A theater can seat 780 people. The number of rows is 4 less than the number of seats in each row. How many rows of seats are there
This is no sequence, since the rows all have the same number of seats. If there are n seats in each row, then there are n-4 rows, so
n(n-4) = 780
n = 30
There are 26 rows of 30 seats each
X seats/row.
x-4 Rows.
x*(x-4) = 780.
x^2 - 4x - 780 = 0,
Using Quadratic Formula,
X = 30.
x-4 = 26.
Why did the theater have a seat problem? Because it rowfused to have one row more! Alright, let's solve this. If we let "x" be the number of seats in each row, the number of rows can be expressed as (x - 4). We know that the total number of seats is 780. So, we can set up the equation x * (x - 4) = 780. Now, let me just grab my calculator... doo-doo-doo... and voilà! After crunching the numbers, we find that x = 30. Therefore, the number of rows would be 30 - 4 = 26. And the theater lived happily ever after (with 26 rows of seats).
To find the number of rows of seats in the theater, we need to determine the number of seats in each row first.
Let's denote the number of seats in each row as 'x'. According to the problem, the number of rows is 4 less than the number of seats in each row. Therefore, we can represent the number of rows as 'x - 4'.
Now, we know that the theater can seat 780 people in total. To find the total number of seats, we multiply the number of seats in each row (x) by the number of rows (x - 4), which gives us:
x * (x - 4) = 780
By solving this quadratic equation, we can determine the value of x, which represents the number of seats in each row. Once we find x, we can substitute it into the equation for the number of rows (x - 4) to get the final answer.
Using the sum of an arithmetic sequence with a=5 and d=4 we have to solve for n (which is the number of rows).
so...
780=(n/2)(2a+(n-1)4)
but we do the math and get down to
0=4n^2 +6n-1560 which needs the quadratic formula to factor. One of the roots of the quadratic formula is inadmissible (the negative one) and the other answer is approximately 19.01
Thus you can double check to see if you have 19 rows or 20 rows by subbing those numbers back into your sum formula where the sum = 780 : )