Chapter 8.1, Problem 9CYU

(a)

To determine

To identify: the independent and dependent variables.

Answer to Problem 9CYU

The required function is $c\left(s\right)=125+15s$

Explanation of Solution

Given:

Spent $215 for family portrait

The portrait package costs $125

photographer charges $15 per person

Calculation:

Let c be the total cost and s be the total number of persons in the portrait

Since the total cost depends on the number of persons in the portrait, total cost c be the dependent variable and total number of persons s be the independent variable.

Words: Total cost = $125 + sitting fee per person times number of persons

Function: $c\left(s\right)=125+15s$

Conclusion: Therefore, the required function is $c\left(s\right)=125+15s$

(b)

To determine

To find: the number of people in the portrait.

Answer to Problem 9CYU

The total number of persons in the portrait is 6.

Explanation of Solution

Calculation:

Need to find the number of people in the portrait using above equation

Consider the equation

  $c\left(s\right)=125+15s$

Substitute $c\left(s\right)=215$ in above equation

  $\begin{array}{l}215=125+15s\hfill \\ 215-125=15s\text{ Simplify}\hfill \\ 90=15s\hfill \\ \frac{90}{15}=s\text{ Divide each side by }15\hfill \\ 6=s\hfill \\ \hfill \\ \hfill \end{array}$

Conclusion: Therefore, the total number of persons in the portrait is 6.