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?
PLEASE ANSWER OPTIMUS PRIME'S QUESTION OR I'LL DIE!
let the number of rows be x
let the number of seats in each row be x-16
x(x-16) = 1161
x^2 - 16x - 1161 = 0
(x-43)(x+27) = 0
x = 43 or x = -27 but x > 0
x = 43
there are 43 rows with 27 seats in each
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 the number of rows is "x." According to the problem, the number of seats in each row is 16 fewer than the number of rows. So, the number of seats in each row would be x - 16.
Since the total number of seats in the theater is 1161, we can equate this to the product of the number of rows and the number of seats in each row.
The equation can be written as:
x * (x - 16) = 1161
To solve this equation, we can either factoring or using the quadratic formula. However, we can quickly check the factors of 1161 to see if there is a whole number solution.
The factors of 1161 are:
1, 3, 9, 129, 387, 1161
If we substitute these factors into the equation, we can find which value(s) of x satisfies the equation.
Let's try the factors one by one:
- For x = 1, the equation becomes 1 * (1 - 16) = -15, which doesn't equal 1161.
- For x = 3, the equation becomes 3 * (3 - 16) = 3 * (-13) = -39, which doesn't equal 1161.
- For x = 9, the equation becomes 9 * (9 - 16) = 9 * (-7) = -63, which doesn't equal 1161.
- For x = 129, the equation becomes 129 * (129 - 16) = 129 * 113 = 14577, which doesn't equal 1161.
- For x = 387, the equation becomes 387 * (387 - 16) = 387 * 371 = 143997, which doesn't equal 1161.
- For x = 1161, the equation becomes 1161 * (1161 - 16) = 1161 * 1145 = 1330365, which is greater than 1161.
After trying out all the factors, we can see that none of them satisfies the equation. Therefore, there might be an error in the problem statement, or the problem may not have a valid solution.