Question

In a movie theatre, the number of seats in a row is $8$ greater than the total number of rows.

How many rows are in the movie theatre, if the total number of seats in the theatre is $884$?

Answer 1

Finding the rows in a movie theatre:

Assuming the number of rows is $\text{R}$

Therefore, the number of seats in a row will be $\text{R+8}$

Number of seats in a row can be taken as the number of columns in theater

Total number of seats will be $=$ Number of columns $\times$ Number of rows

Therefore the total number of seats in the theatre can be expressed as,

$$\begin{gathered} \Rightarrow 884=\left(\text{R+8}\right)\times \text{R} \\ \Rightarrow 884={\text{R}}^2\text{+8R} \\ \Rightarrow {\text{R}}^2\text{+8R-884 =0} \\ \Rightarrow {\text{R}}^2\text{+34R-26R-884 =0} \\ \Rightarrow \text{R}\left(\text{R+34}\right)\text{-26}\left(\text{R+34}\right)\text{=0} \\ \Rightarrow \left(\text{R+34}\right)\left(\text{R-26}\right)\text{=0} \\ \Rightarrow \text{R =-34, R=26} \end{gathered}$$

Now, $\mathrm{R}$ cannot be negative.

So, the number of rows is $26$.

The number of seats in a row will be, $=R+8=26+8=34$.

Hence, number of seats in a row will be equal to $26$ and the number of columns will be equal to $34$.