Question

finding inputs and outputs in a story context
a local catering company charges $9.00 for each person plus a reservation fee of $35. they serve a maximum of 20 people. let $c(x)$ represent the total cost from the catering company and $x$ represent the number of people served. round your answers to the nearest hundredth as needed.
calculate $c(20)$.
complete the following sentence to explain the meaning of your answer.
the cost for having people served is dollars.
find $x$ when $c(x)=89$
complete the following sentence to explain the meaning of your answer.
the cost for having people served is dollars.
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Explanation:

Step1: Determine the cost - function formula

The cost function $C(x)$ is given by the formula $C(x)=9x + 35$, where $9$ is the cost per person and $35$ is the reservation fee.

Step2: Calculate $C(20)$

Substitute $x = 20$ into the formula $C(x)=9x + 35$. So $C(20)=9\times20+35=180 + 35=215$.

Step3: Find $x$ when $C(x)=89$

Set up the equation $9x+35 = 89$. First, subtract 35 from both sides: $9x=89 - 35=54$. Then divide both sides by 9: $x=\frac{54}{9}=6$.

Answer:

The cost for having 20 people served is 215 dollars.
The cost for having 6 people served is 89 dollars.