Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : How To Find The Solution To An Equation

A theme park charges $10 for adults and $5 for kids. How many kids tickets were sold if a total of 548 tickets were sold for a total of $3750?

Possible Answers:

248

431

346

269

157

Correct answer:

346

Explanation:

Let c = number of kids tickets sold. Then (548 – c) adult tickets were sold. The revenue from kids tickets is $5c, and the total revenue from adult tickets is $10(548 – c). Then,

5c + 10(548 – c) = 3750

5c + 5480 – 10c = 3750

5c = 1730

c = 346.

We can check to make sure that this number is correct:

$5 * 346 tickets + $10 * (548 – 346) tickets = $3750 total revenue

Report an Error

Example Question #71 : Algebra

Two palm trees grow next to each other in Luke's backyard. One of the trees gets sick, so Luke cuts off the top 3 feet. The other tree, however, is healthy and grows 2 feet. How tall are the two trees if the healthy tree is now 4 feet taller than the sick tree, and together they are 28 feet tall?

Possible Answers:

11 and 17 feet

12 and 16 feet

cannot be determined

14 and 14 feet

8 and 20 feet

Correct answer:

12 and 16 feet

Explanation:

Let s stand for the sick tree and h for the healthy tree. The beginning information about cutting the sick tree and the healthy tree growing is actually not needed to solve this problem! We know that the healthy tree is 4 feet taller than the sick tree, so h = s + 4.

We also know that the two trees are 28 feet tall together, so s + h = 28. Now we can solve for the two tree heights.

Plug h = s + 4 into the second equation: (s + 4) + s = 28. Simplify and solve for h: 2s = 24 so s = 12. Then solve for h: h = s + 4 = 12 + 4 = 16.

Report an Error

Example Question #22 : How To Find The Solution To An Equation

Solve for z:

3(z + 4)³ – 7 = 17

Possible Answers:

–8

–2

Correct answer:

–2

Explanation:

1. Add 7 to both sides

3(z + 4)³ – 7 + 7= 17 + 7

3(z + 4)³ = 24

2. Divide both sides by 3

(z + 4)³ = 8

3. Take the cube root of both sides

z + 4 = 2

4. Subtract 4 from both sides

z = –2

Report an Error

Example Question #72 : Algebra

Jen and Karen are travelling for the weekend. They both leave from Jen's house and meet at their destination 250 miles away. Jen drives 45mph the whole way. Karen drives 60mph but leaves a half hour after Jen. How long does it take for Karen to catch up with Jen?

Possible Answers:

$\dpi{100} \small 1 \ hour$

$\dpi{100} \small 1.5 \ hours$

$\dpi{100} \small 3 \ hours$

She can't catch up.

$\dpi{100} \small 2 \ hours$

Correct answer:

$\dpi{100} \small 1.5 \ hours$

Explanation:

For this type of problem, we use the formula:

$\dpi{100} \small distance = rate\times time$

When Karen catches up with Jen, their distances are equivalent. Thus,

$\dpi{100} \small rate (Jen) \times time (Jen)=rate(Karen)\times time(Karen)$

We then make a variable for Jen's time, $\dpi{100} \small t$ . Thus we know that Karen's time is $\dpi{100} \small t-.5$ (since we are working in hours).

Thus,

45(t+0.5)=60t

45t+22.5=60t

22.5=15t

$t=1.5\ hours$

There's a logical shortcut you can use on "catching up" distance/rate problems. The difference between the faster (Karen at 60mph) and slower (Jen at 45mph) drivers is 15mph. Which means that every one hour, the faster driver, Karen, gains 15 miles on Jen. We know that Jen gets a 1/2 hour head start, which at 45mph means that she's 22.5 miles ahead when Karen gets started. So we can calculate the number of hours (H) of the 15mph of Karen's "catchup speed" (the difference between their speeds) it will take to make up the 22.5 mile gap:

15H = 22.5

So H = 1.5.

Report an Error

Example Question #24 : How To Find The Solution To An Equation

Bill and Bob are working to build toys. Bill can build $\dpi{100} \small k$ toys in 6 hours. Bob can build $\dpi{100} \small k$ toys in 3 hours. How long would it take Bob and Bill to build $\dpi{100} \small 4k$ toys working together?

Possible Answers:

$\dpi{100} \small 2\ hours$

$\dpi{100} \small 4\ hours$

$\dpi{100} \small 8\ hours$

$\dpi{100} \small 12\ hours$

$\dpi{100} \small 9\ hours$

Correct answer:

$\dpi{100} \small 8\ hours$

Explanation:

Bill builds $\dpi{100} \small \frac{k}{6}$ toys an hour. Bob builds $\dpi{100} \small \frac{k}{3}$ toys an hour. Together, their rate of building is $\dpi{100} \small \frac{k}{6}+\frac{k}{3}=\frac{k}{2}$ . Together they can build $\dpi{100} \small k$ toys in 2 hours. They would be able to build $\dpi{100} \small 4k$ toys in 8 hours.

Report an Error

Example Question #25 : How To Find The Solution To An Equation

A hybrid car gets 40 miles per gallon. Gasoline costs $3.52 per gallon. What is the cost of the gasoline needed for the car to travel 120 miles?

