finding inputs and outputs in a story context\na local catering company charges $9.00 for each person plus a…
finding inputs and outputs in a story context\na 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.\ncalculate $c(20)$.\ncomplete the following sentence to explain the meaning of your answer.\nthe cost for having people served is dollars.\nfind $x$ when $c(x)=89$\ncomplete the following sentence to explain the meaning of your answer.\nthe cost for having people served is dollars.\nquestion help: video message instructor\nsubmit question jump to answer
Answer
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.