document.write( "Question 832135: A candy distributor needs to mix a 10% fat-content chocolate with a 50% fat-content chocolate to create 200 kilograms of a 20% fat-content chocolate. How many kilograms of each kind of chocolate must they use? \n" ); document.write( "

Algebra.Com's Answer #501857 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = kg of 10% fat chocolate needed
\n" ); document.write( "Let $\"+b+\"$ = kg of 50% fat chocolate needed
\n" ); document.write( "------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+200+\"$
\n" ); document.write( "(2) $\"+%28+.1a+%2B+.5b+%29+%2F+200+=+.2+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+.1a+%2B+.5b+=+.2%2A200+\"$
\n" ); document.write( "(2) $\"+.1a+%2B+.5b+=+40+\"$
\n" ); document.write( "(2) $\"+a+%2B+5b+=+400+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+a+%2B+5b+=+400+\"$
\n" ); document.write( "(1) $\"+-a+-+b+=+-200+\"$
\n" ); document.write( " $\"+4b+=+200+\"$
\n" ); document.write( " $\"+b+=+50+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+200+\"$
\n" ); document.write( "(1) $\"+a+=+200+-+50+\"$
\n" ); document.write( "(1) $\"+a+=+150+\"$
\n" ); document.write( "150 kg of 10% fat chocolate is needed
\n" ); document.write( "50 kg of 50% fat chocolate is needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.1a+%2B+.5b+%29+%2F+200+=+.2+\"$
\n" ); document.write( "(2) $\"+%28+.1%2A150+%2B+.5%2A50+%29+%2F+200+=+.2+\"$
\n" ); document.write( "(2) $\"+%28+15+%2B+25+%29+%2F+200+=+.2+\"$
\n" ); document.write( "(2) $\"+40+=+.2%2A200+\"$
\n" ); document.write( "(2) $\"+40+=+40+\"$
\n" ); document.write( "OK \n" ); document.write( "

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