# Combined numbers [closed]

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 $b$

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

$a = 857,\, b = 142$
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.
Start with $\dfrac{1000a+b}{1000b+a}=6$, giving $5999b=994a$ and substitute $a=999-b$.