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HMMT November 2018 U4

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Let a,b,c,na, b, c, n be positive real numbers such that a+ba=3,b+cb=4\frac{a+b}{a}=3, \frac{b+c}{b}=4, and c+ac=n\frac{c+a}{c}=n. Find nn.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{7}{6}

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