We are given the equation $\frac{x+23}{25} + \frac{x+30}{19} + \frac{x+27}{54} = 6$ and we need to solve for $x$.

1. Problem Description

We are given the equation $\frac{x+23}{25} + \frac{x+30}{19} + \frac{x+27}{54} = 6$ and we need to solve for $x$.

2. Solution Steps

The equation is $\frac{x+23}{25} + \frac{x+30}{19} + \frac{x+27}{54} = 6$.

We can rewrite the equation as

$\frac{x}{25} + \frac{23}{25} + \frac{x}{19} + \frac{30}{19} + \frac{x}{54} + \frac{27}{54} = 6$.

Combining the terms with $x$, we get

$x (\frac{1}{25} + \frac{1}{19} + \frac{1}{54}) + \frac{23}{25} + \frac{30}{19} + \frac{27}{54} = 6$.

We have $\frac{27}{54} = \frac{1}{2}$.

So, $x(\frac{1}{25} + \frac{1}{19} + \frac{1}{54}) = 6 - (\frac{23}{25} + \frac{30}{19} + \frac{1}{2})$.

We have $\frac{1}{25} + \frac{1}{19} + \frac{1}{54} = \frac{19 \times 54 + 25 \times 54 + 25 \times 19}{25 \times 19 \times 54} = \frac{1026 + 1350 + 475}{25650} = \frac{2851}{25650}$.

We have $\frac{23}{25} + \frac{30}{19} + \frac{1}{2} = \frac{23 \times 38 + 30 \times 50 + 19 \times 25}{25 \times 19 \times 2} = \frac{874 + 1500 + 475}{950} = \frac{2849}{950}$.

So, $x \frac{2851}{25650} = 6 - \frac{2849}{950} = \frac{6 \times 950 - 2849}{950} = \frac{5700 - 2849}{950} = \frac{2851}{950}$.

Thus, $x = \frac{2851}{950} \times \frac{25650}{2851} = \frac{25650}{950} = \frac{2565}{95} = 27$.

So, we have $x=27$.

Now, we can check this:

$\frac{27+23}{25} + \frac{27+30}{19} + \frac{27+27}{54} = \frac{50}{25} + \frac{57}{19} + \frac{54}{54} = 2 + 3 + 1 = 6$.

So the answer is correct.

3. Final Answer

27