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15 October, 23:18

A man sells a type of nut for $7 per pound and a different one for $4.20 per pound, how much of each type should be used to make 24 pound mixture that sells for $5.37

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  1. 16 October, 01:28
    0
    a type nut is 10 pounds

    a different one is 14 pounds

    Step-by-step explanation:

    let a type of the nut be represented by t

    Let a different one be represented by d

    a type of nut cost $7 per pound

    a different one cost $4.20 per pound

    The cost of the mixture for 24 pounds = 5.37 * 24

    = $128.88

    t + d = 24 ... (1)

    7t + 4.2d = 128.88 ... (2)

    From equation (1), t = 24 - d

    Put t = 24 - d in equation 2

    7 (24 - d) + 4.2d = 128.88

    168 - 7d + 4.2d = 128.88

    168 - 2.8d = 128.88

    -2.8d = 128.88 - 168

    -2.8d = - 39.12

    d = - 39.12 / - 2.8

    d = 13.97

    d = 14 pounds

    t = 24 - d

    t = 24 - 14

    t = 10 pounds

    A type nut is 10 pounds. A different one is 14 pounds
  2. 16 October, 01:36
    0
    type of nut = 10.

    Different type of nut = 14.

    Step-by-step explanation:

    1 pound = $5.37

    24 pound = 5.37 * 24

    = $128.88.

    Let X be the type of nut and Y be the different one.

    Value of the nuts in dollars,

    i. 7X + 4.2Y = 128.88

    Weight of the nuts in pounds,

    ii. X + Y = 24

    Rearranging ii,

    X = 24 - Y inputting into i,

    7 (24 - Y) + 4.2Y = 128.88

    168 - 7Y + 4.2Y = 128.88

    2.8Y = 39.12

    Y = 14

    Inputting the value of Y into ii,

    X = 24 - 14

    = 10
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