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3 August, 23:46

A manager bought 12 pounds of peanuts for $30. He wants to mix $5 per pound cashews with the peanuts to get a batch of mixed nuts that is worth $4 per pound. How many pounds of cashews are needed

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  1. 4 August, 03:11
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    18 pounds of cashews are needed.

    Step-by-step explanation:

    Given;

    A manager bought 12 pounds of peanuts for $30.

    Price of peanut per pound P = $30/12 = $2.5

    Price of cashew per pound C = $5

    Price of mixed nut per pound M = $4

    Let x represent the proportion of peanut in the mixed nut.

    The proportion of cashew will then be y = (1-x), so;

    xP + (1-x) C = M

    Substituting the values;

    x (2.5) + (1-x) 5 = 4

    2.5x + 5 - 5x = 4

    2.5x - 5x = 4 - 5

    -2.5x = - 1

    x = 1/2.5 = 0.4

    Proportion of cashew is;

    y = 1-x = 1-0.4 = 0.6

    For 12 pounds of peanut the corresponding pounds of cashew needed is;

    A = 12/x * y

    A = 12/0.4 * 0.6 = 18 pounds

    18 pounds of cashews are needed.
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