math question

The sum of two numbers is 600.
If one number is 100 less than the other,
what is the smaller number?

$\begin{array}{|lrcll|} \hline (1) & x &=& y-100 \\\\ (2) & x+y &=& 600 \\ & y-100+y &=& 600 \\ & 2y-100 &=& 600 \quad &| \quad +100 \\ & 2y &=& 700 \quad &| \quad :2 \\ & \mathbf{ y } & \mathbf{=} & \mathbf{350} \\\\ & x &=& y-100\\ & x &=& 350-100\\ & \mathbf{ x } & \mathbf{=} & \mathbf{250} \\ \hline \end{array}$

The smaller number is 250