A theatre has 11 rows of seats which have 1 to 10 series. Unmatched numbers have 15 seats and 16 seats have matched numbers . How many sets are there in theatre?
To find the number of seats in the theatre, we need to calculate the sum of seats in each row.
In the theatre, there are 11 rows of seats from 1 to 10, with unmatched numbers having 15 seats and matched numbers having 16 seats.
To calculate the sum of seats in each row, we can use the formula for an arithmetic series:
Sum = (n/2) * (first term + last term),
where n is the number of terms (which is 10 in this case), and the first and last term are the number of seats in the first and last rows.
For unmatched numbers (15 seats), the sum in each row is:
Sum = (10/2) * (15 + 15)
= 5 * 30
= 150
For matched numbers (16 seats), the sum in each row is:
Sum = (10/2) * (16 + 16)
= 5 * 32
= 160
Now, we add up the total number of seats in all rows:
Total number of seats = (number of rows) * (sum in each row)
= 11 * (150 + 160)
= 11 * 310
= 3410
Therefore, there are 3,410 seats in the theatre.