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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
- ?Lv 65 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
