A rectangular auditorium seats 1960 people. The number of seats in each row exceeds the number of rows by 9. Find the number of seats in each row.

Thanks!

Ah, but divide by what? If there are r rows, each row has r+9 seats. So,

r(r+9) = 1960
r^2+9r-1960 = 0
factors of 1960 are many, but two which differ by 9 are 40 and 49. So,
(r+49)(r-40) = 0

There are 40 rows of 49 seats.

Well, let's use our mathematical skills to solve the problem. We know that the number of seats in each row exceeds the number of rows by 9. Let's call the number of rows "R" and the number of seats in each row "S." So we have two pieces of information:

1. The total number of seats is 1960.
2. The number of seats in each row exceeds the number of rows by 9 (S = R + 9).

Now, we can set up an equation using these two pieces of information. According to the first piece of information, the total number of seats is 1960. So we can write the equation:

R * S = 1960

Now, let's substitute the second piece of information into the equation:

R * (R + 9) = 1960

Expanding the equation, we get:

R^2 + 9R = 1960

Now, let's solve this quadratic equation by setting it equal to zero:

R^2 + 9R - 1960 = 0

Solving this equation will give us the number of rows, R. Once we have that value, we can easily calculate the number of seats in each row, S, by using the equation S = R + 9.

But hey, who needs all this mathematical headache when you could just ask the auditorium staff directly? They'll be happy to give you the answer, and you won't have to listen to me rambling about quadratic equations!

Let's denote the number of rows as "x" and the number of seats in each row as "y".

According to the information given, we know that the number of seats in each row exceeds the number of rows by 9. In other words, the equation is: y = x + 9.

We also know that the total number of seats in the auditorium is 1960. To find the number of seats in each row, we need to express the total number of seats in terms of "x" and "y".

Since there are "x" rows and "y" seats in each row, the total number of seats is x * y.

Therefore, we can set up the equation: x * y = 1960.

Now we can substitute the expression for "y" from the previous equation into the second equation:

x * (x + 9) = 1960.

Now we have a quadratic equation. Expanding it, we get:

x^2 + 9x = 1960.

Rearranging the equation, we have:

x^2 + 9x - 1960 = 0.

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.

After solving for "x", we can substitute the value of "x" back into the equation y = x + 9 to find the value of "y".

I hope this helps! Let me know if you have any other questions.

To find the number of seats in each row, let's assume the number of rows is 'x'.

According to the problem, the number of seats in each row exceeds the number of rows by 9. So, the number of seats in each row is 'x + 9'.

Now, we know that the total number of seats in the auditorium is 1960.

Since the number of rows is 'x' and the number of seats in each row is 'x + 9', we can set up an equation to solve for 'x':

x * (x + 9) = 1960

To solve this equation, we can multiply the terms and set it equal to 1960:

x^2 + 9x = 1960

Rearranging the terms, we have:

x^2 + 9x - 1960 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use factoring to solve it.

By factoring, we need to find two numbers whose product is -1960 and whose sum is 9.

After factoring, we get:

(x + 49)(x - 40) = 0

Setting each factor to zero gives us two possible solutions:

x + 49 = 0 or x - 40 = 0

Solving these equations gives us:

x = -49 or x = 40

Since the number of rows cannot be negative, we discard x = -49.

Therefore, the number of rows is 40.

To find the number of seats in each row, we substitute this value of x back into our equation:

Number of seats in each row = x + 9 = 40 + 9 = 49

So, the number of seats in each row is 49.