Total rooms = 80. Single : Double = 3 : 7.<br><br>
[[model:questions/solutions/q10497.png]]<br><br>
Total units = 3 + 7 = 10 units<br>
&bull; 10 units → 80<br>
&bull; 1 unit → 80 ÷ 10 = 8<br>
&bull; Single rooms = 3 units = 3 × 8 = 24<br>
&bull; Double rooms = 7 units = 7 × 8 = 56<br><br>
Now split each group by occupancy:<br>
Single rooms &mdash; occupied : vacant = 2 : 1, so occupied singles = \( \frac{2}{3} \) × 24 = 16<br>
Double rooms &mdash; occupied : vacant = 5 : 2, so occupied doubles = \( \frac{5}{7} \) × 56 = 40<br><br>
Total occupied rooms = 16 + 40 = 56<br>
Check: Vacant singles = 8, vacant doubles = 16. 16 + 40 + 8 + 16 = 80. ✓<br><br>
Final Answer: 56