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how to solve a word problem with 2 variables

How Do You Solve a Word Problem Using an Equation With Variables on Both Sides?

Word problems are a great way to see math in the real world! In this tutorial, you'll see how to take a word problem and use it to write and solve an equation with variables on both sides!

  • reverse order of operations

Background Tutorials

Introduction to algebraic expressions.

How Do You Evaluate an Algebraic Expression?

How Do You Evaluate an Algebraic Expression?

Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.

What is a Variable?

What is a Variable?

You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

What is a Constant?

What is a Constant?

Constants are parts of algebraic expressions that don't change. Check out this tutorial to see exactly what a constant looks like and why it doesn't change.

Properties of Equality

What's the Subtraction Property of Equality?

What's the Subtraction Property of Equality?

Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the subtraction property of equality, and it lets you subtract the same number from both sides of an equation. Watch the video to see it in action!

What's the Division Property of Equality?

What's the Division Property of Equality?

Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the division property of equality, and it lets you divide both sides of an equation by the same number. Watch the video to see it in action!

Solving Equations with Variables on Both Sides

How Do You Solve an Equation with Variables on Both Sides?

How Do You Solve an Equation with Variables on Both Sides?

Trying to solve an equation with variables on both sides of the equal sign? Figure out how to get those variables together and find the answer with this tutorial!

Further Exploration

Solving multi-step equations.

How Do You Solve a Word Problem Using a Multi-Step Equation?

How Do You Solve a Word Problem Using a Multi-Step Equation?

Working with word problems AND fractions? This tutorial shows you how to take a word problem and translate it into a mathematical equation involving fractions. Then, you'll see how to solve and check your answer. Take a look!

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Pre-Algebra : Word Problems with Two Unknowns

Study concepts, example questions & explanations for pre-algebra, all pre-algebra resources, example questions, example question #1 : word problems with two unknowns.

Combined, Megan and Kelly worked 60 hours. Kelly worked twice as many hours as Megan. How many hours did they each work? 

Megan worked for 30 hours and Kelly worked for 60 hours

Megan worked for 15 hours and Kelly worked for 45 hours

Megan worked for 40 hours and Kelly worked for 10 hours

Megan worked for 20 hours and Kelly worked for 40 hours

Megan worked for 10 hours and Kelly worked for 50 hours

Step 1: Megan and Kelly's total hours worked needs to add up to 60, and Kelly worked two times as long as Megan. We can put this into a formula:

how to solve a word problem with 2 variables

Step 2: substitute 2m for k and add the variables 

how to solve a word problem with 2 variables

Step 3: isolate m

how to solve a word problem with 2 variables

Step 4: Now that we know Megan worked 20 hours (m=20), we can multiply her hours worked by 2 to find out how long Kelly worked.

how to solve a word problem with 2 variables

Step 5: check to make sure Megan and Kelly's hours add up to 60

how to solve a word problem with 2 variables

Example Question #52 : Algebraic Equations

Jamal invites 15 people to his birthday party and orders enough cupcakes so that everyone (himself included) will get two cupcakes. How many cupcakes can everyone have if only 7 friends show up to Jamal's party? 

how to solve a word problem with 2 variables

Step 1: find the number of cupcakes ordered by adding up all of the people at the party and then multiplying that number by the 2 cupcakes ordered per person.

how to solve a word problem with 2 variables

Step 2: to find the number of cupcakes each person can have, take the number of cupcakes and divide it by the number of guests, including Jamal.

how to solve a word problem with 2 variables

Example Question #53 : Algebraic Equations

Michael and Tom are brothers. Their combined age is 20, and Tom is 4 years older than Michael. What are Michael and Tom's ages?

Tom is 16 years old and Michael is 4 years old.

Michael is 12 years old and Tom is 8 years old.

Michael is 10 years old and Tom is 10 years old.

Tom is 10 years old and Michael is 4 years old.

Michael is 8 years old and Tom is 12 years old.

To solve this, we can set each of their ages as a variable. Let's say Michael's age is x.

We know Tom is 4 years older than Michael, so Tom's age is x+4.

We also know that their combined age is 20, so if we add both of their ages, we should get 20.

x + (x+4) = 20

So Michael's age is 8, and Tom is 12.

Sarah earns $10 an hour selling calculators, and every time she sells a calculator, she earns an additional $3 comission. Jamie also sells calculators, and earns $30 an hour, but only earns an additional $1 comission for every calculator she sells. 

