A factory produces three types of widgets: A, B, and C. The total production of widgets in one month is 1,000 units, and the production ratios of the three types are as follows:
Widget A : Widget B : Widget C = 4 : 3 : 2
Let the quantity of Widget A produced be represented as $x$, the quantity of Widget B as $y$, and the quantity of Widget C as $z$. From the ratio, we can express these quantities as:
$x = 4k$, $y = 3k$, and $z = 2k$ for some positive integer $k$.
What is the total number of Widget A produced if it is known that the total production of widgets is $1000$ units?