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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

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