How many calculators per hour on average would Sarah have to sell to be making as much as Jamie would per hour, if Jamie sold the same number of calculators?

how to solve a word problem with 2 variables

Answer cannot be determined from the information given 

how to solve a word problem with 2 variables

Example Question #55 : Algebraic Equations

how to solve a word problem with 2 variables

14 dimes and 7 quarters

12 dimes and 12 quarters

11 dimes and 10 quarters

7 dimes and 14 quarters

10 dimes and 11 quarters

how to solve a word problem with 2 variables

Simplifying further we get

how to solve a word problem with 2 variables

We then want to combine like terms (the  d s)

how to solve a word problem with 2 variables

We then want all of our variables on one side and all of our constants on the other, which we can accomplish by subtracting 525 from both sides.

how to solve a word problem with 2 variables

That means Jamarcus has 7 dimes.  If we remember that he had 21 coins in all, that leaves 14 quarters.  Jamarcus has 7 dimes and 14 quarters.

We can double check ourselves.  Seven dimes would total $0.70, and 14 quarters would total $3.50, bringing the grand total to the correct value of $4.20.

Example Question #56 : Algebraic Equations

The sum of two numbers is 128.  The first number is 18 more than the second number.  What are the two numbers?

how to solve a word problem with 2 variables

We can then combine like terms (our variables), giving us

how to solve a word problem with 2 variables

We then want all of our constant terms on the right side, which we can accomplish by subtracting 18 from both sides.

how to solve a word problem with 2 variables

The last step to solving the equation is to divide both sides by 2.

how to solve a word problem with 2 variables

Therefore, our second number is 55.  Since our first number is 18 more than that, it must equal 73.  Double checking, we can confirm that the sum of 55 and 73 is indeed 128.

Turn the word equation into symbols.

The product of three and s and the difference of 12 and 7 is 14.

how to solve a word problem with 2 variables

We need to translate the English words into a mathematical statement.

Product means multiply.

Difference means subtraction.

Is means equals.

Product of 3 and s is 3s.

Difference of 12 and 7 is 12 - 5.

Therefore, the equation becomes,

how to solve a word problem with 2 variables

There are a total of 14 coins when dimes and nickels are combined.  The total amount is 80 cents.  How many dimes and nickels are there, respectively?

how to solve a word problem with 2 variables

Write two equations to represent the scenario.  There are two equations and two unknowns.

how to solve a word problem with 2 variables

Nickels are 5 cents, and dimes are 10 cents.  The total is 80 cents.  Write the second equation.

how to solve a word problem with 2 variables

Multiply the second equation by 10 and use the elimination method to cancel out the dimes variable.

how to solve a word problem with 2 variables

There are 12 nickels.  

Substitute this into the first equation to find the number of dimes.

how to solve a word problem with 2 variables

There are 2 dimes and 12 nickels.  

Example Question #59 : Algebraic Equations

You go to the store and buy  x  bags of carrots and  y  bananas.  Each bag of carrots costs $1.50 and each banana is $0.25.  You spend $6.50.  The total number of items you purchase is 11.  How many bags of carrots did you buy?  How many bananas did you buy?

4 bags of carrots, 7 bananas

5 bags of carrots, 6 bananas

3 bags of carrots, 8 bananas

8 bags of carrots, 3 bananas

6 bags of carrots, 5 bananas

Given the information, we have 2 equations. We know each bag of carrots is $1.50 and each banana is $0.25.  We also know the total amount we spend is $6.50.  So, we can write the equation

how to solve a word problem with 2 variables

where  x is the number of bags of carrots and  y is the number of bananas.  

We also know the total number of items we purchased is 11.  We can write the equation as

how to solve a word problem with 2 variables

where  x is number of bags of carrots and  y is the number of bananas.

To solve, we will solve for one variable in one equation and substitute it into the other equation.  So,

how to solve a word problem with 2 variables

Now, we can substitute the value of  y into the first equation.  We get,

how to solve a word problem with 2 variables

We distribute.

how to solve a word problem with 2 variables

We combine like terms.

how to solve a word problem with 2 variables

We solve for  x  by getting  x alone.  

how to solve a word problem with 2 variables

Therefore, the number of bags of carrots we bought is 3.  To find the number of bananas, we simply substitute  x  into the equation.

how to solve a word problem with 2 variables

Therefore, the number of bananas we bought is 8.

So we bought 3 bags of carrots and 8 bananas.

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Algebra Topics  - Introduction to Word Problems

Algebra topics  -, introduction to word problems, algebra topics introduction to word problems.

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Algebra Topics: Introduction to Word Problems

Lesson 9: introduction to word problems.

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What are word problems?

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem. For instance, does this sound familiar?

Johnny has 12 apples. If he gives four to Susie, how many will he have left?

You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you're supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as:

12 - 4 = 8 , so you know Johnny has 8 apples left.

Word problems in algebra

If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems.

