Question

A theater manager predicts that 1000 tickets to a play will be sold if each ticket costs $60.The manager predicts that 20 less tickets will be sold for every increase in price. For what prices can the manager predict that at least 800 tickets will be sold?

Answer 1

To determine the prices at which the manager can predict that at least 800 tickets will be sold, an equation is set up and solved. The possible prices range from $60 to $70.

Step-by-step explanation:

To determine the prices at which the manager can predict that at least 800 tickets will be sold, we need to set up an equation and solve for the ticket prices. Let's start by setting up an equation:

x = price increase in dollarst

(x) = number of tickets sold when the price increases by x dollars

We know that when the ticket price is $60, 1000 tickets are sold. So we have:

t(0) = 1000 (when x = 0, the price increase is $0)

The manager predicts that 20 less tickets will be sold for every increase in price, so we can write the equation as:

t(x) = 1000 - 20x

We want to find the prices at which at least 800 tickets will be sold, so we set up the inequality:

1000 - 20x ≥ 800

To solve for x, we subtract 800 from both sides:

-20x ≥ -200

Next, divide both sides by -20, remembering to reverse the inequality:

x ≤ 10

Therefore, the manager can predict that at least 800 tickets will be sold for prices up to $10 above the base price of $60. So the possible prices range from $60 to $70.