## REAL WORLD PROBLEMS:

How to Write Equations Based on Algebra Word Problems

I know that you often sit in class and wonder, "Why am I forced to learn about equations, Algebra and variables?"

But... trust me, there are real situations where you will use your knowledge of Algebra and solving equations to solve a problem that is not school related. And... if you can't, you're going to wish that you remembered how.

It might be a time when you are trying to figure out how much you should get paid for a job, or even more important, if you were paid enough for a job that you've done. It could also be a time when you are trying to figure out if you were over charged for a bill.

This is important stuff - when it comes time to spend YOUR money - you are going to want to make sure that you are getting paid enough and not spending more than you have to.

Ok... let's put all this newly learned knowledge to work.

Click here if you need to review how to solve equations.

There are a few rules to remember when writing Algebra equations:

### Writing Equations For Word Problems

- First, you want to identify the unknown, which is your variable. What are you trying to solve for? Identify the variable: Use the statement, Let x = _____. You can replace the x with whatever variable you are using.
- Look for key words that will help you write the equation. Highlight the key words and write an equation to match the problem.
- The following key words will help you write equations for Algebra word problems:

#### Addition

altogether

increase

more

plus

sum

total

combine

#### subtraction

difference

decrease

less

fewer

reduce

minus

#### multiplication

per

times

product

double (2x)

triple (3x)

quadruple (4x)

#### division

quotient

divided by

divided into

per

share

split

Let's look at an example of an algebra word problem.

### Example 1: Algebra Word Problems

Linda was selling tickets for the school play. She sold 10 more adult tickets than children tickets and she sold twice as many senior tickets as children tickets.

- Let x represent the number of children's tickets sold.
- Write an expression to represent the number of adult tickets sold.
- Write an expression to represent the number of senior tickets sold.
- Adult tickets cost $5, children's tickets cost $2, and senior tickets cost $3. Linda made $700. Write an equation to represent the total ticket sales.
- How many children's tickets were sold for the play? How many adult tickets were sold? How many senior tickets were sold?

As you can see, this problem is massive! There are 5 questions to answer with many expressions to write.

### Solution

A few notes about this problem

1. In this problem, the variable was defined for you. Let x represent the number of children’s tickets sold tells what x stands for in this problem. If this had not been done for you, you might have written it like this:

Let x = the number of children’s tickets sold

2. For the first expression, I knew that 10 more adult tickets were sold. Since more means add, my expression was **x +10**. Since the direction asked for an expression, I don’t need an equal sign. An equation is written with an equal sign and an expression is without an equal sign. At this point we don’t know the total number of tickets.

3. For the second expression, I knew that my key words, twice as many meant two times as many. So my expression was **2x**.

4. We know that to find the total price we have to multiply the price of each ticket by the number of tickets. Take note that since x + 10 is the quantity of adult tickets, you must put it in parentheses! So, when you multiply by the price of $5 you have to distribute the 5.

5. Once I solve for x, I know the number of children’s tickets and I can take my expressions that I wrote for #1 and substitute 50 for x to figure out how many adult and senior tickets were sold.

### Where Can You Find More Algebra Word Problems to Practice?

Word problems are the most difficult type of problem to solve in math. So, where can you find quality word problems WITH a detailed solution?

The Algebra Class E-course provides a lot of practice with solving word problems for every unit! The best part is.... if you have trouble with these types of problems, you can always find a step-by-step solution to guide you through the process!

Click here for more information.

The next example shows how to identify a constant within a word problem.

### Example 2 - Identifying a Constant

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for *m* minutes is $21.20.

1. Write an equation that models this situation.

2. How many minutes were charged on this bill?

### Solution

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for *m* minutes is $21.20.

1. Write an equation that models this situation.

### Notes For Example 2

- $12.95 is a monthly rate. Since this is a set fee for each month, I know that this is a constant. The rate does not change; therefore, it is not associated with a variable.
- $0.25 per minute per call requires a variable because the total amount will change based on the number of minutes. Therefore, we use the expression 0.25m
- You must solve the equation to determine the value for m, which is the number of minutes charged.

The last example is a word problem that requires an equation with variables on both sides.

### Example 3 - Equations with Variables on Both Sides

You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week. How long will it be before you and your sister have the same amount of money? Write an equation and solve.

