A grocer wants to make a 10 pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and c

Question

A grocer wants to make a 10 pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

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Ruby 3 weeks 2021-10-01T17:48:12+00:00 1 Answer 0

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    2021-10-01T17:49:14+00:00

    Answer: 7 pounds of peanuts and 3 pounds of cashew should be used.

    Step-by-step explanation:

    Let x represent the number of pounds of peanuts that he would use in the mixture.

    Let y represent the number of pounds of cashews that he would use in the mixture.

    The total mixture would be 10 pounds. It means that

    x + y = 10

    The mixture of peanuts and cashews would be sold at $4.75 per pound. This means that the total cost of the mixture is

    10 × 4.75 = $47.5

    If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, it means that

    4x + 6.5y = 47.5- – – – – – – – – – – – 1

    Substituting x = 10 – y into equation 1, it becomes

    4(10 – y) + 6.5y = 47.5

    40 – 4y + 6.5y = 47.5

    – 4y + 6.5y = 47.5 – 40

    2.5y = 7.5

    y = 7.5/2.5

    y = 3

    x = 10 – y = 10 – 3

    x = 7

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