As an international student, I got a lot of problems when the question use dialects, such as "nickels" and "quartes" instead of using "5-cent coin" and "25-cent coin". I will face this type of dialect in SAT?

As far as I know, on the SAT, they can mention nickels and quarters but they can't expect you to know their values. For example, on the April 2017 SAT, there was a math question that asked you to find the probability of a nickel and a quarter landing heads-up or tails-up when flipped. You don't need to know the value for that or anything, just do the probability question. Alternatively, the question could tell you that a nickel is worth 5 cents in the question itself. On the real SAT, you shouldn't have to know the monetary values of any of the coins. That being said, here is a list: penny = 1 cent coin nickel = 5 cent coin dime = 10 cent coin quarter = 25 cent coin half-dollar = 50 cent coin dollar = 1 dollar (100 cents)

will the real test provides information abt nickels, quarters etc? i'm scared that there will be terms that i'm not familiar with

i don't think so, i did it in January and it didn't have any

shouldn't the answer to the last problem be 10?

If you take Sally's experience as 10 years then that would mean Mike has 16 years of experience himself

where do we get 0.05 for nickels.

A nickel is 1/20 of a dollar, while a quarter is 1/4. Hope this helps ^^

Main content

Course: Digital SAT Math > Unit 2

Lesson 6: Systems of linear equations word problems: foundations

Systems of linear equations word problems | Lesson

Google Classroom

A guide to systems of linear equations word problems on the digital SAT

What are systems of linear equations word problems?

Systems of linear equations word problems ask us to translate real-world scenarios into a system of two linear equations with two variables. Often, we'll also be asked to solve the system.

This lesson builds upon an understanding of the following skills:

Understanding linear relationships
Solving systems of linear equations

You can learn anything. Let's do this!

How do I solve systems of linear equations word problems?

Systems of equations examples

Khan Academy video wrapper

Systems of equations with elimination: apples and orangesSee video transcript

Khan Academy video wrapper

Systems of equations with substitution: coinsSee video transcript

How do I write systems of linear equations?

Word problems that require us to write systems of linear equations have two unknown quantities and two different ways to relate them.

This means we need to write two linear equations, and each contains the two unknowns as variables. The Understanding linear relationships lesson details how to translate verbal descriptions into equations.

After we write the equations, we can solve the system using our preferred method(s) for solving systems of linear equations covered in the Solving systems of linear equations lesson.

To solve a system of linear equations word problem:

Select variables to represent the unknown quantities.
Using the given information, write a system of two linear equations relating the two variables.
Solve the system of linear equations using either substitution or elimination.

Let's look at an example!

A theater production charges

$ 21

for adult tickets and

$ 15

for student tickets. If the production sold

102

tickets for its opening night and made

$ 1,932

in ticket sales, how many of each type of tickets were sold?

Let's use

a

to represent the number of adult tickets told and

s

to represent the number of student tickets sold.

Since a total of

102

tickets were sold:

a + s = 102

Since each adult ticket costs

$ 21

, the sales from

a

adult tickets is

21 a

dollars. Since each student ticket costs

$ 15

, the sales from

s

student tickets is

15 s

dollars. Since the total ticket sales was

1,932

dollars:

21 a + 15 s = 1,932

Together, our system of equations is:

\begin{aligned} a + s & = 102 \\ 21 a + 15 s & = 1,932 \end{aligned}

We can solve the system by elimination. First, we multiply both sides of the first equation by

15

\begin{aligned} a + s & = 102 \\ 15 \cdot (a + s) & = 15 \cdot 102 \\ 15 a + 15 s & = 1,530 \end{aligned}

Next, we subtract the above equation from the second equation in the system to eliminate the

s

-terms and solve for

a

\begin{aligned} 21 a + 15 s & = 1,932 \\ - 15 a + 15 s & = 1,530 \\ 6 a & = 402 \\ \frac{6 a}{6} & = \frac{402}{6} \\ a & = 67 \end{aligned}

For

a = 67

\begin{aligned} a + s & = 102 \\ 67 + s & = 102 \\ 67 + s - 67 & = 102 - 67 \\ s & = 35 \end{aligned}

$67$ ‍ adult tickets and $35$ ‍ student tickets were sold.

Try it!

Try: translate a scenario into equations

The player of a trivia game receives

100

points for each correct answer and loses

25

points for each incorrect answer. Leona answered a total of

30

questions and scored a total of

2,125

points.

Write an equation that relates the total number of questions Leona answered to

C

, the number of questions she answered correctly and

I

, the number of questions she answered incorrectly.

= 30

Leona received

100

points for each correct answer. Write an expression for the number of points she received from answering

C

questions correctly.

Because Leona loses

25

points for each incorrect answer, the quantity

25 I

should be

the number of points she received from answering questions correctly.

Write an equation that models the total number of points Leona scored using

C

and

I

= 2,125

Your turn!

Practice: write a system of linear equations

At Beans & Bagels, a bagel costs

$ 1

more than a cup of coffee. If

4

cups of coffee and

6

bagels cost

$ 31

, which of the following systems of equations can be used to determine the price of a bagel,

b

, and the price of a cup of coffee,

c

Practice: solve a system of linear equations

A group of

41

people are going to a concert together in

7

vehicles. Some of the vehicles can hold

7

people each, and the rest can hold

5

people each. Assuming all the vehicles are filled to capacity, exactly how many of the vehicles can hold

7

people?

