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5 August, 21:20

A sample of vinaigrette salad dressing has a total mass of 188 g, a total volume of 196 cm3, and consists only of oil (density = 0.899 g/cm3) and vinegar (density = 1.056 g/cm3). What is the volume of each component in this mixture? Assume that the volumes are additive.

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  1. 5 August, 23:02
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    Answer;

    111 cm³ and 85 cm³

    Explanation;

    Equation 1: 0.885x + 1.056y = 188

    Equation 2: x + y = 196

    let x and y represent volume. x is volume for oil and y is volume for vinegar. Volume multiplied by density would leave you with grams, so since the salad dressing has total mass of 188, we'll set the 1st equation to that. x + y = total volume.

    Solve the system of equations.

    Multiply 2nd equation by - 0.885

    -0.885 (x + y = 196) - --> - 0.885x - 0.885y = - 173.46

    Add both equations.

    0.885x + 1.056y = 188

    -0.885x - 0.885y = - 173.46

    X variable cancels out, leaving you with:

    0.171y = 14.54

    y = 85cc

    Plug y back into 1st equation or 2nd.

    0.885x + 1.056 (85) = 188

    0.885x = 98.24

    x = 111cc

    Verify: Plug x and y into 2nd equation

    111cc + 85cc = 196cc check

    So, x = 111 and y = 85
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