A rectangular auditorium seats 1920 people. The number of seats in each row exceeds the number of rows by 8. Find the number of seats in each row.

Question

A rectangular auditorium seats 1920 people. The number of seats in each row exceeds the number of rows by 8. Find the number of seats in each row.

Answer 1

Hello Shannon.

 

If you let x = number of seats per row, what is the number of rows?

 

Since there are 8 more seats per row than there are rows, you have (x-8) rows.

 

The number of seats = 1920 = (# seats/row) * (# rows).

 

Thus x(x-8) = 1920, which gives you your quadratic equation to solve:

 

x² - 8x - 1920 = 0.

 

You need to find two factors of 1920 that differ by 8. These are 40 and 48. Thus (x+40)(x-48) = 0 is your equation, the solutions of which are x = -40 and x = 48.

 

Since a row cannot have -40 seats, your number of seats per row is 48.