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### Course: Digital SAT Math>Unit 2

Lesson 6: Systems of linear equations word problems: foundations

# Systems of linear equations word problems | Lesson

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

#### Let's look at an example!

A theater production charges $\mathrm{}21$ for adult tickets and $\mathrm{}15$ for student tickets. If the production sold $102$ tickets for its opening night and made $\mathrm{}1,932$ in ticket sales, how many of each type of 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 $25I$ 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 $\mathrm{}1$ more than a cup of coffee. If $4$ cups of coffee and $6$ bagels cost $\mathrm{}31$, 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, $c$ ?
Choose 1 answer:

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?
Choose 1 answer:

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?

## Want to join the conversation?

• 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?
(151 votes)
• 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)
(330 votes)
• I just wanna say that I love this: "You can learn anything. Let's do this." :) very encouraging!
(183 votes)
• who's gonna pass the sat on 7th oct??
(48 votes)
• Hallelujah and Amen
(24 votes)
• Throughout the heavens and the earth, I alone am the cooked one
(46 votes)
• All hail the cooked one.
(15 votes)
• will the real test provides information abt nickels, quarters etc? i'm scared that there will be terms that i'm not familiar with
(20 votes)
• i don't think so, i did it in January and it didn't have any
(3 votes)
• shouldn't the answer to the last problem be 10?
(5 votes)
• If you take Sally's experience as 10 years then that would mean Mike has 16 years of experience himself
(24 votes)
• why we multiply nickel by 0.05 and quarters by 0.25 ?
what is the reason?
(13 votes)
• taking sat as an international student are the currency in US dollars
(11 votes)
• yes you pay in us dollars
(0 votes)
• where do we get 0.05 for nickels.
(4 votes)
• A nickel is 1/20 of a dollar, while a quarter is 1/4. Hope this helps ^^
(14 votes)
• it was pretty obvious that the oranges cost 1, so could it just go straight to solve the 2nd equation?
(7 votes)
• Better to be sure I guess
(1 vote)