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15 January, 23:20

Maria is making trail mix to sell for a fundraiser. She wants to use a nut mix that is 10% peanuts and another that is 50% peanuts. She wants to make 40 pounds of that mix that is 25% peanuts. How much of each type should she use?

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  1. 15 January, 23:38
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    Amount of pounds for nut mix 1 = 25

    Amount of pounds for nut mix 2 = 15

    Step-by-step explanation:

    Let the amount of pounds for nut mix 1 = x

    and amount of pounds for nut mix 2 = y

    Amount of total mixture = 40 pounds

    So, x + y = 40 ... Equation 1

    10% peanuts for nut mix 1 = 0.1*x = 0.1x

    50% peanuts for nut mix 2 = 0.5*y = 0.5y

    25% peanuts for the mixture = 0.25*40 = 10

    So, 0.1x + 0.5y = 10 ... Equation 2

    So, we have the system of equations

    x + y = 40 ... Equation 1

    0.1x + 0.5y = 10 ... Equation 2

    Multiply equation 1 by 0.1

    0.1x + 0.1y = 40*0.1 = 4 ... Equation 3

    We then have,

    0.1x + 0.5y = 10 ... Equation 2

    0.1x + 0.1y = 4 ... Equation 3

    Subtract equation 3 from equation 2

    0.1x - 0.1x + 0.5y - 0.1y = 10 - 4

    0.4y = 6

    Divide both sides by 0.1

    0.4y/0.4 = 6/0.4

    y = 15 pounds

    Use y = 15 in equation 1

    x + 15 = 40

    x = 40 - 15

    x = 25 pounds
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