Question

finding inputs and outputs in a story context
a local pet groomer charges $9.50 for each dog plus a reservation fee of $35. they wash a maximum of 60 dogs. let $c(x)$ represent the total cost from the pet groomer and $x$ represent the number of dogs washed. round your answers to the nearest hundredth as needed.
calculate $c(12)$.
complete the following sentence to explain the meaning of your answer.
the cost for having blank dogs washed is blank dollars.
find $x$ when $c(x)=187$
complete the following sentence to explain the meaning of your answer.
the cost for having blank dogs washed is blank dollars.
question help: video message instructor

Explanation:

Step1: Determine the cost - function formula

The cost function $C(x)$ is given by the sum of the reservation fee and the cost per dog times the number of dogs. So, $C(x)=9.5x + 35$.

Step2: Calculate $C(12)$

Substitute $x = 12$ into the cost - function: $C(12)=9.5\times12+35$. First, calculate $9.5\times12 = 114$. Then, $C(12)=114 + 35=149$.

Step3: Find $x$ when $C(x)=187$

Set up the equation $187=9.5x + 35$. Subtract 35 from both sides: $187−35=9.5x$, which simplifies to $152 = 9.5x$. Then, divide both sides by 9.5: $x=\frac{152}{9.5}=16$.

Answer:

The cost for having 12 dogs washed is 149 dollars.
The cost for having 16 dogs washed is 187 dollars.