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?
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x(x-16)=1161
~Then factor and solve for x.
To find the number of seats in each row of a theater, we need to solve a mathematical equation based on the given information.
Let's assume the number of rows in the theater is represented by the variable 'x'.
According to the given information, the number in each row is 16 fewer than the number of rows. So, the number of seats in each row can be represented as 'x - 16'.
We know that the theater has a total of 1161 seats. Since each row has 'x - 16' seats, the total number of seats can be calculated by multiplying the number of rows ('x') by the number of seats in each row ('x - 16').
Therefore, we can set up the equation:
x * (x - 16) = 1161
Now, we solve the equation for 'x' to find the number of rows in the theater:
x^2 - 16x - 1161 = 0
To solve the quadratic equation, we can factor it or use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case:
a = 1, b = -16, c = -1161
Using the quadratic formula:
x = (-(-16) ± √((-16)^2 - 4(1)(-1161))) / (2(1))
x = (16 ± √(256 + 4644)) / 2
x = (16 ± √4900) / 2
x = (16 ± 70) / 2
Now, we solve for both solutions:
x₁ = (16 + 70) / 2 = 86 / 2 = 43
x₂ = (16 - 70) / 2 = -54 / 2 = -27
We discard the negative solution since the number of rows cannot be negative. Therefore, the number of rows in the theater is 43.
Now, to find the number of seats in each row, we substitute 'x' with 43 in the expression 'x - 16':
Number of seats in each row = x - 16 = 43 - 16 = 27
Therefore, each row of the 1161-seat theater has 27 seats.