Chapter 4, Problem 26CCSR

(a)

To determine

To identify: Independent and dependent variables

Answer to Problem 26CCSR

Independent variable: Number of loads of laundry

Dependent variable: Gallons of water used

Explanation of Solution

Given information:

For every load of laundry, washing machine uses an average of 41 gallons of water

Definition:

Independent variable is a variable the controller changes and dependent variable is a variable that is affected by the changes in independent variable.

For every loads of laundry, 41 gallons of water is used. Usage of water depends on the number of loads of laundry. So, independent variable is the number of loads of laundry.

Amount of water used depends on the loads. So dependent variable is the amount of water used

Independent variable: Number of loads of laundry

Dependent variable: Gallons of water used

(b)

To determine

To write: A function rule to represent the given situation

Answer to Problem 26CCSR

  $f(n)=41n$

Explanation of Solution

Given information:

For every load of laundry, washing machine uses an average of 41 gallons of water

Calculation:

The amount of water used is directly proportional to the number of loads of laundry. So we apply function rule

  $f(x)=mx$

Let ‘n’ represents the number of loads and f(n ) represents the gallons of water

Slope m is the average gallons of water used.

  $\begin{array}{l}f(x)=mx\\ m=41\\ Function-rule\\ f(n)=41n\end{array}$

(c )

To determine

To calculate: The number of loads of laundry you wash when 533 gallons of water is used

Answer to Problem 26CCSR

13 loads

Explanation of Solution

Given information: 533 gallons of water is used. We know the function rule

  $f(n)=41n$

where ‘n’ represents the number of loads and f(n ) represents the gallons of water

Calculation: Substitute 533 for f(n) and solve for n

  $\begin{array}{l}f(n)=41n\\ 533=41n\\ \frac{533}{41}=\frac{41n}{41}\\ 13=n\\ n=13\end{array}$

So, 13 loads of laundry washed using 533 gallons of water