Hotel capacity occupancy

In the hotel, half of the people live on the first floor, a third on the second floor, and the remaining 40 guests live in the attic. What is the capacity of the hotel if it is 3/4 occupied?

Final Answer:

n =  320

Step-by-step explanation:

$$\begin{gathered} \frac{a}{2}+\frac{a}{3}+40=a \\ a/2+a/3+40=a \\ a=240 \\ a=\frac{3}{4}\cdot n \\ 240=\frac{3}{4}\cdot n \\ 240=3/4\cdot n \\ 3n=960 \\ n=\frac{960}{3}=320 \\ n=320 \end{gathered}$$

Try another example