Question

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?

Answer 1

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

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:

`x + y = 6,000`

and

`28x+40y = 193,200`

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
`x + y = 6,000`, and subtracting x to the other side, to get y alone:

`y = 6,000 - x`

Now lets plug in y to our second equation:

`28x + 40(6,000-x) = 193,2000`

=

`28x+240,000-40x = 193,200`

Now combining like terms and solving for x we get:

`-12x + 240,000 = 193,200`

=

`-12x = -46,800`

=

`x=3,900`

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

`3,900 + y = 6,000`

=

`y = 2,100`

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