SOLUTION: suppose that a supermarket sells cashews for 4.50 per pound and pecans for 6.50 a pound how many pounds of each are needed to obtain a mixture of 40lbs that can be sold for 5.85 pe

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Question 127588: suppose that a supermarket sells cashews for 4.50 per pound and pecans for 6.50 a pound how many pounds of each are needed to obtain a mixture of 40lbs that can be sold for 5.85 per pound
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(price/lb cashews)x(lbs cashews) + (price/lb pecans)x(lbs pecans)
divided by (lbs of cashews and pecans)
= (price per lb of mixture)
Let c = pounds of cashews needed
Let p = pounds of pecans needed
%284.5c+%2B+6.5p%29+%2F+%28p+%2B+c%29+=+5.85
c+%2B+p+=+40
p+=+40+-+c
%284.5c+%2B+6.5p%29+%2F+%28p+%2B+c%29+=+5.85
%284.5c+%2B+6.5%2840+-+c%29%29+%2F+40+=+5.85
4.5c+%2B+260+-+6.5c+=+40%2A5.85
-2c+=+234+-+260
-2c+=+-26
c+=+13
p+=+40+-+c
p+=+27
13 pounds of cashews and 27 pounds of pecans are needed
check:
%284.5c+%2B+6.5p%29+%2F+40+=+5.85
%284.5%2A13+%2B+6.5%2A27%29+%2F+40+=+5.85
%2858.5+%2B+175.5%29+%2F+40+=+5.85
234%2F40+=+5.85
234+=+5.85%2A40
234+=+234