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Lê Quốc Trần Anh Coordinator

03/08/2017 at 08:48
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Find a,b,c \(\left(a,b,c\ne\right)\) so that:

\(a,bc:\left(a+b+c\right)=0,25\)




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    Lãng Tử Hào Hoa 03/08/2017 at 10:18

    Transform: \(\overline{a,bc}\div\left(a+b+c\right)=0,25\)

    \(\Leftrightarrow\overline{abc}=25\left(a+b+c\right)\Rightarrow\overline{abc}⋮25\)

    \(\Rightarrow\overline{bc}=\left\{25;50;75\right\}\) (attention: kind \(\overline{bc}=00\) because \(b=c\))

    +) If  \(\overline{bc}=25\Rightarrow\overline{a25}=25\left(a+7\right)\)

    \(\Rightarrow100a+25=25a+175\Rightarrow75a=150\Rightarrow a=2\) (unsatisfactory)

    +) If  \(\overline{bc}=50\Rightarrow\overline{a50}=25\left(a+5\right)\)

    \(\Rightarrow100a+50=25a+125\Rightarrow75a=75\Rightarrow a=1\)

    +) If  \(\overline{bc}=75\Rightarrow\overline{a75}=25\left(a+12\right)\)

    \(\Rightarrow100a+75=25a+300\Rightarrow75a=225\Rightarrow a=3\)

    Conclude:...

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