Smile 發問時間: 科學及數學數學 · 2 個月前

Maths problem: how to do, thanks?

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2 個解答

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  • 2 個月前
    最佳解答

    The current weight of beans is 32 g.

    The current weight of rice is 50 - 32 = 18 g.

    Suppose Fanny's claim is correct.

    Then she adds 5k (in g) and 2k (in g) of rice and beans, respectively, to the mixture, where k is a positive constant.

    The new weight of beans is (32 + 2k) g.

    The new weight of rice is (18 + 5k) g.

    Consider (18 + 5k):(32 + 2k) = 7:9.

    9(18 + 5k) = 7(32 + 2k)

    162 + 45k = 224 + 14k

    31k = 62

    k = 2

    Because the value of k can be solved as a positive constant, Fanny's claim is correct and agreed.

    Note:

    If k cannot be solved, or k is solved to be a non-positive number, then the claim is not agreed.

  • SC147
    Lv 6
    2 個月前

    Suppose Fanny adds 5x g rice & 2x g beans so that wt. of rice:beans=7:9

    (18+5x):(32+2x) = 7:9

    18+5x   7

    --------- = ---

    32+2x   9

    7(32+2x) = 9(18+5x)

    224+14x = 162+45x

    224-162 = 45x-14x

    62 = 31x

    ∴ x = 2

    Yes, I agree that she can add 5(2)=10 g rice & 2(2)=4 g beans

    so that wt. of rice:wt. of beans = 7:9

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