nbra7445
Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

A 6,000​-seat theater has tickets for sale at ​$28 and ​$40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of ​$​193,200?

Sagot :

bowmaian000

Answer:

2,100 $28 tickets were sold, and 3,900 $40 tickets were sold!

Step-by-step explanation:

So, we need to write two equations in order to solve this:

We will think of 28 dollar tickets as x, 40 dollar tickets as y.

Now lets make those equations:

[tex]x + y = 6,000[/tex]

             and

[tex]28x+40y = 193,200[/tex]

Now, to solve for x and y, lets set a value for x or y. In this case I will set the value of y:

I will do this by taking [tex]x + y = 6,000[/tex], and subtracting x to the other side, to get y alone:

[tex]y = 6,000 - x[/tex]

Now lets plug in y to our second equation:

[tex]28x + 40(6,000-x) = 193,2000[/tex]

=

[tex]28x+240,000-40x = 193,200[/tex]

Now combining like terms and solving for x we get:

[tex]-12x + 240,000 = 193,200[/tex]

=

[tex]-12x = -46,800[/tex]

=

[tex]x=3,900[/tex]

Now that we know x, lets solve for y by plugging into our first equation!

[tex]3,900 + y = 6,000[/tex]

=

[tex]y = 2,100[/tex]

So now we know that our answer is:

2,100 $28 tickets were sold, and 3,900 $40 tickets were sold!

Hope this helps! :3

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.