
\n" ); document.write( "Then 500-x=amount of 15% coffee needed\r
\n" ); document.write( "\n" ); document.write( "Now we know that the amount of pure caffine in the 35% coffee(0.35x) plus the amount of pure caffine in the 15% coffee(0.15(500-x)) has to equal the amount of pure caffine in the final mixture(0.18*500). So our equation to solve is:\r
\n" ); document.write( "\n" ); document.write( "0.35x+0.15(500-x)=0.18*500 get rid of parens\r
\n" ); document.write( "\n" ); document.write( "0.35x+75-0.15x=90 subtract 75 from each side\r
\n" ); document.write( "\n" ); document.write( "0.35x+75-75-0.15x=90-75 collect like terms\r
\n" ); document.write( "\n" ); document.write( "0.20x=15 divide both sides by 0.20\r
\n" ); document.write( "\n" ); document.write( "x=75 lb amount of 35% coffee needed\r
\n" ); document.write( "\n" ); document.write( "500-x=500-75=425 lb---------------------amount of 15% coffee needed\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "0.35*75+0.15*425=0.18*500\r
\n" ); document.write( "\n" ); document.write( "26.25+63.75=90
\n" ); document.write( "90=90\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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