Canola oil and olive oil mixture

While shopping for groceries, you notice a new cooking oil product consisting of a blend of canola oil and olive oil. The label does not say in what proportions the oils are mixed, but the Nutrition Facts panel says that a 14 gram serving has 1 gram of saturated fat, 9 grams of monounsaturated fat, and 4 grams of polyunsaturated fat. What percentage of olive oil does the blend contain?

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pnikam Expert Asked on 18th August 2015 in Puzzles.
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    To calculate the proportion of the constituents of the blend, we need to find out the fatty acid profiles of canola oil and olive oil, and then determine what combination would yield the fatty acid profile of the mixture. We start by looking at the fatty acid composition table:

    Percent by weight of total fatty acids.

    Oil or Fat Unsat./Sat.
    ratio
    Saturated Mono
    unsaturated
    Poly
    unsaturated
    Capric
    Acid

    C10:0

    Lauric
    Acid

    C12:0

    Myristic
    Acid

    C14:0

    Palmitic
    Acid

    C16:0

    Stearic
    Acid

    C18:0

    Oleic
    Acid

    C18:1

    Linoleic
    Acid (ω6)

    C18:2

    Alpha
    Linolenic
    Acid (ω3)
    C18:3
     Canola Oil 15.7 4 2 62 22 10
     Olive Oil 4.6 13 3 71 10 1

    We calculate the percentage of saturated (%sat), monounsaturated (%mono), and polyunsaturated (%poly) fat for the mixture, and tabulate the saturation profiles for the three oils.

    Calculation of the fatty acid percentages for the oil mixture:

    %sat = 100×1/14 = 7%
    %mono = 100×9/14 = 64%
    %poly = 100×4/14 = 29%

    Saturation profiles for Canola oil, Olive oil, and the unknown mixture
    Oil  %sat  %mono  %poly
    Canola 6 62 32
    Olive 16 71 11
    Mixture 7 64 29

    We notice that the percentages do not add to 100% for olive oil due to rounding and other constituents not listed. This just means that our answer will not be as accurate as it could be with better analytical data.

    If X represents the fraction of olive oil in the mixture, (1-X) is the fraction of canola oil. The proportion of the components can be calculated for the saturated, monounsaturated, and polyunsaturated components separately to arrive at three different answers.

    anikam Expert Answered on 18th August 2015.
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