Question

the cost of holding a childrens birthday party at a rollerskating rink is a function of n, the number of people in the party. the cost function, c, can be represented with this set of rules:
$c(n)=\

$$\begin{cases}150, & 0 < n \\leq 12 \\\\ 260, & 12 < n \\leq 20 \\\\ 400, & 20 < n \\leq 30\\end{cases}$$

$
how much does it cost to have a party with 9 people? what about 20 people?
type the answers in the boxes below.

9 people: $\square$

20 people: $\square$

Explanation:

Step1: Determine cost for 9 people

Check the domain for \( n = 9 \). Since \( 0 < 9 \leq 12 \), use \( C(n)=150 \).

Step2: Determine cost for 20 people

Check the domain for \( n = 20 \). Since \( 12 < 20 \leq 20 \) (matches \( 12 < n \leq 20 \)), use \( C(n)=260 \).

Answer:

9 people: $150
20 people: $260