Question

assume 5 seats in a movie theater take up 35 square ft how many seats are there in a auditorium that is 40 wide and 60 long?

Answer 1

The question is comparing two quantities - the number of seats and the area of the movie theatre.

Given:

`\begin{gathered} 5\text{ seats occupy 35 square f}eet \\ 5\text{seats}=35ft^2 \end{gathered}`

This means the area covered within the auditorium by the 5 seats is 35 square feet.

The dimension of the auditorium is given by;

`\begin{gathered} width=40ft \\ \text{length}=60ft \\ \text{Area}=\text{length}* width \\ \text{Area}=60*40 \\ \text{Area}=2400ft^2 \end{gathered}`

To get the number of seats in the auditorium, we compare both quantities;

Let x be the total number of seats in the auditorium

`\begin{gathered} 5\text{seats}=35ft^2 \\ x\text{ number of seats=2400 square f}eet \\ \\ \text{Cross multiplying, we have;} \\ 35* x=5*2400 \\ 35x=12000 \\ \text{Dividing both sides by }35\text{ to get x;} \\ x=(12000)/(35) \\ x=342.857 \end{gathered}`

Therefore, the total number of seats in the auditorium is approximately 342 seats.

This is because we can not have a seat as a fraction, hence, we discard the remainder.

Hence, we select the whole part alone which is 342 seats.