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28 February, 19:23

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar and the second brand contains 15% vinegar. The chef wants to make 280 milliliters of a dressing that is 14% vinegar. How much of each brand should she use?

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  1. 28 February, 19:37
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    35ml of the first brand

    245ml of the second brand

    Step-by-step explanation:

    The chef wishes to use two brands of an Italian dressing

    The first brand constitutes of 7% vinegar

    Let A represent the first brand

    The second brand contains 15% vinegar

    Let B represent the second brand

    280 militers of dressing will be used to preoare both the first and second brands

    A+B=280

    The total mixture contains 14% vinegar, therefore it will be represented as

    0.07A+0.15B = 0.14*280

    0.07+0.15B = 39.2

    We have to find the value of A and B inorder to get the amount of both brands.

    0.07A+0.15B=39.2

    0.07A + 0.15 (280-A) = 39.2

    0.07A+42-0.15A=39.2

    Collect the co-efficient for both sides

    0.07A-0.15B=39.2-42

    -0.08A = - 2.8

    Divide both sides by - 0.08

    -0.08A/-0.08 = - 2.8/-0.08

    A=35

    To find B, substitute 35 for A in the equation below

    A+B=280

    35+B=280

    B = 280-35

    B = 245

    Thus, the chef will be needing 35ml of the first brand and 245ml of the second brand.
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