document.write( "Question 688262: The peanut pub has pecans that sell for $7.50 per kilogram and almonds that sell for $8.75. The owner wants to make a 10-kg mixture of these two varieties, which will sell for $8.00 per kg. How many kg of each variety will he need to use to produce the desired mixture. Thank you for the help in advance. \n" ); document.write( "

Algebra.Com's Answer #425561 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = kg of pecans needed
\n" ); document.write( "Let $\"+b+\"$ = kg of almonds needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(2) $\"+%28+7.5a+%2B+8.75b+%29+%2F+10+=+8+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+7.5a+%2B+8.75b+=+80+\"$
\n" ); document.write( "(2) $\"+750a+%2B+875b+=+8000+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+750+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+750a+%2B+875b+=+8000+\"$
\n" ); document.write( "(1) $\"+-750a+-+750b+=+-7500+\"$
\n" ); document.write( " $\"+125b+=+500+\"$
\n" ); document.write( " $\"+b+=+4+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(1) $\"+a+%2B+4+=+10+\"$
\n" ); document.write( "(1) $\"+a+=+6+\"$
\n" ); document.write( "6 kg of pecans are needed
\n" ); document.write( "4 kg of almonds are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+7.5a+%2B+8.75b+%29+%2F+10+=+8+\"$
\n" ); document.write( "(2) $\"+%28+7.5%2A6+%2B+8.75%2A4+%29+%2F+10+=+8+\"$
\n" ); document.write( "(2) $\"++45+%2B+35+=+80+\"$
\n" ); document.write( "(2) $\"+80+=+80+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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