A 6000 ​seat theater has tickets for sale at ​$25 and ​$40? How many tickets should be sold at each price for a performance to get total revenue of ​$174000?

Question

due in an hour please help very confused

Answer 1

Here is an easy way to understand the problem and to do the calculations. This a simultaneous equations problem. You are given both of them when you are told that there are six thousand seats of two kinds, which may be called X and Y; that the prices of the tickets are $25 and $40; and that the revenue must add up to $174,000.

 

The number of X and Y seats is 6,000.

So X + Y = 6,000

The number of dollars can then be matched up to form the other equation by finding all the facts with a dollar sign.

So, there are X seat at $25 each and Y seats at $40 each totaling $174,000. "At" means multiply.

This is the same thing as saying 25X + 40Y = 174,000.

 

But we don't like two variables. It would be nice for one of them to subtract out before we go any further.

So if we take our easier equation and multiply all of its terms by the smallest number in the other equation, we get:

(25)X + (25)Y = (25) 6,000

Which simplifies to: 25X + 25Y = 150,000

 

Now put the equations together and subtract to get rid of one of the variables:

 

25X + 40Y = 174,000

25X + 25Y = 150,000

__________________

 

          15Y = 24,000  Divide each side by 15 to get

              Y =  1,600

 

Now 25X + 40 (1,600) = 174,000  Which simplifies to:

 

        25X +     64,000   = 174,000  Subtract 64,000 from both sides to get:

 

       25X             =  110,000  Divide each side by 25 to get:

    

          X             =    4,400

 

To summarize, 1,600 $40 tickets plus 4,400 $25 tickets gets you $174,000.

Answer 2

Hi Sophie,

 

X = number of $25 tickets

 

Y = number of $40 tickets

 

X + Y = 6000

 

25X + 40Y = 174,000

 

25(6000 - Y) + 40Y = 174,000

 

150,000 -25Y + 40Y = 174000

 

15Y = 24000

 

Y = 1600

 

X + 1600 = 6000

 

X = 4400

 

4400 $25 tickets should be sold and 1600 $40 tickets

 

Have a good night