Question

A ticket owner wants to divide a 3600-seat theater into three sections, with tickets costing $40, $70, or $100, depending on the section. He wants to have twice as many $40 tickets as the sum of the other two types, and he wants to earn $192,000 from a full hour. Find how many seats he should have in each section.

Answer 1

To solve the division of a 3600-seat theater into sections with different ticket prices to meet a revenue goal, we set up a system of equations based on provided conditions and solve for the number of seats in each section.

Step-by-step explanation:

The question asks us to solve a problem involving dividing a 3600-seat theater into three sections with different ticket prices and certain conditions to meet a revenue goal. To find out how many seats should be in each section, we need to define variables for the number of tickets in each section and set up equations based on the given conditions. Let x be the number of $40 tickets, y the number of $70 tickets, and z the number of $100 tickets.

According to the problem, the following conditions are given:

1. The total number of seats is 3600: x + y + z = 3600
2. There are twice as many $40 tickets as the sum of the other two types: x = 2(y + z)
3. The total revenue from selling all the tickets is $192,000: 40x + 70y + 100z = 192,000

Using these three equations, we can solve for x, y, and z to determine the number of tickets in each section.