To determine the correct function that describes the average cost per person for Sarah's party in terms of [tex]\( x \)[/tex], the number of people attending the party, let's break down the components of the cost.
1. Cost Calculation:
- The cafe charges [tex]\( \$15 \)[/tex] per person.
- There is an additional flat fee of [tex]\( \$22 \)[/tex] for music.
2. Total Cost:
- If [tex]\( x \)[/tex] is the number of people attending the party, the total cost from the per-person charge would be [tex]\( 15x \)[/tex] dollars.
- Adding the flat fee of [tex]\( \$22 \)[/tex], the total cost can be expressed as:
[tex]\[
\text{Total Cost} = 15x + 22
\][/tex]
3. Average Cost Per Person:
- To find the average cost per person, we divide the total cost by the number of people ([tex]\( x \)[/tex]).
[tex]\[
\text{Average Cost Per Person} = \frac{15x + 22}{x}
\][/tex]
4. Selection of the Correct Function:
- We need to match this expression with one of the given options.
- Option D is: [tex]\( C(x) = \frac{15x + 22}{x} \)[/tex]
Therefore, the correct function that describes the average cost per person for Sarah's party in terms of [tex]\( x \)[/tex], the number of people attending the party, is:
[tex]\[
\boxed{4}
\][/tex]
