Problema Solution
On a certain route, an airline carries 10,000 passengers per month, each paying $130. A market survey indicates that for each $1 decrease in the ticket price, the airline will gain 60 passengers.
a. Express the number of passengers per month, N, as a function of the ticket price, x.
b. Express the monthly revenue for the route, R, as a function of the ticket price, x.
Answer provided by our tutors
Let x equals the ticket price as it says in the problem.
Now let’s express the decrease in the ticket price. We start with $130, and since we are decreasing the ticket price, we need to use subtraction, so our expression is 130 – x.
Now we need to find the increase in passenger due to the fare decrease.
The increase in passengers is equal to 60 times whatever the decrease in price is: 60(130 – x).
The number of passengers depends on the ticket price. This is the original number, 10,000 plus the number added due to the decrease:
N(x) = 10,000 + 60(130 - x)
We can simplify
N(x) = 17,800 - 60x
For the second question we want to know the monthly revenue for the route.
Revenue is equal to price times quantity. In our case it is the ticket price (x) times the number of passengers, N(x):
R(x) = x*N((x)
R(x) = x*(17,800 - 60x)
R(x) = 17,800x - 60x^2