Question

The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 80 balcony tickets and 53 general admission floor tickets for Friday’s show, for a total of 5,485 in receipts. For saturday’s show, 78 balcony tickets and 48 genera admission floor tickets have been sold, equaling 5,256 in receipts. How much does each ticket cost?

Answer 1

Using a system of linear equations, we found that the cost of a balcony ticket is approximately $51.34, and the cost of a general admission floor ticket is $26.

Step-by-step explanation:

To solve this problem, let’s use a system of linear equations. We have two types of tickets, balcony and general admission floor tickets, and the total receipts provide us with the equations. For Friday’s show, the equation based on the given information is:

80B + 53G = 5485

And for Saturday’s show, the equation is:

78B + 48G = 5256

We can solve this system of equations using either substitution or elimination methods. Let's use the elimination method for this example.

To eliminate one of the variables, we can multiply the entire first equation by 78, and the second by 80, giving us:

(1) 6240B + 4134G = 428,130

(2) 6240B + 3840G = 420,480

Now, let's subtract equation (2) from (1) to eliminate B:

4134G - 3840G = 428,130 - 420,480

294G = 7,650

G = 7,650 / 294

G = 26

We now have the price of a general admission floor ticket. Let’s substitute G back into one of our original equations to find B:

80B + 53(26) = 5485

80B + 1378 = 5485

80B = 4107

B = 4107 / 80

B = 51.34

Thus, the cost of a balcony ticket is approximately $51.34, and the cost of a general admission floor ticket is $26.