Question

A 6000-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 $189600?

Answer 1

Answer:

4200 tickets of $\ 28$ and 1800 tickets of $\ 40$ were sold

Step-by-step explanation:

Given:

Tickets are sold at price $\ 28$ and $\ 40$.

Let Number of tickets sold at price $\ 28$ be $x$.

Let Number of tickets sold at price $\ 40$ be $y$.

Theater has maximum capacity of 6000 seat.

Hence,

$x+y=6000 \ \ \ \ equation \ 1$

Total revenue to be generated is $\ 189600$

$\therefore 28x + 40y= 189600 \ \ \ \ equation \ 2$

Now Multiplying equation 1 by 40 we get,

$x+y=6000\\40x+40y=240000\ \ \ \ equation \ 3$

Now Subtracting equation 2 by equation 3 we get,

$(40x+40y=240000)- (28x + 40y= 189600)\\12x=50400\\\\x=\frac{50400}{12}=4200$

Now substituting value of x in equation 1 we get,

$x+y=6000\\4200+y=6000\\y=6000-4200= 1200$

Hence a total of 4200 tickets of $\ 28$ and 1800 tickets of $\ 40$ were sold