Select the correct answer.

Sarah is planning a party at a cafe. The cafe charges a fee of [tex]$\$[/tex] 15[tex]$ per person, plus an additional flat fee of $[/tex]\[tex]$ 22$[/tex] for music.

Which of the following functions describes the average cost per person for Sarah's party in terms of [tex]$x$[/tex], the number of people attending the party?

A. [tex]$C(x)=\frac{\$[/tex] 15+\[tex]$ 22 x}{37}$[/tex]

B. [tex]$C(x)=\frac{\$[/tex] 37}{x}[tex]$

C. $[/tex]C(x)=\frac{\[tex]$ 15+\$[/tex] 22 x}{x}[tex]$

D. $[/tex]C(x)=\frac{\[tex]$ 15 x+\$[/tex] 22}{x}$



Answer :

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]