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10 April, 11:46

You have one type of chocolate that sells for $2.40/lb and another type of chocolate that sells for $9.90/lb. You would like to have 30 lbs of a chocolate mixture that sells for $4.20/lb. How much of each chocolate will you need to obtain the desired mixture

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  1. 10 April, 11:52
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    We need 22.8 lbs of the first type of chocolate and 7.2 lbs of the second type of chocolate

    Step-by-step explanation:

    Step 1:

    Let x represent the quantity of the first type of chocolate

    and y represent the quantity of the second type of chocolate

    The quantity of the final mixture required = 30 lbs

    Hence

    x + y = 30

    Step 2:

    Price of the first type of chocolate = $ 2.40 / lb

    Price of the second type of chocolate = $9.90/lb

    The total price of the final mixture = $4.20 / lb

    Hence the price for 30 lbs = 4.2 * 30 = $126

    Hence the equation representing this would be

    2.4 x + 9.9 y = 126

    Step 3:

    Solving the equations obtained in step 1 and 2 for x and y we get,

    2.4 x + 2.4 y = 72

    2.4 x + 9.9 y = 126

    Subtracting equation 2 from 1 we get,

    -7.5 y = - 54 = > y = 7.2

    x + y = 30 = > x = 30 - y = 30 - 7.2 = 22.8

    Step 4:

    Answer:

    We need 22.8 lbs of the first type of chocolate and 7.2 lbs of the second type of chocolate
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