You can tackle any word problem by following these five steps:

  • Read through the problem carefully, and figure out what it's about.
  • Represent unknown numbers with variables.
  • Translate the rest of the problem into a mathematical expression.
  • Solve the problem.
  • Check your work.

We'll work through an algebra word problem using these steps. Here's a typical problem:

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive?

It might seem complicated at first glance, but we already have all of the information we need to solve it. Let's go through it step by step.

Step 1: Read through the problem carefully.

With any problem, start by reading through the problem. As you're reading, consider:

  • What question is the problem asking?
  • What information do you already have?

Let's take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out?

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many miles did she drive?

There's only one question here. We're trying to find out how many miles Jada drove . Now we need to locate any information that will help us answer this question.

There are a few important things we know that will help us figure out the total mileage Jada drove:

  • The van cost $30 per day.
  • In addition to paying a daily charge, Jada paid $0.50 per mile.
  • Jada had the van for 2 days.
  • The total cost was $360 .

Step 2: Represent unknown numbers with variables.

In algebra, you represent unknown numbers with letters called variables . (To learn more about variables, see our lesson on reading algebraic expressions .) You can use a variable in the place of any amount you don't know. Looking at our problem, do you see a quantity we should represent with a variable? It's often the number we're trying to find out.

Since we're trying to find the total number of miles Jada drove, we'll represent that amount with a variable—at least until we know it. We'll use the variable m for miles . Of course, we could use any variable, but m should be easy to remember.

Step 3: Translate the rest of the problem.

Let's take another look at the problem, with the facts we'll use to solve it highlighted.

The rate to rent a small moving van is $30 per day , plus $0.50 per mile . Jada rented a van to drive to her new home. It took 2 days , and the van cost $360 . How many miles did she drive?

We know the total cost of the van, and we know that it includes a fee for the number of days, plus another fee for the number of miles. It's $30 per day, and $0.50 per mile. A simpler way to say this would be:

$30 per day plus $0.50 per mile is $360.

If you look at this sentence and the original problem, you can see that they basically say the same thing: It cost Jada $30 per day and $0.50 per mile, and her total cost was $360 . The shorter version will be easier to translate into a mathematical expression.

Let's start by translating $30 per day . To calculate the cost of something that costs a certain amount per day, you'd multiply the per-day cost by the number of days—in other words, 30 per day could be written as 30 ⋅ days, or 30 times the number of days . (Not sure why you'd translate it this way? Check out our lesson on writing algebraic expressions .)

$30 per day and $.50 per mile is $360

$30 ⋅ day + $.50 ⋅ mile = $360

As you can see, there were a few other words we could translate into operators, so and $.50 became + $.50 , $.50 per mile became $.50 ⋅ mile , and is became = .

Next, we'll add in the numbers and variables we already know. We already know the number of days Jada drove, 2 , so we can replace that. We've also already said we'll use m to represent the number of miles, so we can replace that too. We should also take the dollar signs off of the money amounts to make them consistent with the other numbers.

30 ⋅ 2 + .5 ⋅ m = 360

Now we have our expression. All that's left to do is solve it.

Step 4: Solve the problem.

This problem will take a few steps to solve. (If you're not sure how to do the math in this section, you might want to review our lesson on simplifying expressions .) First, let's simplify the expression as much as possible. We can multiply 30 and 2, so let's go ahead and do that. We can also write .5 ⋅ m as 0.5 m .

60 + .5m = 360

Next, we need to do what we can to get the m alone on the left side of the equals sign. Once we do that, we'll know what m is equal to—in other words, it will let us know the number of miles in our word problem.

We can start by getting rid of the 60 on the left side by subtracting it from both sides .

The only thing left to get rid of is .5 . Since it's being multiplied with m , we'll do the reverse and divide both sides of the equation with it.

.5 m / .5 is m and 300 / 0.50 is 600 , so m = 600 . In other words, the answer to our problem is 600 —we now know Jada drove 600 miles.

Step 5: Check the problem.

To make sure we solved the problem correctly, we should check our work. To do this, we can use the answer we just got— 600 —and calculate backward to find another of the quantities in our problem. In other words, if our answer for Jada's distance is correct, we should be able to use it to work backward and find another value, like the total cost. Let's take another look at the problem.

According to the problem, the van costs $30 per day and $0.50 per mile. If Jada really did drive 600 miles in 2 days, she could calculate the cost like this:

$30 per day and $0.50 per mile

30 ⋅ day + .5 ⋅ mile

30 ⋅ 2 + .5 ⋅ 600

According to our math, the van would cost $360, which is exactly what the problem says. This means our solution was correct. We're done!

While some word problems will be more complicated than others, you can use these basic steps to approach any word problem. On the next page, you can try it for yourself.

