Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to use the direct variation formula

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : Algebra

Phillip can paint square feet of wall per minute. What area of the wall can he paint in 2.5 hours?

Possible Answers:

$300y\ ft^2$

$50y\ ft^2$

$2.5y\ ft^2$

$150y\ ft^2$

$25y\ ft^2$

Correct answer:

$150y\ ft^2$

Explanation:

Every minute Phillip completes another square feet of painting. To solve for the total area that he completes, we need to find the number of minutes that he works.

There are 60 minutes in an hour, and he paints for 2.5 hours. Multiply to find the total number of minutes.

$(60\frac{min}{hr})(2.5hr)=150min$

If he completes square feet per minute, then we can multiply by the total minutes to find the final answer.

$(y\frac{ft^2}{min})(150min)=150y\ ft^2$

Report an Error

Example Question #1 : Direct And Inverse Variation

The value of varies directly with the square of and the cube of . If y=24 when x=1 and z=2 , then what is the value of when x=3 and z=1 ?

Possible Answers:

Correct answer:

Explanation:

Let's consider the general case when y varies directly with x. If y varies directly with x, then we can express their relationship to one another using the following formula:

y = kx, where k is a constant.

Therefore, if y varies directly as the square of x and the cube of z, we can write the following analagous equation:

y = kx²z³, where k is a constant.

The problem states that y = 24 when x = 1 and z = 2. We can use this information to solve for k by substituting the known values for y, x, and z.

24 = k(1)²(2)³ = k(1)(8) = 8k

24 = 8k

Divide both sides by 8.

3 = k

k = 3

Now that we have k, we can find y if we know x and z. The problem asks us to find y when x = 3 and z = 1. We will use our formula for direct variation again, this time substitute values for k, x, and z.

y = kx²z³

y = 3(3)²(1)³ = 3(9)(1) = 27

y = 27

The answer is 27.

Report an Error

Example Question #1 : How To Use The Direct Variation Formula

In a growth period, a population of flies triples every week. If the original population had 3 flies, how big is the population after 4 weeks?

Possible Answers:

$729$

$27$

$243$

$81$

$2187$

Correct answer:

$243$

Explanation:

We know that the initial population is 3, and that every week the population will triple.

The equation to model this growth will be i(r)^n , where is the initial size, is the rate of growth, and is the time.

In this case, the equation will be 3(3)^4 .

3(3)^4=3(81)=243

Alternatively, you can evaluate for each consecutive week.

Week 1: 3(3)=9

Week 2: 3(9)=27

Week 3: 3(27)=81

Week 4: 3(81)=243

Report an Error

Example Question #1 : Direct And Inverse Variation

varies directly as and inversely as ; $A = 6s^{2}$ and $V= s^{3}$ . Assuming that no other variables affect , which statement is true of concerning its relationship to ?

Possible Answers:

varies directly as .

None of the other statements are correct.

varies directly as the fifth power of .

varies inversely as the fifth power of .

varies inversely as .

Correct answer:

varies inversely as .

Explanation:

varies directly as and inversely as , meaning that for some constant of variation ,

$\frac{LV}{A}= K$ .

Setting $A = 6s^{2}$ and $V= s^{3}$ , the formula becomes

$\frac{Ls^{3}}{6s^{2}}= K$

$\frac{Ls }{6 }= K$

Ls= 6K

Setting K' = 6K as the new constant of variation, the variation equation becomes

Ls= K' ,

so varies inversely as .

Report an Error

Example Question #1 : How To Use The Direct Variation Formula

varies directly as both and the cube of . Which statement is true of concerning its relationship to ?

Possible Answers:

varies inversely as the cube root of .

varies directly as the cube root of .

varies inversely as the cube of .

None of the other statements is true.

varies directly as the cube of .

Correct answer:

varies inversely as the cube root of .

Explanation:

varies directly as both and the cube of , meaning that for some constant of variation ,

$\frac{x}{yz^{3}} = K$ .

Take the reciprocal of both sides, and the equation becomes

$\frac{yz^{3}}{x} =\frac{1}{ K}$

Take the cube root of both sides, and the equation becomes

$\frac{z\sqrt[3]{y}}{\sqrt[3]{x}} = \sqrt[3]{\frac{1}{ K}}$

$K' = \sqrt[3]{\frac{1}{ K}}$ takes the role of the new constant of variation here, and we now have

$\frac{z\sqrt[3]{y}}{\sqrt[3]{x}} =K'$

so varies inversely as the cube root of .

Report an Error

View PSAT Mathematics Tutors

Joseph
Certified Tutor

CUNY College of Staten Island, Bachelor in Arts, Applied Psychology. New York University, Master of Arts, Applied Psychology.

View PSAT Mathematics Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View PSAT Mathematics Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Phoenix, Spanish Tutors in San Francisco-Bay Area, Computer Science Tutors in Atlanta, GRE Tutors in Seattle, Spanish Tutors in Houston, Calculus Tutors in Philadelphia, MCAT Tutors in Denver, Statistics Tutors in Dallas Fort Worth, Statistics Tutors in New York City, Algebra Tutors in Miami

Popular Courses & Classes

SAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Miami, LSAT Courses & Classes in Phoenix, MCAT Courses & Classes in Los Angeles, ACT Courses & Classes in Phoenix, GRE Courses & Classes in Los Angeles, LSAT Courses & Classes in Atlanta, Spanish Courses & Classes in Boston, SSAT Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in Denver, LSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Boston, GRE Test Prep in Los Angeles, SAT Test Prep in Phoenix, GRE Test Prep in Miami, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Chicago, MCAT Test Prep in Houston, GRE Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

PSAT Math : How to use the direct variation formula

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #61 : Algebra

Example Question #1 : Direct And Inverse Variation

Example Question #1 : How To Use The Direct Variation Formula

Example Question #1 : Direct And Inverse Variation

Example Question #1 : How To Use The Direct Variation Formula

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: