Use the main ratio to find how many of each room type, then apply the sub-ratios.<br><br>
&bull; Single : Double = 2 : 3, total 100 rooms.<br>
&bull; Single rooms = \(\frac{2}{5} \times 100 = 40\); Double rooms = \(\frac{3}{5} \times 100 = 60\).<br>
&bull; Vacant single rooms = \(\frac{1}{3+1} \times 40 = \frac{1}{4} \times 40 = 10\).<br>
&bull; Vacant double rooms = \(\frac{1}{4+1} \times 60 = \frac{1}{5} \times 60 = 12\).<br>
&bull; Total vacant rooms = 10 + 12 = 22.<br><br>
Final Answer: 22