Let's practice with a couple more problems. You can solve these problems the same way we solved the first one—just follow the problem-solving steps we covered earlier. For your reference, these steps are:

If you get stuck, you might want to review the problem on page 1. You can also take a look at our lesson on writing algebraic expressions for some tips on translating written words into math.

Try completing this problem on your own. When you're done, move on to the next page to check your answer and see an explanation of the steps.

A single ticket to the fair costs $8. A family pass costs $25 more than half of that. How much does a family pass cost?

Here's another problem to do on your own. As with the last problem, you can find the answer and explanation to this one on the next page.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo. Between the two of them, they donated $280. How much money did Mo give?

Problem 1 Answer

Here's Problem 1:

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

Answer: $29

Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1.

Step 1: Read through the problem carefully

The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it . Let's look at the problem again. The question is right there in plain sight:

So is the information we'll need to answer the question:

  • A single ticket costs $8 .
  • The family pass costs $25 more than half the price of the single ticket.

Step 2: Represent the unknown numbers with variables

The unknown number in this problem is the cost of the family pass . We'll represent it with the variable f .

Step 3: Translate the rest of the problem

Let's look at the problem again. This time, the important facts are highlighted.

A single ticket to the fair costs $8 . A family pass costs $25 more than half that . How much does a family pass cost?

In other words, we could say that the cost of a family pass equals half of $8, plus $25 . To turn this into a problem we can solve, we'll have to translate it into math. Here's how:

  • First, replace the cost of a family pass with our variable f .

f equals half of $8 plus $25

  • Next, take out the dollar signs and replace words like plus and equals with operators.

f = half of 8 + 25

  • Finally, translate the rest of the problem. Half of can be written as 1/2 times , or 1/2 ⋅ :

f = 1/2 ⋅ 8 + 25

Step 4: Solve the problem

Now all we have to do is solve our problem. Like with any problem, we can solve this one by following the order of operations.

  • f is already alone on the left side of the equation, so all we have to do is calculate the right side.
  • First, multiply 1/2 by 8 . 1/2 ⋅ 8 is 4 .
  • Next, add 4 and 25. 4 + 25 equals 29 .

That's it! f is equal to 29. In other words, the cost of a family pass is $29 .

Step 5: Check your work

Finally, let's check our work by working backward from our answer. In this case, we should be able to correctly calculate the cost of a single ticket by using the cost we calculated for the family pass. Let's look at the original problem again.

We calculated that a family pass costs $29. Our problem says the pass costs $25 more than half the cost of a single ticket. In other words, half the cost of a single ticket will be $25 less than $29.

  • We could translate this into this equation, with s standing for the cost of a single ticket.

1/2s = 29 - 25

  • Let's work on the right side first. 29 - 25 is 4 .
  • To find the value of s , we have to get it alone on the left side of the equation. This means getting rid of 1/2 . To do this, we'll multiply each side by the inverse of 1/2: 2 .

According to our math, s = 8 . In other words, if the family pass costs $29, the single ticket will cost $8. Looking at our original problem, that's correct!

So now we're sure about the answer to our problem: The cost of a family pass is $29 .

Problem 2 Answer

Here's Problem 2:

Answer: $70

Let's go through this problem one step at a time.

Start by asking what question the problem is asking you to solve and identifying the information that will help you solve it . What's the question here?

To solve the problem, you'll have to find out how much money Mo gave to charity. All the important information you need is in the problem:

  • The amount Flor donated is three times as much the amount Mo donated
  • Flor and Mo's donations add up to $280 total

The unknown number we're trying to identify in this problem is Mo's donation . We'll represent it with the variable m .

Here's the problem again. This time, the important facts are highlighted.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo . Between the two of them, they donated $280 . How much money did Mo give?

The important facts of the problem could also be expressed this way:

Mo's donation plus Flor's donation equals $280

Because we know that Flor's donation is three times as much as Mo's donation, we could go even further and say:

Mo's donation plus three times Mo's donation equals $280

We can translate this into a math problem in only a few steps. Here's how:

  • Because we've already said we'll represent the amount of Mo's donation with the variable m , let's start by replacing Mo's donation with m .

m plus three times m equals $280

  • Next, we can put in mathematical operators in place of certain words. We'll also take out the dollar sign.

m + three times m = 280

  • Finally, let's write three times mathematically. Three times m can also be written as 3 ⋅ m , or just 3 m .

m + 3m = 280

It will only take a few steps to solve this problem.

  • To get the correct answer, we'll have to get m alone on one side of the equation.
  • To start, let's add m and 3 m . That's 4 m .
  • We can get rid of the 4 next to the m by dividing both sides by 4. 4 m / 4 is m , and 280 / 4 is 70 .

