#### Answer

The number of rooms with kitchen facilities are $50$ and the number of rooms without kitchen facilities are $150$.

#### Work Step by Step

Let us assume x to be the number of rooms with kitchen facilities and y to be the number of rooms without kitchen facilities.
This gives:
Rent for the x rooms with kitchen facilities equal to $\$100x$.
Rent for the y rooms without kitchen facilities equal to $\$80y$.
The provided data can be represented in the form of equations as follows:
$x+y=200$ (I)
$100x+80y=17000$ (II)
And multiplying equation (I) with $-80$ , we get:
$-80x-80y=-16000$ (III)
Now add equation (II) and (III) and solve for x as follows:
$\begin{align}
& 100x+80y-80x-80y=17,000-16,000 \\
& 20x=1000 \\
& x=\frac{1000}{20} \\
& x=50
\end{align}$
Put the value of x in equation (I):
$\begin{align}
& 50+y=200 \\
& y=200-50 \\
& y=150
\end{align}$
Thus, the number of rooms with kitchen facilities is $50$ and the number of rooms without kitchen facilities is $150$.