A rectangular auditorium seats 1120 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row

Question

 Application: quadratic equations

Answer 1

s=# of seats in each row

s-12=# of rows

# of seats times # of rows equals # of people

s(s-12)=1120

s²-12s-1120=0

factor 1120 as a product of prime factors

1120=2*2*2*2*2*5*7=(2*2*2*5)*(2*2*7)=40*28 and 40-28=12, the coefficient of the middle term

(s-40)(s+28)=0

s-40=0

s=40 seats in each of 28 rows

40*28=1120

 

Answer 2

Let x = number of rows

"number of seats in each row" = x+12

 

Total number of seats:

     (x) * (x+12) = 1120       [rectangular]

 

   x² + 12x - 1120 = 0       [put all values on one side]

  (x + 40)(x - 28) = 0          [either factor or use quadratic formula]

 

Either x = -40 or x=28 or both.          [Multiplicative Property of Zero]

   x=-40 does not make sense because it is a negative value.

 

   x = 28

 

The number of rows is 28 and the number of seats in each row is 40.

 

28*40 = 1120