We've got our answer: m = 70 . In other words, Mo donated $70 .

The answer to our problem is $70 , but we should check just to be sure. Let's look at our problem again.

If our answer is correct, $70 and three times $70 should add up to $280 .

  • We can write our new equation like this:

70 + 3 ⋅ 70 = 280

  • The order of operations calls for us to multiply first. 3 ⋅ 70 is 210.

70 + 210 = 280

  • The last step is to add 70 and 210. 70 plus 210 equals 280 .

280 is the combined cost of the tickets in our original problem. Our answer is correct : Mo gave $70 to charity.

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how to solve a word problem with 2 variables

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  • Quiz: Word Problems

Here are some examples for solving number problems with two variables.

The sum of two numbers is 15. The difference of the same two numbers is 7. What are the two numbers?

First, circle what you're looking for— the two numbers. Let x stand for the larger number and y stand for the second number. Now, set up two equations.

The sum of the two numbers is 15.

The difference is 7.

Now, solve by adding the two equations.

how to solve a word problem with 2 variables

Now, plugging into the first equation gives

how to solve a word problem with 2 variables

The numbers are 11 and 4.

The sum of twice one number and three times another number is 23 and their product is 20. Find the numbers.

First, circle what you must find— the numbers . Let x stand for the number that is being multiplied by 2 and y stand for the number being multiplied by 3.

Now set up two equations.

The sum of twice a number and three times another number is 23.

2 x + 3 y = 23

Their product is 20.

x ( y ) = 20

Rearranging the first equation gives

3 y = 23 – 2 x

Dividing each side of the equation by 3 gives

how to solve a word problem with 2 variables

Now, substituting the first equation into the second gives

how to solve a word problem with 2 variables

Multiplying each side of the equation by 3 gives

23 x – 2 x 2 = 60

Rewriting this equation in standard quadratic form gives

2 x 2 – 23 x + 60 = 0

Solving this quadratic equation using factoring gives

(2 x – 15)( x – 4) = 0

Setting each factor equal to 0 and solving gives

how to solve a word problem with 2 variables

With each x value we can find its corresponding y value.

how to solve a word problem with 2 variables

Therefore, this problem has two sets of solutions.

how to solve a word problem with 2 variables

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  • April 14, 2020

Variable Expressions: Word Problems

how to solve a word problem with 2 variables

Lesson Intro: Expressions with Variables

In this lesson, Juni Mathematics instructor Kadyn talks about variables and variable expressions – foundational concepts in pre-algebra. Variables are important to know for higher levels of math, and are even used similarly in other subjects like computer science!

Read Kadyn’s Intro to Variable Expressions lesson first to understand what variables are and how to use them in expressions. Then, use what you’ve learned with Kadyn’s word problems below to translate sentences and real-life problems into expressions with unknown variables. Learn to solve for unknowns, and tackle real-world applications.

Once you’ve checked your answers, you can also keep practicing using variables with Variable Expressions Drills and Warmup Problems .

Word Problems

Write out the following mathematical expression in full and then in simplified form: negative three times the difference of five times x and the absolute value of negative two minus three.

Ted is hosting a birthday party. If you take the number of friends he invited and multiply it by 4 and subtract it by 7, you get 53. How many people did Ted invite to his party?

Carmen wants to collect stamps and the store charges $3 for a pack of 12 stamps. How many stamps will Carmen have if she spent $36 on stamps? (disregard taxes)

Peter wants to build a rectangular fence around his yard. One side of the fence is 3m shorter than 4 times the other side. If the shorter side of the fence is 15m, what is the perimeter of the fence in meters?

Elliott and Gretchen are renting their own apartments in the city. Elliott has paid $10,000 in rent so far and Gretchen has paid $8,000. If both of them have been renting their own place for the same number of months and Gretchen’s monthly rate is $1,000, how much is Elliott’s monthly rent?

Find Solutions Below

-3 ⋅ (5x – |-2 -3|) = -3 ⋅ (5x – 5) = -15x + 15

Full form: -3 ⋅ (5x – |-2 -3|)

Simplified form: -15x + 15

Ted invited 15 people to his birthday party.

Let the number of people at Ted’s birthday party be n. Then n ⋅ 4 – 7 = 53 → n ⋅ 4 = 60. Then we know that n = 15.

Carmen has 144 stamps.

Let the number of stamps that Carmen has be s. Since she spent $36 on stamps and each pack of stamps cost $3, she then bought 36 3 = 12 packs. Since each pack comes in with 12 stamps, she has 12 ⋅ 12 = 144 stamps.

The perimeter of the fence is 144m.

