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)
a+b = 4000
50a+40b = 180000
a = b = 2000
a=2000, b=2000
Please show your steps clearly
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!
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.