Question

In an auditorium, seats are arranged in rows and columns. The number of rows are equal to the number of seats in each row in the beginning. When the number of rows is doubled and the number of seats in each row is reduced by 10, the total number of seats increases by 300.

Based on the given information, answer the following questions.

1. Taking x as the number of rows in the beginning, represent the above situation by a quadratic equation. 
2. How many rows are there in the original arrangement? 
3. How many seats are there in the auditorium in the beginning? 
4. How many seats are there in the auditorium after rearrangement?

Answer 1

i. \[2x(x-10)-x^{2}=300\]

\[\Rightarrow x^{2}-20x-300=0\] 

ii. \[x^{2}-20x-300=0\]

\[\Rightarrow (x+10)(x-30)=0\] so x = –10 (rejected) or x = 30. 

Original rows = 30. 

iii. Seats in the beginning = \[x^{2}\]

\[=30\times 30\]

\[=900\] 

iv. Seats after rearrangement = \[2x(x-10)\]

\[=2\times 30\times 20\]

\[=1200\]