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 theater, we can use the given information that the number in each row is 16 less than the number of rows.
Let's represent the number of rows as x. According to the information given, the number of seats in each row will be x - 16.
Now, we need to solve for x using the information that there are 1161 seats in the theater. We can set up an equation to represent this:
Number of rows * Number of seats in each row = Total number of seats in the theater
x * (x - 16) = 1161
We can simplify this equation:
x^2 - 16x = 1161
x^2 - 16x - 1161 = 0
Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. Since it doesn't factor easily, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation x^2 - 16x - 1161 = 0, the coefficients are:
a = 1
b = -16
c = -1161
Plugging these values into the quadratic formula, we get:
x = (-(-16) ± √((-16)^2 - 4(1)(-1161))) / (2(1))
x = (16 ± √(256 + 4644)) / 2
x = (16 ± √4900) / 2
x = (16 ± 70) / 2
Now we have two possible solutions for x:
x1 = (16 + 70) / 2 = 86 / 2 = 43
x2 = (16 - 70) / 2 = -54 / 2 = -27
Since the number of rows cannot be negative, we discard the solution x2 = -27.
Therefore, the number of seats in each row of the 1161-seat theater is x - 16 = 43 - 16 = 27.