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The Manager Of A Bulk Foods Establishment Sells A Trail Mix For $8 Per Pound And Premium Cashews For $15 Per Pound. The Manager Wishes To Make A 35 Pound Trail Mix Cashew Mixture That Will Sell For $14 Per Pound. How Many Pounds Of Each Should Be Use?

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Oddman answered
Let c represent the number of pounds of cashews in the mix. The total cost of goods will be   8(35-c) + 15(c) = 14*35    (each product is (dollars/pound)*(pounds))   8*35 - 8c + 15c = 14*35    (use the distributive property to eliminate parentheses)   7c = 6*35    (subtract 8*35 from both sides, collect terms)   c = 6*5    (divide both sides by 7)
The mix should consist of 30 pounds of cashews and 5 pounds of trail mix.
These mixture problems tend to work out much more nicely if you let the variable represent the amount of the high-cost item. Math Check   30*15 + 5*8 = 35*14   450 + 40 = 490    (yes)  Reasonableness Check This makes a nice math problem, but this particular mixture is a bad idea from a business point of view. The mixture will be unattractive because of its heavy cashew content. The mixture will be less profitable because the cost of labor of making the mix is not reimbursed by any extra profit. As a practical matter, there should be more trail mix and fewer cashews.

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