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Lets imagine we have two numbers (positive, whole numbers) $a$ and $b$ ($a>b$).

We know that $a + b = 999$

and when we combine a and b, its scale is exactly $6$


for example:

$a=888, b=111 $

$ \dfrac{888111}{111888} = 6 $ (false in this case)

find $a$ and $b$

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    $\begingroup$ This is just a math question about solving a system of equations; it doesn't really count as a puzzle. $\endgroup$ – DylanSp May 26 '16 at 13:43
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By inspectionjks:

$a = 857,\, b = 142$
We have $a+b =999,\,1000a + b = 6(1000b + a)$, which is a simple system of two linear equations in two variables, and can be solved uniquely to obtain the above solution.

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a=857, b=142

Start with $\dfrac{1000a+b}{1000b+a}=6$, giving $5999b=994a$ and substitute $a=999-b$.

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