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a store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. the manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. how many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

  • finitemath -

    Equate total selling price of mixture to total selling price of components. Solve for weight of cashews.

    x=weight of cashews to be added
    Total price of mixture
    = 3(30+x)
    Total price of components
    = 30*1.5 + 5x

    Equate and solve for x:
    3(30+x) = 30*1.5 + 5x
    Isolate x and solv
    5x-3x = 3(30)-30(1.5)
    2x = 45
    x = 22.5 lbs

  • finitemath -

    thanks a million!

  • finitemath -

    The grocery store sells kumquats for $3.75 a pound and Asian pears for $2.25 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $14.

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