Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : How To Find The Solution To An Equation

If the diameter of a car wheel is 1 foot, how many miles has the car gone after 3500 revolutions?

Possible Answers:

$3.5$

$50.1$

$13.5$

$2.1$

$10.2$

Correct answer:

$2.1$

Explanation:

The circumference of the tire is therefore pi, meaning that in 3500 revolutions the car will go 10,995.6 feet. Dividing by 5280 feet per mile yields 2.1 miles.

Report an Error

Example Question #1781 : Act Math

A chemistry student needs to dilute 1 L of 75%-acid solution. How much water should be added to yield a 25%-acid solution?

Possible Answers:

1 L

2.5 L

3 L

2 L

1.75 L

Correct answer:

2 L

Explanation:

$V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}$ where = volume and = percent

Pure water = 0% and pure acid = 100%

So the equation to solve becomes

x(0) + 1 (0.75) = (x + 1)(0.25)

0.75 = 0.25 + 0.25x

So 2 L of pure water should be added to 1 L 75%-acid solution to yield 25%-acid solution.

Report an Error

Example Question #1782 : Act Math

The Teddy Bear Parade makes teddy bears. Their monthly fixed costs are $550. It costs $25 to make each bear and they sell for $50 each.

What is the monthly break-even point?

Possible Answers:

Correct answer:

Explanation:

The break-even point occurs when the costs are the same as the revenue.

Let = number of teddy bears sold

Revenue: 50x

Costs: 25x + 550

So when Costs = Revenue we have the break-even point thus the equation to solve becomes 50x = 25x + 550 or 25 x = 550 .

So to break-even, 22 teddy bears must be sold.

Report an Error

Example Question #11 : Equations / Inequalities

The Teddy Bear Parade makes teddy bears. Their monthly fixed costs are $550. It costs $25 to make each bear and they sell for $50 each.

To make a profit of $750, how many teddy bears must be sold?

Possible Answers:

Correct answer:

Explanation:

Profits = Revenue - Costs

Let = number of teddy bears sold.

Revenue: 50x

Costs: 25x + 550

Profits = 50x - (25x + 550) or 25x -550

So the equation to solve becomes 750 = 25x - 550

So to make a profit of $750, 52 teddy bears must be sold.

Report an Error

Example Question #1784 : Act Math

How much pure acid should be added to 1 L of 50%-acid solution to yield a 75%- acid solution?

Possible Answers:

1 L

0.50 L

0.75 L

2.50 L

1.50 L

Correct answer:

1 L

Explanation:

Pure water is 0% and pure acid is 100%.

$V_{1}P_{1} +V_{2}P_{2} = V_{f}P_{f}$ where = volume and = percent.

Let = amount of pure acid to add.

So the equation to solve becomes

(1)(0.50) + (x)(1.00) = (1 + x)(0.75)

Thus 1 L of 50%-acid solution added to 1 L of pure acid solution yields 2 L of 75%-acid solution.

Report an Error

Example Question #292 : Algebra

Charlie's Cookies sells desserts. Their monthly fixed costs are $350. It costs $10 to make a dozen cookies. They sell each dozen for $15.

How many cookies must be sold each month to break-even?

Possible Answers:

$840 \; cookies$

$960 \; cookies$

$720 \; cookies$

$700 \; cookies$

$880 \; cookies$

Correct answer:

$840 \; cookies$

Explanation:

The break-even point occurs when the revenues equal the costs.

Let = number of dozens of cookies sold.

Costs : 10x + 350

Revenues : 15x

Costs = Revenues to break-even.

So the equation to solve becomes 10x + 350 = 15x

350 = 5x

So 70 dozen cookies must be sold to break-even, thus $70\cdot 12 = 840$ cookies.

Report an Error

Example Question #1782 : Act Math

Charlie's Cookies sells desserts. Their monthly fixed costs are $350. It costs $10 to make a dozen cookies. They sell each dozen for $15.

The company wants to make a profit of $500. How many dozens of cookies must be sold to reach their profit goal?

Possible Answers:

$145 \; dozen$

$125 \; dozen$

$70 \; dozen$

$200 \; dozen$

$170 \; dozen$

Correct answer:

$170 \; dozen$

Explanation:

Profit = Revenue - Costs

Let = number of dozens of cookies sold.

Profit = 15x - (10x + 350) = 5x - 350

So the equation to solve becomes 500 = 5x - 350 .

So the company must sell 170 dozen cookies to make a $500 profit.

Report an Error

Example Question #12 : Equations / Inequalities

Mike and Joey live 215 miles apart. They meet at a campground between them. Mike drove 50 mph and Joey drove 60 mph and left one hour after Mike. How far did Mike travel?

Possible Answers:

$100 \; miles$

$150 \; miles$

$90 \; miles$

$85 \; miles$

$125 \; miles$

Correct answer:

$125 \; miles$

Explanation:

The distance Mike traveled plus the distance Joey traveled is the total distance between them.

$Distance = Rate \cdot Time$

Let = hours traveled

So the equation to sovle becomes 50t + 60(t - 1) = 215

Thus t = 2.5 hours traveled

So Mike traveled $50 \; mph \cdot 2.5 \; hr = 125\; miles$ .

And Joey traveled $60 \; mph \cdot 1.5 \; hr = 90 \; miles$ .

Report an Error

Example Question #12 : How To Find The Solution To An Equation

What is the value of when 7 + 3x = 6x - 5 ?

Possible Answers:

$\frac{3}{2}$

$\frac{1}{4}$

$\frac{2}{3}$

Correct answer:

Explanation:

Simply solve for by adding five to both sides and then dividing both sides by three to get by itself.

Report an Error

Example Question #16 : How To Find The Solution To An Equation

By how much is the value of 5x^2 - y greater than the value of 4x^2 - 2y when x=2 and y=6 ?

Possible Answers:

Correct answer:

Explanation:

Input and into both equations. Solve them and then find the difference between the two answers.

Report an Error

View ACT Math Tutors

Nate
Certified Tutor

University of Wisconsin-Oshkosh, non degree, Prepharmacy. University of Wisconsin-Madison, Pharmaceutical Chemist, Pharmacy.

View ACT Math Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

View ACT Math Tutors

Jason
Certified Tutor

Brigham Young University, Bachelor, Neuroscience.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

GMAT Courses & Classes in Atlanta, Spanish Courses & Classes in Denver, MCAT Courses & Classes in Philadelphia, GRE Courses & Classes in Houston, LSAT Courses & Classes in Atlanta, SAT Courses & Classes in Atlanta, SAT Courses & Classes in New York City, GMAT Courses & Classes in Miami, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in San Francisco-Bay Area, MCAT Test Prep in Chicago, SSAT Test Prep in Atlanta, LSAT Test Prep in Boston, ACT Test Prep in Houston, LSAT Test Prep in Chicago, MCAT Test Prep in San Diego, GMAT Test Prep in Philadelphia, GRE Test Prep in Philadelphia, SSAT Test Prep in San Francisco-Bay Area

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

ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : How To Find The Solution To An Equation

Example Question #1781 : Act Math

Example Question #1782 : Act Math

Example Question #11 : Equations / Inequalities

Example Question #1784 : Act Math

Example Question #292 : Algebra

Example Question #1782 : Act Math

Example Question #12 : Equations / Inequalities

Example Question #12 : How To Find The Solution To An Equation

Example Question #16 : How To Find The Solution To An Equation

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: