Answer
In 2010, there were approximately 187,258 Marines who were men.
Work Step by Step
We are told that in 2010, 185 out of every 200 people in the Marines were men, and we want to approximate the total number of Marines who were men given that there were 202,441 total people in the Marines.
So let $x$ be the total number of Marines who are men.
Then we must have $$\dfrac{x}{202,441}=\dfrac{185}{200}.$$
We first cross multiply, then solve for $x$:
$$200x=37,451,585 \\ x=187,257.925.$$
Since we can't have a fraction of a person, we round our value to the nearest whole number, which is 187,258.
Thus in 2010, there were approximately 187,258 Marines who were men.