Since the shorter side of the fence is 15m long, the longer side of the fence is 4 ⋅ 15 – 3 = 57m long. Then the perimeter of the fence is 15 + 15 + 57 + 57 = 144m.

Elliott’s monthly rent is $1,250.

Since Gretchen has paid $8,000 in rent and her monthly rent is $1,000, she has lived at her place for 8,000 1,000 = 8 months. Since Gretchen has lived at her place as long as Elliott has lived at his, we know that Elliott has lived at his place for 8 months as well. Then since Elliott has paid $10,000 in rent, his monthly rate is $10,000 8 = $1,250.

More Exercises on Variables

We hope you enjoyed Kadyn’s Word Problems with Variable Expressions! This lesson falls under our Pre-Algebra A course curriculum .

Continue practicing variable expressions with warmup problems and practice drills below. Or, review key terms and concepts with Kadyn’s Intro to Variables lesson.

  • Intro to Variable Expressions: Definitions and Approaches
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  • Variable Expressions Drills

Need help or want to keep learning?

To keep practicing or learning, please check out all of our math and coding tutorials on our Home Learning Resources page .

Need help? Looking up your questions is one of the best ways to learn! Another great way to learn is from an experienced math instructor. Read more about our online math courses or speak with a Juni Advisor by calling __(650) 263-4306__ or emailing [email protected]__.

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SOLVING LINEAR INEQUALITIES WORD PROBLEMS IN TWO VARIABLES

A statement involving the symbols ‘>’, ‘<’, ‘ ≥’, ‘≤’ is called an inequality. 

By understanding the real situation, we have to use two variables to represent each quantities

Problem 1 :

Katie has $50 in a savings account at the beginning of the summer. She wants to have at least $20 in the account by the end of the summer. She withdraws $2 each week for food, clothes, and movie tickets. Write an inequality that expresses Katie’s situation and display it on the graph below. For how many weeks can Katie withdraw money?

Let x be the number of weeks 

50 - 2x  ≥  20

2x  ≤  30

x  ≤  15 weeks

how to solve a word problem with 2 variables

Problem 2 :

Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party. Write an inequality that models her situation and display it on the graph below. How many people can attend Joann's party.

Assume x people can attend the party.

y = 50 + 4x

50 + 4x ≤ 100

So, 12 people can attend Joan’s party.

Problem 3 :

Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make at least $60. Sarah knows she will sell more than 10 bracelets. Write inequalities to represent the income from jewelry sold and number of bracelets sold. Find two possible solutions.

Let x be the number of bracelets sold.

Let y be the number of earrings sold.

2x + 3y ≥ 60

If x = 11, then 2(11) + 3y  ≥ 60

3y  ≥ 60 - 22

3y  ≥ 38

Since y is the number of earrings, x = 11 is not possible.

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  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
  • \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
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  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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Wordle Answer And Hints - February 26, 2024 Solution #982

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Letter hints, today's wordle answer #982.

Are you ready to tackle today's Wordle ? If you find yourself struggling to solve today's word then don't worry, we've got everything you need right here and we'll help you keep your precious streak intact.

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Wordle: Beginner Tips

We've got a breakdown of all the letters, some general word clues, or, if you just want the full answer, we've got that here too. All the answers are hidden from view, so don't worry about any accidental spoilers.

Are you looking for the answer for February 25, 2024 ? You can find that here .

A Wordle grid that says 'Hints'.

Simply expand the box of the letter you wish to reveal just below.

If you want to know what the first letter of the word is, please expand this box to see below.

Warning - spoilers ahead

The first letter today is ' O '

If you want to know what the second letter of the word is, please expand this box to see below.

The second letter today is ' F '

The third letter today is ' T '

If you want to know what the fourth letter of the word is, please expand this box to see below.

The fourth letter today is ' E '

If you want to know what the fifth letter of the word is, please expand this box to see below.

The fifth letter today is ' N '

A Wordle grid that says 'CLUES'.

Would you like a clue or two?

  • It contains two vowels.
  • There are no duplicate letters.
  • It's an adverb .
  • Synonyms include 'frequently' and 'repeatedly' .

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Here's the answer!

If you want to cut to the chase and find out what the Wordle of the day is, please expand this box to see below.

The word today is ' OFTEN '.

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How to Solve Word Problems to Identify Independent and Dependent Variables

In this article, you will learn how to solve word problems to identify independent and dependent variables.

How to Solve Word Problems to Identify Independent and Dependent Variables

A step-by-step guide to solving word problems to identify independent and dependent variables

An Independent variable is one whose value does not depend on the other variable.

The dependent variable is the one whose value depends on the other variable.

