theater has 650 seats. Regular seats cost $20 balcony seats cost $12. Total ticket sales for one performance were $11,600. How many balcony seats in theater?

Question

I have done so many of these but for some reason I cant figure a couple out, please help.

Answer 1

Hi Caleb,

 

Let's begin by assigning a letter to our unknown:

    x (number of balcony seats)

 

Next, we'll come up with an expression to represent the number of regular seats in terms of the number of balcony seats:

    650 - x (total seats - number of balcony seats)

 

Now we'll come up with an equation to represent the give total ticket sales in terms of the given price for each kind of seat and our expressions for the numbers of kind of seat:

    (20)(x) + (12)(650 - x) = 11,600

 

Now we'll solve our equation for our unknown (x):

    20x + 7,800 - 12x = 11,600

    8x + 7,800 = 11,600

    8x = 11,600 - 7,800

    8x = 3800

      x = 3800/8

      x = 475 (number of balcony seats)

 

We can verify that our answer is correct by plugging in our value for x and see if the sum of the ticket sales for each kind of seat is equal to the given total ticket sales:

    (20)(x) + (12)(650 - x) = 11,600

    (20)(475) + (12)(650 - 475) = 11,600

    9,500 + 12(175) = 11,600

    9,500 + 2,100 = 11,600

    11,600 = 11,600 (answer is correct)  

 

Once we were able to express our desired unknown in terms of the other needed unknown, we were able to come up with the right equation to get our answer. 

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.