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?
Well, well, well, it seems like our theater is in quite a puzzle! Let's see if we can solve it with a touch of humor.
Now, if the number of seats in each row is 16 fewer than the number of rows, we can express this mathematically as follows:
(Number of rows) * (Number of seats per row) = Total number of seats
But the number of seats in each row is 16 fewer than the number of rows. So, we'll replace "number of seats per row" with "(number of rows) - 16":
(Number of rows) * ((Number of rows) - 16) = Total number of seats
Now, we know that our theater has 1161 seats. So, we can set up our equation:
(Number of rows) * ((Number of rows) - 16) = 1161
Oh, boy! It seems like we've stumbled upon a quadratic equation! Don't worry; we'll make it funny and solve it!
Before we do that, though, let's set up the equation in a more digestible form:
(Number of rows)^2 - 16(Number of rows) - 1161 = 0
Now, we can use some mathematical magic, or in this case, the quadratic formula:
The quadratic formula is:
x = (-b ± √(b² - 4ac)) / (2a)
Don't worry; I'll do the math for you!
In our equation, a = 1, b = -16, and c = -1161.
Plugging these values into the quadratic formula, we get:
(Number of rows) = (-(-16) ± √((-16)² - 4(1)(-1161))) / (2(1))
Calculating further, we obtain two possible values for the number of rows.
(Number of rows) ≈ 37 or (Number of rows) ≈ -31
Oh no, negative rows don't exist! So, we can happily discard -31 as a solution.
Therefore, the number of rows in our theater is approximately 37.
Now that we know the number of rows, we can find the number of seats in each row, which is 16 less than the number of rows:
(Number of seats per row) = (Number of rows) - 16
≈ 37 - 16
≈ 21
So, in our 1161-seat theater, there are approximately 21 seats in each row.
I hope I was able to solve this theater puzzle while putting a smile on your face!
Let's denote the number of rows as "x" and the number of seats in each row as "y".
According to the given information, the number in each row is 16 fewer than the number of rows, which can be expressed as:
y = x - 16
We also know that the total number of seats is 1161, so we can write another equation using this information:
x * y = 1161
Now we have a system of two equations:
y = x - 16
x * y = 1161
To find the values of x and y, let's substitute the first equation into the second equation:
x * (x - 16) = 1161
Expanding the equation:
x^2 - 16x = 1161
Rearranging the equation to bring all terms to one side:
x^2 - 16x - 1161 = 0
To solve this quadratic equation for x, we can factorize or use the quadratic formula. Using the quadratic formula, we have:
x = (-(-16) ± sqrt((-16)^2 - 4 * 1 * (-1161))) / (2 * 1)
x = (16 ± sqrt(256 + 4644)) / 2
x = (16 ± sqrt(4900)) / 2
x = (16 ± 70) / 2
We have two possible values for x:
1. x = (16 + 70) / 2 = 86 / 2 = 43
2. x = (16 - 70) / 2 = -54 / 2 = -27 (Discarding this negative value since the number of rows cannot be negative)
So, the number of rows is 43. Now, substituting this back into the first equation:
y = x - 16
y = 43 - 16
y = 27
Therefore, there are 27 seats in each row of the 1161-seat theater.
To find the number of seats in each row of a theater with a total of 1161 seats, we need to set up an equation based on the given information.
Let's assume that there are "x" rows in the theater. According to the information given, the number of seats 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).
Since the total number of seats in the theater is 1161, we can set up the following equation:
x * (x - 16) = 1161
Now, we can solve this equation to find the value of x.
x^2 - 16x = 1161
x^2 - 16x - 1161 = 0
We can solve this quadratic equation by factoring or using the quadratic formula. After solving, we find that x = 49.
Therefore, there are 49 rows in the theater.
Now that we know the number of rows, we can find the number of seats in each row.
Number of seats in each row = x - 16
Number of seats in each row = 49 - 16
Number of seats in each row = 33
So, there are 33 seats in each row of a 1161-seat theater.