To solve a word problem, first, you must list the information and then find the independent variable and dependent variable.

Here’s a step-by-step guide to solving word problems to identify independent and dependent variables:

Step 1: Read the problem carefully. Make sure you understand what is being asked in the problem. Look for keywords that will help you identify the variables, such as “depends on”, “varies with”, or “changes according to”.

Step 2: Identify the variables. Look for two variables in the problem – the independent variable and the dependent variable. The independent variable is the one that is being manipulated or changed in the problem, while the dependent variable is the one that is affected by the independent variable.

Step 3: Determine the relationship between the variables. Look for clues in the problem to help you determine the relationship between the variables. For example, if the problem says that “the cost of the ticket depends on the number of people attending”, then the independent variable is the number of people attending, and the dependent variable is the cost of the ticket. In this case, the more people attend, the higher the cost of the ticket.

Step 4: Write the equation. Once you have identified the independent and dependent variables and determined the relationship between them, you can write an equation to represent the problem. For example, if the problem states that “the temperature of the water varies with the amount of heat applied”, you can write the equation as Temperature = f(Heat).

Step 5: Solve the problem. Once you have the equation, you can use it to solve the problem. For example, if the problem asks you to find the temperature of the water when a certain amount of heat is applied, you can substitute the given value for heat in the equation and solve for temperature.

By following these steps, you can easily identify the independent and dependent variables in a word problem and solve it efficiently.

Solve Word Problems to Identify Independent and Dependent Variables – Example 1

Meg is making sandwiches to sell. The number of hotdogs she needs to use will affect how many the number of sandwiches she makes. s\(=\)The number of sandwiches she makes. h\(=\)The number of hotdogs she needs to use. Which of the variables is independent and which is dependent?

Find the dependent variable. Since the number of sandwiches depends on how many hotdogs to use, the number of sandwiches is the dependent variable. So, s is the dependent variable. Since the number of hotdogs, does not depend on how many sandwiches she makes; the hotdogs are the independent variable. So, h is the independent variable.

by: Effortless Math Team about 1 year ago (category: Articles )

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Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

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IMAGES

  1. Solving Word Problems with Two Variables

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  2. Word Problems 2 Variables Linear Equations: Part 1

    how to solve a word problem with 2 variables

  3. ShowMe

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  4. How to solve Word Problems involving linear equations in two variables

    how to solve a word problem with 2 variables

  5. Solving a Word Problem with Two Unknowns Using a Linear Equation

    how to solve a word problem with 2 variables

  6. Solving two variable word problems via a chart

    how to solve a word problem with 2 variables

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  1. Word problems in linear equations

  2. Linear Equation

  3. 176E. SOLVING WORD PROBLEMS BY EQUATIONS WITH TWO UNKNOWNS (PART2)

  4. How to Solve Word Problems with Two Variables A Simple Approach

  5. How to solve Word Problems involving linear equations in two variables?

  6. Word Problems In Quadratic Equation Class 10

COMMENTS

  1. Two-Variable Word Problems

    Math Worksheets Examples, videos, worksheets, solutions, and activities to help Algebra 1 students learn how to solve two-variable word problems. Algebra - Solving Word Problems with Two Variables (1 of 5) Provides explanation of how to solve word problems using two variables. The sum of a two-digit number is 11.

  2. Algebraic word problems

    How do we solve algebraic word problems? Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation.

  3. How to Solve Word Problems by Finding Two-Variable Equations?

    Solution: Look for relationships between the number of packs and cookies. Find c by multiplying the number of packs by cookies. So, \ (8×2=16\) \ (c=16\) Solving Word Problems by Finding Two-Variable Equations - Example 2 Solve the relationships in the word problem.

  4. Word Problems With 2 Unknowns

    This video illustrates how to solve a word problem involving a system of 2 equations with 2 variables. For many more instructional Math videos, as well as e...

  5. How to Solve Two-variable Linear Equations Word Problems

    Step 1: Initial Gathering of Thoughts: Before anything else, immerse yourself in the story the problem tells. Without rushing to solve, familiarize yourself with the narrative. Step 2: Key Element Identification: Discover and underline essential entities (like quantities or amounts) and the relationships between them.

  6. How to write word problems as equations

    The first step in solving a word problem like this is to define the variables. What that means is to state the particular quantity that each variable stands for. In this problem, we have two quantities: Mary's age and John's age.

  7. Algebra

    0:00 / 3:23 Algebra - Solving Word Problems with Two Variables (1 of 5) Michel van Biezen 994K subscribers Subscribe Subscribed 141 Share 38K views 10 years ago ALGEBRA 0 Visit...

