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Lê Quốc Trần Anh Coordinator

11/01/2018 at 09:36
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If a positive two-digit integer is c times the sum of its digits, the number formed by interchanging the digits is the sum of the digits multiplied by what expression that involves c?




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    Phan Thanh Tinh Coordinator 11/01/2018 at 11:27

    Let \(\overline{ab}\) be the number

    \(\overline{ba}=\overline{ab}+\overline{ba}-\overline{ab}=10a+b+10b+a-c\left(a+b\right)\)

    \(=11\left(a+b\right)-c\left(a+b\right)=\left(11-c\right)\left(a+b\right)\)

    So, the answer is 11 - c


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