One seat in an auditorium is broken. It is in the 3rd row from the front of the auditorium and in the 18th row from the back of the auditorium. There are 12 seats to its left and 17 seats to its right. If every row has the same number of seats, what is the total number of seats in that auditorium?
600
600
because there are 30 rows, There are 12 seats to its left and 17 seats to its right. 12+17+1=30
It is the 3rd row from the front, and 18th row from the back, 3rd row overall, 20=1, 19=2, 18=3... 3 will then be 18! There will be 20 rows in total.
Then, we multiply 20 by 30 and will get 600!
12...x...17
so each row has 30 seats
Now do the same idea to get the number of rows.
To find the total number of seats in the auditorium, we need to determine the number of seats in each row and multiply it by the number of rows.
First, let's determine the position of the broken seat from the front and back of the auditorium. We know that the broken seat is in the 3rd row from the front and the 18th row from the back.
Since every row has the same number of seats, we can infer that the number of rows between the broken seat and the last row is the same as the number of rows between the broken seat and the first row.
So, the number of rows in front of the broken seat is 3 - 1 = 2, and the number of rows behind the broken seat is 18 - 1 = 17.
Next, let's determine the number of seats on each side of the broken seat.
To the left of the broken seat, there are 12 seats, and to the right, there are 17 seats. Adding these two numbers together gives us the total number of seats on one side of the broken seat: 12 + 17 = 29.
Since the number of seats on one side is the same as the number of seats on the other side, the total number of seats in each row is 29 × 2 = 58.
Finally, to find the total number of seats in the auditorium, we need to multiply the number of seats in each row by the total number of rows: 58 × (2 + 17 + 1) = 58 × 20 = 1160.
Therefore, the total number of seats in the auditorium is 1160.