in an Auditorium the number of rows equal to number of seats WHEN THE ROWS WAS DOUBLED AND THE NUMBER OF SEATS WERE REDUCED BY 12, THEN THE NUMBER OF SEATS INCREASED BY 1300. HOW MANY ROWS ARE THERE. NO SPAM ANSWERS
Answers
Answer:
Given that:
▪ Number of rows = Number of seats
▪ When number of rows are doubled and seats reduced by 12, total seats are increased by 1300
To find:
Total rows
Method:
Let number of rows = r
Let number of seats = s
Then: r = s ...(1)
2r(s - 12) = rs + 1300 [when number of rows are doubled and seats reduced by 12, total seats are increased by 1300] ...(2)
(1) in (2):
=> 2r(r - 12) = r^2 + 1300
=> 2r^2 - 24r = r^2 + 1300
=> r^2 - 24r - 1300 = 0
=> r^2 - 50r + 26r - 1300 = 0
=> r(r - 50) + 26(r - 50) = 0
=> (r - 50)(r + 26) = 0
=> r = 50, (-26)
Since number of rows can't be negative, answer is 50.
__________
Answer: 50
Step by step explanation:
Given:
Number of rows are equal to Number of seats.
When number of rows are doubled and seats are reduced by 12, seats are increased by 1300.
To find: Number of rows
Solution:
Let the number of rows be x
Let the number of seats = y
As per the Ques,
x = y...(1)
Now, As per the next condition,
2x(y - 12) = xy + 1300...(2)
Putting (1) in (2),
=> 2x(x - 12) = x² + 1300
=> 2x² - 24x = x² + 1300
=> x² - 24x - 1300 = 0
=> x² - 50x + 26x - 1300 = 0
=> x(x - 50) + 26(x - 50) = 0
=> (x - 50)(x + 26) = 0
=> x = 50 or x = -26
But number of rows cannot be negative, so the answer is 50.
Total number of rows are 50.