The seats in a theater are arranged in parallel rows that form a rectangular region. The number in each row is 16 fewer than the number of rows. How many seats are in each row of 1161 -seat theater?
To find the number of seats in each row of a 1161-seat theater, we need to set up an equation based on the given information.
Let's assume there are 'x' rows in the theater.
According to the problem, the number in each row is 16 fewer than the number of rows. This can be expressed as:
Number of seats in each row = Number of rows - 16
Since the number of seats in each row is unknown, let's represent it as 'y'.
Therefore, we have the equation:
y = x - 16
We know that the total number of seats in the theater is 1161. Since there are 'x' rows, and 'y' seats in each row, the total number of seats can be calculated as:
Total number of seats = Number of rows * Number of seats in each row
1161 = x * y
Substituting the value of 'y' from the first equation, we get:
1161 = x * (x - 16)
Simplifying this equation gives us a quadratic equation:
x^2 - 16x - 1161 = 0
Now we can solve this equation to find the value of 'x', which represents the number of rows in the theater. The value of 'x' will be a positive integer.
After finding the value of 'x', we can substitute it back into the equation y = x - 16 to get the number of seats in each row.
Therefore, by solving the quadratic equation x^2 - 16x - 1161 = 0, you can determine the number of seats in each row of a 1161-seat theater.