Certainly! Let's break this down step by step:
1. Identify the Variables:
- Let [tex]\( x \)[/tex] be the number of unsold seats.
- The plane holds 100 passengers.
2. Number of People Flying:
Since [tex]\( x \)[/tex] accounts for the unsold seats, the number of people flying is:
[tex]\[
\text{Number of people flying} = 100 - x
\][/tex]
3. Price per Ticket:
The fare per person is [tex]$\$[/tex]300[tex]$, and an additional $[/tex]\[tex]$30$[/tex] is charged for each unsold seat. Therefore, the price per ticket is:
[tex]\[
\text{Price per ticket} = 300 + 30x
\][/tex]
4. Total Revenue Expression:
The total revenue [tex]\( R(x) \)[/tex] is the number of people flying multiplied by the price per ticket. Therefore, we multiply the expressions from steps 2 and 3:
[tex]\[
R(x) = (100 - x) \times (300 + 30x)
\][/tex]
Therefore, the expression for the total revenue received for the flight, [tex]\( R(x) \)[/tex], is:
[tex]\[
R(x) = (100 - x) \times (300 + 30x)
\][/tex]
