Question

The number of seats in a row has been increased at a rectangular-shape movie theater after renovation so that it is now five more than the total number of rows. How many rows are in in the theater, if its total seating capacity is 126 people now?

Answer 1

Let the number of rows be = r

Let the number of seats per row be = s

we know that the number of seats is 126.

So, $s\times r=126$    ..... (1)

As given, there are five more seats per row than the number of rows, so we can say that:

$s=r+5$

Putting this in equation (1)

$(r+5)*r=126$

$r^{2}+5r=126$

$r^{2}+5r-126=0$

$r^{2}+14r-9r-126=0$

$(r+14)(r-9)=0$

r=-14 and r=9 (neglecting the negative value) we get r=9

And s=r+5

so, s =9+5=14

Hence, there are 5 rows and 14 seats per row.