一个三位数各位上的数字之和是11,如果把百位上的数字与个位上的数字对调,所得的数比原数大693,如果把十

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  • 设百位为x,十位为y,个位为z

    则有:x+y+z = 11 (1)

    100z + 10y + x -(100x + 10y +z) = 693

    ==> 99z - 99x = 693

    ==> z - x = 7

    ==> x = z-7 (2)

    100x + 10z + y -(100x +10y + z) = 54

    ==> 9z - 9y = 54

    ==> z - y = 6

    ==> y = z-6 (3)

    将(2)和(3)代入(1)中得

    z-7 + z-6 + z = 11

    ==> 3z = 24

    ==> z = 8

    代入(2)中解得 x = z-7 = 8-7 = 1

    代入(3)中解得 y = z-6 = 8-6 = 2

    所以这个三位数是 128

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