Determine the value of $x$ if $30\%$ of $4200+35\%$ of $2400=x\%$ of $4200$.

Let's write down the equation from the given statement:
$$\frac{30}{100}\times 4200+\frac{35}{100}\times 2400=\frac{x}{100}\times 4200$$

Simplify each component:

* $30\%$ of $4200=30\times 42=1260$
* $35\%$ of $2400=35\times 24=840$

Substitute these back into the equation:

$$1260+840=x\times 42$$

$$2100=42x$$

$$x=\frac{2100}{42}=50$$

Thus, the value of $x$ is $50$.