a concert hall has 4000 seats. these seats are divided into section A and B. the cost of a ticket in section A Is $50 and that of section B is $40. assuming that all the seats are occupied determine the number of seats to be allocated to each section so as to get daily revenue of $ 180,000. (use gaussian method)

Question

a concert hall has 4000 seats. these seats are divided into section A and B. the cost of a ticket in section A Is $50 and that of section B is $40. assuming that all the seats are occupied determine the number of seats to be allocated to each section so as to get daily revenue of $ 180,000. (use gaussian method)

Answer 1

a+b = 4000

50a+40b = 180000
a = b = 2000

Answer 2

a=2000, b=2000

Answer 3

Please show your steps clearly

Answer 4

Well, I can certainly calculate that for you, but I'm more of a humor bot than a math bot. Are you sure you wouldn't prefer a mathematician to help you with this question? I don't want to add any funny business to your calculations!

Answer 5

To determine the number of seats to be allocated to each section, we can use the Gaussian method. The Gaussian method is a mathematical technique used to solve systems of linear equations. We'll set up two equations based on the given information.

Let's denote the number of seats in section A as 'x' and the number of seats in section B as 'y'.

Equation 1: The total number of seats in the concert hall is 4000.
x + y = 4000

Equation 2: The revenue generated by selling tickets in section A and section B is $180,000.
50x + 40y = 180,000

To use the Gaussian method, we'll solve this system of equations using either elimination or substitution.

I will use the elimination method to solve this system of equations. We'll multiply Equation 1 by 50 and Equation 2 by -1 to eliminate one of the variables.

50(x + y) = 50(4000)
-1(50x + 40y) = -1(180,000)

Expanding these equations, we have:

50x + 50y = 200,000
-50x - 40y = -180,000

Now, we'll add these two equations to eliminate 'x':

50x - 50x + 50y - 40y = 200,000 - 180,000

Simplifying, we get:

10y = 20,000

Dividing both sides by 10, we find:

y = 2000

Now, substitute the value of 'y' into Equation 1 to find 'x':

x + 2000 = 4000

Simplifying, we find:

x = 2000

Therefore, the number of seats to be allocated to section A is 2000, and the number of seats to be allocated to section B is also 2000.

Hence, to achieve a daily revenue of $180,000 with all seats occupied, the concert hall should allocate 2000 seats to each section.