A 5000 -seat theater has tickets for sale at $\$ 27$ and $\$ 40$. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $\$ 150,600$ ?

Step 1 ：Let's denote the number of $27 tickets as x and the number of $40 tickets as y.

Step 2 ：We know that the total number of tickets is 5000, so we can write the equation as \(x + y = 5000\).

Step 3 ：We also know that the total revenue is $150,600, so we can write another equation as \(27x + 40y = 150600\).

Step 4 ：We can solve this system of equations to find the values of x and y.

Step 5 ：The solution to the system of equations is x = 3800 and y = 1200.

Step 6 ：This means that 3800 tickets should be sold at $27 and 1200 tickets should be sold at $40 to generate a total revenue of $150,600.

Step 7 ：Final Answer: \(\boxed{3800 \text{ tickets at } \$27 \text{ and } 1200 \text{ tickets at } \$40}\).