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 $1
increase in price. For what prices p can the manager predict that at least 800 tickets
will be sold?

Answer 1

Answer:

$p\leq\ 70.$

Step-by-step explanation:

The 1000 tickets will be sold when each ticket costs $60.

The manager wants to sell at least 800 tickets which is maximum

1000-800=200 tickets less than 1000.

Given that for 20 less tickets will be sold for every $1  increase in price.

So, 20x2=40 less tickets will be sold for $1x2=$2  increase in price.

Proceeding in a similar way, for any natural number n:

20 x n less tickets will be sold for $1 x n=$n  increase in price.

Here, 200=20x10, so n=10

So, 20x10 less tickets will be sold for $1x10=$10  increase in price.

Hence, the manager can increase the price of each ticket up to $10.

So, to sell at least 800 tickets, the maximum price of each ticket can be $60+$10=$70.

Hence, the value of $p$ is

$p\leq\ 70.$