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Lv 5
發問時間: 科學數學 · 5 年前

Mr. Ong is arranging his students into groups for the school debate.?

Mr. Ong is arranging his students into groups for the school debate. When he groups them into 5, 4 and 7, there remainder of 2, 1 and 4 respectively. What is the least number of students Mr. Ong has?

1 個解答

評分
  • ?
    Lv 6
    5 年前
    最佳解答

    Let x be the number of students

    x = 5*4n₁ + 4*7n₂ + 5*7n₃ + (5*4*7)R

    x = 20n₁ + 28n₂ + 35n₃ + 140R

    When x is divided by 5, the remainder is 2.

    Consider 28n₂,

    28(4) = 112 is divided by 5, the remainder is 2.

    n₂ = 4

    When x is divided by 4, the remainder is 1.

    Consider 35n₃,

    35(3) = 105 is divided by 4, the remainder is 1.

    n₃ = 3

    When x is divided by 7, the remainder is 4.

    Consider 20n₁,

    20(3) = 60 is divided by 7, the remainder is 4.

    n₁ = 3

    ∴ x = 20(3) + 28(4) + 35(3) + 140R = 277 + 140R

    The least number of students = 137

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