FINDING DEPENDENT AND INDEPENDENT VARIABLES

Problem 1 :

A plumber charges $35 to make a house call, plus $25 an hour for labor. The following equation represents c, the total cost of a visit for h hours:

c = 25h + 35

What is the independent variable?

A) Number of hours worked

B) Amount of money paid

C) Price of labor

D) House call charge

Solution :

Here "h" represents the number of hours he worked, based on this value the total cost paid will differ.

So, h(number of hours he worked) is the independent and c is dependent.

Problem 2 :

The table below represents the relationship between the number of gallons of gas in a gas tank and the number of miles that can be driven. What is the independent variable in this situation?

A) Miles that can be driven

B) Gallons of gas in tank

C) Miles per gallon

D) Price per gallon

Solution :

Variables involved = gallons in the tank and miles can drive

Independent variable = gallons of gas in the tank

Problem 3 :

Maurice answered all 25 questions on a multiple-choice history exam. His score was computed by multiplying the number of wrong answers by 4 and then subtracting that number from 100.

What quantity represents the independent variable and what quantity represents the dependent variable in this situation? 

Solution :

Total number of questions answered incorrectly = x and total score = y.

y = 100 - 4x

Based on number of questions answered incorrectly the total score will change. So, 

Independent variable = x (number of questions answered incorrectly)

and dependent variable = y (Total score)

Problem 4 :

The cost for copying a document is a function of the number of pages in the document. In this situation, what is the dependent variable?

A) The cost         B) The number of pages

C) The document       D) The function

Solution :

Independent variable = number of pages in the document

The cost = dependent variable.

Problem 5 :

Sean partially filled a container with water. The container was shaped like a rectangular prism and had dimensions 9 inches long, 8 inches wide, and 10 inches high.

If h represents the height of the water (in inches), and the volume V (in cubic inches) of the water is given by the formula V = 72h , which quantity is the independent variable?

A) The height of the container

B) The volume of the container

C) The height of the water in the container

D) The volume of the water in the container

Solution :

h is the independent variable, height of water in the container.

Problem 6 :

A taxi driver charges an initial fee of $2.00 plus $0.30 per mile. What is the independent variable quantity in this situation?

A) The initial fee

B) The total cost charged by the driver

C) The cost per each mile driven

D) The number of miles driven 9

Solution :

Initial cost = $2

0.30 per mile

So, cost per mile driven will be the independent variable.

Problem 7 :

A long distance telephone company charges $4.95 per month and $0.07 per minute for phone calls. What is the dependent variable quantity in this situation?

A) The cost per minute for a long distance call

B) The total cost for a 10-minute long distance call

C) The total monthly charge for long distance service

D) The number of minutes of a long distance call

Solution :

Based on the number of minutes, the amount we pay at last will differ. So,

independent variable = number of minutes of a long distance call

dependent variable = total monthly charge for long distance service.

Problem 8 :

Connie received a statement from her bank listing the balance in her savings account for the past four years. What is the dependent quantity in this table?

Solution :

By observing the table, as every year increasing, the amount is also increasing. So, dependent quantity is balance.

Problem 9 :

For a car traveling at a speed of 50 miles per hour, the relationship between the distance traveled, d, and the time traveled, t, is described by the function d = 50t. Which statement is true?

A) The time traveled depends on the distance traveled.

B) The distance traveled depends on the time traveled.

C) The speed of the car depends on the distance traveled.

D) The speed of the car depends on the time traveled.

Solution :

When t = 1, d = 50.

When t = 2, d = 100

So, the distance traveled depends on the time traveled.

Problem 10 :

To find c, the total cost of an order of DVDs from a certain website, the equation c = 19.99 n + 4.99 can be used, where n represents the number of DVDs ordered. If c is a function of n, which of the following best describes this relationship?

A) The value of n is constant in relation to c.

B) The value of n is dependent on c.

C) The value of c is constant in relation to n.

D) The value of c is dependent on n.

Solution :

The value of c is dependent on n.

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