#### Answer

103 stations can operate in the broadcast band.

#### Work Step by Step

We can find the frequency when the wavelength is $190~m$:
$f = \frac{c}{\lambda} = \frac{3.0\times 10^8~m/s}{190~m} = 1.58\times 10^6~Hz = 1580~kHz$
We can find the frequency when the wavelength is $550~m$:
$f = \frac{c}{\lambda} = \frac{3.0\times 10^8~m/s}{550~m} = 5.45\times 10^5~Hz = 545~kHz$
We can find the range:
$1580~kHz - 545~kHz = 1035~kHz$
We can find the number of frequency bands 10 kHz wide that can fit inside this range:
$\frac{1035~kHz}{10~kHz} = 103.5$
103 stations can operate in the broadcast band.