Question

A rectangular auditorium seats 1749 people. The number of seats in each row exceeds the number of rows by 20. Find the number of seats in each row.

Answer 1

$\huge\bf\mathfrak\red{Answer}$

Given - Number of Seats = 1749

The number of seats in each row exceeds by 20.

To find - Number of seats in each row.

Calculation -

Let the number of seats be x

the number of seats in each row exceeds the total number of rows by 20.

Thus, seats per row will be - x + 20

seats = Number of rows × number of seats in each row.

1749 = x (x + 20)

1749 = x² + 20x

0 = x² + 20x - 1749

Factorising we get,

(x - 33) ( x+ 53)

Thus, x = 33 and x = -53.

As we know we can't have negative number of seats will make the negative term into positive.

Thus x = 33 + 20 = 53 seats in each row

and there are 33 seats in total.

Answer - The number of seats in each row is 53 and the total number of seats 33.

Answer 2

GIVEN

Let the number of rows be x

The number of seats in each row will be (x + 20)

Total number of seats is 1749

TO FIND :- The number of seats in each row.

SOLUTION

Total no. of seats

= No. of rows × No. of seats in each row

=> 1749 = x( x + 20 )

=> x^2 + 20x - 1749 = 0

Lets go for discriminant

d = b^2 - 4ac

= 20^2 + 4 × 1 × 1749

= 400 + 6,996

= 7396

Now, x = (- b +/- root of d) / 2a

=> (- 20 + 86)/2 or (-20 - 86)/2

=> 33 or (this is not possible as its -ve)

Hence number of rows is 33 but number of seats in each row = 33 + 20 = 53 (ANS)