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 this problem down step-by-step.
1. Identify the components of the total cost:
- The cafe charges [tex]\( \$ 15 \)[/tex] per person. Therefore, if [tex]\( x \)[/tex] people attend the party, the total cost for this part is [tex]\( 15x \)[/tex].
- There is an additional flat fee of [tex]\( \$ 22 \)[/tex] for music.
2. Formulate the total cost:
- The total cost for the party, combining both the per-person charge and the flat music fee, is:
[tex]\[
\text{Total cost} = 15x + 22
\][/tex]
3. Calculate the average cost per person:
- To find the average cost per person, we need to divide the total cost by the number of people attending the party, [tex]\( x \)[/tex]:
[tex]\[
\text{Average cost per person} = \frac{15x + 22}{x}
\][/tex]
4. Identify the correct function:
- From the given options, the function that matches the formulation we derived is:
[tex]\[
D. \ C(x) = \frac{15x + 22}{x}
\][/tex]
Thus, the correct function that describes the average cost per person for Sarah's party in terms of [tex]\( x \)[/tex] is:
Option D: [tex]\( C(x) = \frac{15x + 22}{x} \)[/tex]
Therefore, the correct answer is:
Option D: [tex]\( C(x) = \frac{15x + 22}{x} \)[/tex]
