Question

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $184,000?The number of tickets for sale at $24 should be….The number of tickets for sale at $40 should be….

Answer 1

The number of tickets for sale at $24 should be 3,500.

The number of tickets for sale at $40 should be 2,500.

Step-by-step explanation

Let the number of tickets sold for $24 be x.

Let the number of tickets sold for $40 be y.

The total number of seats is 6000. This implies that:

`x+y=6000`

The total revenue that is to be generated is $184,000. This implies that:

`24x+40y=184,000`

Now, we have two simultaneous equations:

`\begin{gathered} x+y=6000 \\ 24x+40y=184,000 \end{gathered}`

From the first equation, make x subject of the formula:

`x=6000-y`

Substitute that into the second equation:

`\begin{gathered} 24(6000-y)+40y=184,000 \\ 144,000-24y+40y=184,000 \\ \Rightarrow16y=184,000-144,000=40,000 \\ \Rightarrow y=(40,000)/(16) \\ y=2,500 \end{gathered}`

Substitute the value of y into the equation for x:

`\begin{gathered} x=6000-2500 \\ x=3,500 \end{gathered}`

Therefore, the number of tickets for sale at $24 should be 3,500 and the number of tickets for sale at $40 should be 2,500.