Possible Answers:

$\dpi{100} \small \$ 9.54$

$\dpi{100} \small \$ 10.56$

$\dpi{100} \small \$ 12.53$

$\dpi{100} \small \$ 14.08$

$\dpi{100} \small \$ 10.36$

Correct answer:

$\dpi{100} \small \$ 10.56$

Explanation:

The car will be using $\dpi{100} \small \frac{120\ miles}{40\ mpg}=3\ gallons$ of gas during this trip. Thus, the total cost would be $\dpi{100} \small 3\times \$ 3.52=\$ 10.56$ .

Report an Error

Example Question #73 : Algebra

Jon invested part of $16,000 at 3% and the rest at 5% for a total return of $680.

Quantity A: The amount Jon invested at 5% interest

Quantity B: The amount Jon invested at 3% interest

Possible Answers:

Quantity A is greater

The relationship cannot be determined from the information given

Quantity B is greater

The two quantities are equal

Correct answer:

Quantity A is greater

Explanation:

First, let $\dpi{100} \small x$ represent the invested amount at 3% and set up an equation like this:

$\dpi{100} \small .03x+.05(16,000-x)=680$

Solve for $\dpi{100} \small x$ , and you'll find that Jon invested $6,000 at 3% and $10,000 at 5%.

Report an Error

Example Question #74 : Algebra

Audrey, Penelope and Clementine are all sisters. Penelope is 8 years older than Clementine and 2 years younger than Audrey. If the sum of Penelope and Clementine's age is Audrey's age, how old is Clementine's age?

Possible Answers:

Correct answer:

Explanation:

Let = Audrey's age, = Penelope's age, and = Clementine's age.

Since A=P+C , then C=A-P .

Furthermore, P=C+8 , and A=P+2 .

Through substitution, C = [(C + 8) + 2] - (C + 8), C = 2 .

Report an Error

Example Question #75 : Algebra

If $\dpi{100} \small 3x+y =13$ and $\dpi{100} \small x-2y=-12$ , what is the value of $\dpi{100} \small x$ ?

Possible Answers:

$\dpi{100} \small 2$

$\dpi{100} \small 1$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small \frac{2}{3}$

$\dpi{100} \small 3$

Correct answer:

$\dpi{100} \small 2$

Explanation:

We could use the substitution or elimination method to solve the system of equations. Here we will use the elimination method.

To solve for $\dpi{100} \small x$ , combine the equations in a way that makes the $\dpi{100} \small y$ terms drop out. The first equation has $\dpi{100} \small y$ and the second $\dpi{100} \small -2y$ , so multiplying the first equation times 2 then adding the equations will eliminate the $\dpi{100} \small y$ terms.

Multiplying the first equation times 2: $\dpi{100} \small 2(3x+y = 13)\rightarrow 6x+2y = 26$

Adding this result to the second equation: $\dpi{100} \small 6x+x + 2y - 2y = 26-12\rightarrow 7x=14$

Isolate $\dpi{100} \small x$ by dividing both sides by 7:

$\dpi{100} \small \frac{7x}{7}=\frac{14}{7}$

$\dpi{100} \small x=2$

Report an Error

Example Question #32 : How To Find The Solution To An Equation

If $\frac{1}{4}x-\frac{1}{6}y=\frac{1}{6}$ and $\frac{y}{z}=\frac{1}{2}$ , then what is the value of 3x-z ?

Possible Answers:

Correct answer:

Explanation:

Since the expression we want just involves z and x, but not y, we start by solving $\frac{y}{z}=\frac{1}{2}$ for y $(y=\frac{1}{2}z)$ .

Then we can plug that expression in for y in the first equation.

$\frac{1}{4}x-\frac{1}{6}y=\frac{1}{6}$

$\frac{1}{4}x-\frac{1}{6}(\frac{1}{2}z)=\frac{1}{6}$

$\frac{1}{4}x-\frac{1}{12}z=\frac{1}{6}$

Multiply everything by 12 to get rid of fractions.

$\small 3x - z = 2$

Report an Error

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View SAT Mathematics Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

View SAT Mathematics Tutors

Miriam
Certified Tutor

Washington University in St Louis, Bachelor in Arts, Biology, General.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

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

Popular Courses & Classes

SSAT Courses & Classes in Miami, SSAT Courses & Classes in Denver, SAT Courses & Classes in New York City, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Boston, Spanish Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Washington DC, SAT Courses & Classes in Atlanta, Spanish Courses & Classes in Philadelphia

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Houston, LSAT Test Prep in Washington DC, GRE Test Prep in Seattle, GRE Test Prep in San Diego, MCAT Test Prep in Los Angeles, SSAT Test Prep in Philadelphia, ISEE Test Prep in Philadelphia, SAT Test Prep in Seattle, SAT Test Prep in Philadelphia

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

SAT Math : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : How To Find The Solution To An Equation

Example Question #71 : Algebra

Example Question #22 : How To Find The Solution To An Equation

Example Question #72 : Algebra

Example Question #24 : How To Find The Solution To An Equation

Example Question #25 : How To Find The Solution To An Equation

Example Question #73 : Algebra

Example Question #74 : Algebra

Example Question #75 : Algebra

Example Question #32 : How To Find The Solution To An Equation

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: