Answer
$\color{blue}{\bf{(a) N(x)=100-x }}$
$\color{blue}{\bf{(b) G(x)=20 +5x }}$
$\color{blue}{\bf{(c) C(x)=(100-x)(20 +5x) }}$
$\color{blue}{\bf{(d) $9600 }}$
Work Step by Step
100 people or fewer attend a party, $x$ is the number less than 100 that attend, or $x=100 - \text{ number of attendees}$.
$\bf{(a)}$ The number of attendees $N$ can be modeled as a function of the number of people who don't attend, $x$.
$\color{blue}{\bf{N(x)=100-x }}$
$\bf{(b)}$ if 100 people attend, it costs $20$ per guest, if less than 100 people attend the cost is $5$ extra per guest.
The cost for each guest is modeled as $G(x)$
$\color{blue}{\bf{G(x)=20 +5x }}$
$\bf{(c)}$ Multiplying the formula for the number of people who attend, $N(x)$, by the formula for the cost for each guest,$G(x)$ gives us the total cost $C(x)$.
$C(x)=N(x)*G(x)$
$\color{blue}{\bf{C(x)=(100-x)(20 +5x) }}$
$\bf{(d)}$ if $80$ people attend:
$x=100-80$
$x=20$
$C(20)=(100-20)(20 +5(20))$
$C(20)=(100-20)(20 +100)$
$C(20)=(80)(120)$
$\color{blue}{\bf{$9600 }}$