  8. Two-variable inequalities word problems (practice)

    Algebra 1 > Inequalities (systems & graphs) > Modeling with linear inequalities Two-variable inequalities word problems Google Classroom Wang Hao wants to spend at most $ 15 on dairy products. Each liter of goat milk costs $ 2.40 , and each liter of cow's milk costs $ 1.20 .

  9. Linear Equations in 2 Variables

    Don't Memorise brings learning to life through its captivating FREE educational videos. To Know More, visit https://InfinityLearn.comNew videos every week. T...

  10. How Do You Solve a Word Problem Using an Equation With Variables on

    multi-step Background Tutorials Introduction to Algebraic Expressions How Do You Evaluate an Algebraic Expression? Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial. What is a Variable?

  11. Word Problems with Two Unknowns

    Correct answer: Megan worked for 20 hours and Kelly worked for 40 hours Explanation: Step 1: Megan and Kelly's total hours worked needs to add up to 60, and Kelly worked two times as long as Megan. We can put this into a formula: Step 2: substitute 2m for k and add the variables Step 3: isolate m

  12. Algebra Topics: Introduction to Word Problems

    Step 1: Read through the problem carefully. With any problem, start by reading through the problem. As you're reading, consider: What question is the problem asking? What information do you already have? Let's take a look at our problem again. What question is the problem asking?

  13. Number Problems with Two Variables

    Here are some examples for solving number problems with two variables. Example 1 The sum of two numbers is 15. The difference of the same two numbers is 7. What are the two numbers? First, circle what you're looking for— the two numbers. Let x stand for the larger number and y stand for the second number. Now, set up two equations.

  14. Solving Addition Word Problems with Two or More Variables

    Word problems with two or more variables can appear complex but can be translated into algebraic expressions to be more easily solved. Follow the steps in writing these equations and...

  15. How to Write Two-variable Inequalities Word Problems?

    In two-variable inequalities word problems problems, there are two variables, often represented by x and y, and an inequality symbol. Two-variable inequalities word problems involve using two variables and an inequality symbol to represent a relationship between two quantities in a real-world scenario.

  16. Variable Expressions: Word Problems

    Answer Key Problem 1 -3 ⋅ (5x - |-2 -3|) = -3 ⋅ (5x - 5) = -15x + 15 Full form: -3 ⋅ (5x - |-2 -3|) Simplified form: -15x + 15 Problem 2 Ted invited 15 people to his birthday party. Let the number of people at Ted's birthday party be n. Then n ⋅ 4 - 7 = 53 → n ⋅ 4 = 60. Then we know that n = 15. Problem 3

  17. Two-variable inequalities

    Unit 1 Introduction to algebra. Unit 2 Solving basic equations & inequalities (one variable, linear) Unit 3 Linear equations, functions, & graphs. Unit 4 Sequences. Unit 5 System of equations. Unit 6 Two-variable inequalities. Unit 7 Functions. Unit 8 Absolute value equations, functions, & inequalities. Unit 9 Quadratic equations & functions.

  18. Word Problem: Linear Equation in two Variables

    http://www.greenemath.com/In this video we demonstrate how to set up and solve a word problem that involves a linear equation in two variables.

  19. Solving Linear Inequalities Word Problems in Two Variables

    SOLVING LINEAR INEQUALITIES WORD PROBLEMS IN TWO VARIABLES. A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. By understanding the real situation, we have to use two variables to represent each quantities. Problem 1 : Katie has $50 in a savings account at the beginning of the summer.

  20. Word Problems Calculator

    How do you solve word problems? To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform.

  21. PDF 26. Word Problems

    To solve using more than one variable, you read the question to find out what you are looking for and label those. Let's look at an example. EXAMPLE: The sum of two consecutive even numbers is 62. Find the numbers. First, we'll do the problem in one variable like we have done before. We are looking two numbers. I will call them # 1 and # 2.

  22. Two-step equation word problem: computers (video)

    The opposite of a positive is negative, and opposite of negative number is positive. So supposing the number is positive, then the 3 is multiplied by a negative number. This is what I think it looks like. 68-3x=x Add 3x to both sides. 68=4x Divide by 4.

  23. How To Solve Today's New York Times Wordle

    If you find yourself struggling to solve today's word then don't worry, we've got everything you need right here and we'll help you keep your precious streak intact. Related ... some general word clues, or, if you just want the full answer, we've got that here too. All the answers are hidden from view, so don't worry about any accidental spoilers.

  24. How to Solve Word Problems to Identify Independent and Dependent Variables

    The dependent variable is the one whose value depends on the other variable. To solve a word problem, first, you must list the information and then find the independent variable and dependent variable. Here's a step-by-step guide to solving word problems to identify independent and dependent variables: Step 1: Read the problem carefully.