[Decimal numeral system]

A three-digit number. A three-digit number starts with the digit 4. If this digit is moved to the end of the number, the resulting number is 0.75 of the original number. Find the original number.

#
Let's write the equation $\underline{x} \underline{y}_{\mathbf{z}}=0.75 \cdot \underline{x} \underline{y}$, transform it to $\underline{x} \underline{y}_{\mathbf{2}} \cdot 10+4=0.75 \cdot\left(\underline{x} \underline{y}_{\mathbf{2}}+400\right)$, from which we get $\underline{x} \underline{y}_{\mathbf{z}}=32$.

## Answer

432