Question

A charter flight charges a fare of $300 per person, plus $6 per person for each unsold seat on the plane. The plane holds 200 passengers, and x represents the number of unsold seats.

(a) Find an expression for the total revenue received for the flight.

A) Rx) = 200(300 + 6x)
B) Rx) = 300(200 - x) + 6x
C) Rx) = 300(200 + x) - 6x
D) Rx) = 200(300 - 6x)

Answer 1

The correct expression for the total revenue received for the charter flight, with x representing the number of unsold seats, is B) R(x) = 300(200 - x) + 6x. This formula accounts for both the revenue from sold seats and the additional charge for unsold seats.

Step-by-step explanation:

The question is asking to find an expression for the total revenue received from a charter flight that charges $300 per person and additionally charges $6 for each unsold seat on the plane, which can hold 200 passengers. Let x represent the number of unsold seats on the plane.

To determine the total revenue (R(x)), you calculate the amount made from the seats that are sold (200 - x seats are sold at $300 each) and the amount made from the unsold seats (x seats each bring an additional $6). So the total revenue is given by the equation:

R(x) = 300(200 - x) + 6x

This simplifies to:

R(x) = 60000 - 300x + 6x

R(x) = 60000 - 294x

Given the options available, the correct expression that represents the total revenue received for the flight is:

B) R(x) = 300(200 - x) + 6x