Answer
The center of gravity is at the point $~x = 5.83~m$
Work Step by Step
In general the center of gravity is: $x_{cog} = \frac{\sum (w_i~x_i)}{\sum w_i}$, where $w_i$ is the weight of each object, and $x_i$ is the position of each object.
We can find the center of gravity:
$x_{cog} = \frac{(5.0~kg)(9.80~m/s^2)(0)+(15.0~kg)(9.80~m/s^2)(5.0~m)+(10.0~kg)(9.80~m/s^2)(10.0~m)}{(5.0~kg)(9.80~m/s^2)+(15.0~kg)(9.80~m/s^2)+(10.0~kg)(9.80~m/s^2)}$
$x_{cog} = 5.83~m$
The center of gravity is at the point $~x = 5.83~m$.