Practice: solve a system of linear equations

Mike and Sally are math teachers at the same high school. If Mike has

6

more years of teaching experience than Sally has, and the two of them have

16

years of teaching experience combined, how many years of teaching experience does Sally have?

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Cristofer Silva
Posted a year ago. Direct link to Cristofer Silva's post “As an international stude...”
As an international student, I got a lot of problems when the question use dialects, such as "nickels" and "quartes" instead of using "5-cent coin" and "25-cent coin".

I will face this type of dialect in SAT?
Button navigates to signup pageComment on Cristofer Silva's post “As an international stude...”
(109 votes)
Answer
- Hecretary Bird
  Posted a year ago. Direct link to Hecretary Bird's post “As far as I know, on the ...”
  As far as I know, on the SAT, they can mention nickels and quarters but they can't expect you to know their values. For example, on the April 2017 SAT, there was a math question that asked you to find the probability of a nickel and a quarter landing heads-up or tails-up when flipped. You don't need to know the value for that or anything, just do the probability question. Alternatively, the question could tell you that a nickel is worth 5 cents in the question itself. On the real SAT, you shouldn't have to know the monetary values of any of the coins.
  That being said, here is a list:
  penny = 1 cent coin
  nickel = 5 cent coin
  dime = 10 cent coin
  quarter = 25 cent coin
  half-dollar = 50 cent coin
  dollar = 1 dollar (100 cents)
  Comment on Hecretary Bird's post “As far as I know, on the ...”
  (240 votes)
Nina Lukka
Posted a year ago. Direct link to Nina Lukka's post “I just wanna say that I l...”
I just wanna say that I love this: "You can learn anything. Let's do this." :) very encouraging!
Button navigates to signup pageComment on Nina Lukka's post “I just wanna say that I l...”
(135 votes)
Answer
lacourtame
Posted 8 months ago. Direct link to lacourtame's post “who's gonna pass the sat ...”
who's gonna pass the sat on 7th oct??
Button navigates to signup pageComment on lacourtame's post “who's gonna pass the sat ...”
(37 votes)
Answer
- Rouf
  Posted 8 months ago. Direct link to Rouf's post “Hallelujah and Amen”
  Hallelujah and Amen
  Comment on Rouf's post “Hallelujah and Amen”
  (19 votes)
eunikejovina
Posted a year ago. Direct link to eunikejovina's post “will the real test provid...”
will the real test provides information abt nickels, quarters etc? i'm scared that there will be terms that i'm not familiar with
Button navigates to signup pageComment on eunikejovina's post “will the real test provid...”
(17 votes)
Answer
- leti.24
  Posted a year ago. Direct link to leti.24's post “i don't think so, i did i...”
  i don't think so, i did it in January and it didn't have any
  Comment on leti.24's post “i don't think so, i did i...”
  (3 votes)
Shia
Posted 9 months ago. Direct link to Shia's post “shouldn't the answer to t...”
shouldn't the answer to the last problem be 10?
Button navigates to signup pageComment on Shia's post “shouldn't the answer to t...”
(4 votes)
Answer
- usharwan008
  Posted 9 months ago. Direct link to usharwan008's post “If you take Sally's exper...”
  If you take Sally's experience as 10 years then that would mean Mike has 16 years of experience himself
  Comment on usharwan008's post “If you take Sally's exper...”
  (22 votes)
bisrathaile1919
Posted 8 months ago. Direct link to bisrathaile1919's post “why we multiply nickel by...”
why we multiply nickel by 0.05 and quarters by 0.25 ?
what is the reason?
Button navigates to signup pageComment on bisrathaile1919's post “why we multiply nickel by...”
(12 votes)
Answer
Jose
Posted 2 months ago. Direct link to Jose's post “Throughout the heavens an...”
Throughout the heavens and the earth, I alone am the cooked one
Button navigates to signup pageComment on Jose's post “Throughout the heavens an...”
(10 votes)
Answer
- DevonC
  Posted a month ago. Direct link to DevonC's post “All hail the cooked one.”
  All hail the cooked one.
  Button navigates to signup page
  (2 votes)
olimjonovazizbek0000
Posted a year ago. Direct link to olimjonovazizbek0000's post “where do we get 0.05 for ...”
where do we get 0.05 for nickels.
Button navigates to signup pageComment on olimjonovazizbek0000's post “where do we get 0.05 for ...”
(4 votes)
Answer
- kate
  Posted a year ago. Direct link to kate's post “A nickel is 1/20 of a dol...”
  A nickel is 1/20 of a dollar, while a quarter is 1/4. Hope this helps ^^
  Comment on kate's post “A nickel is 1/20 of a dol...”
  (12 votes)
elinamazorliade
Posted a year ago. Direct link to elinamazorliade's post “taking sat as an internat...”
taking sat as an international student are the currency in US dollars
Button navigates to signup pageComment on elinamazorliade's post “taking sat as an internat...”
(9 votes)
Answer
- hasmoustafa
  Posted a year ago. Direct link to hasmoustafa's post “yes you pay in us dollars”
  yes you pay in us dollars
  Button navigates to signup page
  (0 votes)
Ana Cecília
Posted a year ago. Direct link to Ana Cecília's post “it was pretty obvious tha...”
it was pretty obvious that the oranges cost 1, so could it just go straight to solve the 2nd equation?
Button navigates to signup pageComment on Ana Cecília's post “it was pretty obvious tha...”
(7 votes)
Answer