Question

A charter airline finds that on its Saturday flights from Philadelphia to London all 180 seats will be sold if the ticket price is $200. However, for each $3 increase in ticket price, the number of seats sold decreases by one. (a) Find a formula for the number of seats sold S if the ticket price is P dollars.

Answer 1

Answer:

$S = -\dfrac{1}{3}P+\dfrac{740}{3}$

Step-by-step explanation:

Given that:

Number of seats sold is 180 with ticket price $200.

Number of seats decreases by one when the ticket price is increased by $3.

To find:

The formula for the number of seats sold (S) when the ticket price is P dollars.

Solution:

It is linear dependency of number of seats sold, S on ticket price, P.

$S\propto P$

It can be written as:

$S = kP+C$

Where $k$ is the constant of proportionality and

$C$ is a constant.

Now, putting the given values:

$180 = 200k +C ..... (1)$

$179 = 203k+C$ ...... (2)

Subtracting (1) from (2):

$3k = -1\\\Rightarrow k =-\dfrac{1}{3}$

Putting the value in (1):

$\Rightarrow C = 180+\dfrac{200}{3} = \dfrac{740}{3}$

Therefore the equation becomes:

$S = -\dfrac{1}{3}P+\dfrac{740}{3}$