SOLUTION: The nutty shoppe has 10kg of mixed pecans and cashews which sell for $8.40 per kilogram. Cashews alone sell for $8.00 per kilogram, and pecans sell for $9.00 per kilogram. How many

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The nutty shoppe has 10kg of mixed pecans and cashews which sell for $8.40 per kilogram. Cashews alone sell for $8.00 per kilogram, and pecans sell for $9.00 per kilogram. How many      Log On


   



Question 596032: The nutty shoppe has 10kg of mixed pecans and cashews which sell for $8.40 per kilogram. Cashews alone sell for $8.00 per kilogram, and pecans sell for $9.00 per kilogram. How many kilograms of pecans are there in the mix?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = kg of pecans
Let +c+ = kg of cashews
Cost of pecans used = +9p+
Cost of cashews used = +8c+
Cost of mixture = +8.4%2A10+=+84+
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(1) +9p+%2B+8c+=+84+
(2) +p+%2B+c+=+10+
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Multiply both sides of (2) by +8+
and subtract (2) from (1)
(1) +9p+%2B+8c+=+84+
(2) +-8p+-+8c+=+-80+
+p+=+4+
and, since
(2) +p+%2B+c+=+10+
(2) +4+%2B+c+=+10+
(2) +c+=+6+
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There are 4 kg of pecans in the mixture
check answer:
(1) +9p+%2B+8c+=+84+
(1) +9%2A4+%2B+8%2A6+=+84+
(1) +36+%2B+48+=+84+
(1) +84+=+84+
OK