### Solution

Notes for Example 3

- $60 and $120 are constants because this is the amount of money that they each have to begin with. This amount does not change.
- $7 per week and $5 per week are rates. They key word "per" in this situation means to multiply.
- The key word "same" in this problem means that I am going to set my two expressions equal to each other.
- When we set the two expressions equal, we now have an equation with variables on both sides.
- After solving the equation, you find that x = 30, which means that after 30 weeks, you and your sister will have the same amount of money.

I'm hoping that these three examples will help you as you solve real world problems in Algebra!

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## Math Word Problem Keywords {Free Cheat Sheets}

Tackling word problems in math can be challenging for kids to learn and not any easier to teach. We called them story problems when I was in school. Check out this blog post for **math word problem keywords with free cheat sheets** to begin teaching this challenging math operations subject in your homeschool.

### Introducing word problems in math

There is no doubt that mathematical operations using words are difficult for kids. They go from counting numbers to doing math equations with numbers.

Then all of a sudden… there are words, *just words*. All of a sudden algebraic expressions and mathematical operations are POOF – words.

The lack of numbers and shift in mindset can completely throw off a lot of students. If kids have difficulty with reading, then that is yet another struggle for kids as they try to learn basic problems in math.

### Why do some kids struggle with word problems?

A key proponent in different operations in math is learning the keywords that prompt kids to understand which operation skill they need to use to solve the problem.

This means that they should master regular math problems first and be able to read with comprehension. You will shortly find that if these two skills aren’t somewhat mastered first, then word problems will become an issue.

Many times math is a subject best taught in sequential order. If one step is missed, then the future steps falter. This is much like how it is when teaching word problems.

**The best thing for your children is for them to first:**

- Be able to read well.
- Understand math concepts and phrases.
- Know to not rush, but focus on keywords, identify relevant information, and understand the text.

### What are keywords in math word problems?

Keywords in mathematical word operations are the words or phrases that will signal or show a student which type of math operation to choose in order to solve the math word problem.

The words used in operations are a strategy that helps the math problem make sense and draw connections to how it can be answered.

Basically, when using keywords, students must decipher whether they need to solve the math equation via addition, subtraction, multiplication, or division.

### What are the common keywords for math word problems?

Thankfully, there are keywords that our children can learn that help them work through their word problems. They are prompts that point them in the right direction.

Just like a different language needs words translated for comprehension, students translate the words… into *math*.

### Common special words that help with problem solving:

#### Keywords to identify addition in word problems

- total
- combine
- together
- add
- altogether
- increased by
- increase
- more than
- plus
- sum
- together
- both
- in all
- larger
- larger than
- more
- in addition to
- how much in all

#### Keywords used in subtraction word problems

- take away
- left over
- decreased
- difference
- fewer than
- gave away
- how many more
- how many less
- less
- minus
- remain
- shorter than
- smaller than

#### Keywords for multiplication word problems

- cubed
- times
- each
- groups
- area
- product of
- per
- triple
- quadruple
- increased by
- multiplied by
- double/twice

#### Keywords used for division word problems

- divide
- equal group
- average
- each
- half of
- quarter
- ratio
- quotient
- share
- split by
- as much
- cut up
- how many in each
- percent

You can print off a free cheat sheet that has the above math keywords for word problems and add it to your homeschool binder.

### How can we help kids learn keywords for solving numberless word problems?

Teach kids steps for solving word problems until it becomes a habit or they get comfortable with the steps. First, they can look for the important information and write those down. (Read the problem carefully). Next, kids need to define or find the variables in the math equation.

From the keywords, kids can now determine what math operation to use. *Translate the words to math. *Then, kids can solve the math equation. This is where the skills of solving numbered equations are important.

Finally, students have to put their answers in the form of a word sentence. NOTE: *Many times kids think after solving the equation they are done. However, the key to making sure they understand that word problems need word answers.*

### Different Strategies to Familiarize Keywords in Word Operations

You can use some of these keywords as key **vocabulary words** in your homeschool.

Students can display subtraction, addition, multiplication, and multiplication handy reference **posters on a bulletin board** in your homeschool area. Students can also just list them on **dry erase boards**. These are perfect visual reminders for what keywords go with what math word problems.

Your students can also keep their keywords for math word problems with them as they study. They can place the list of keywords in a **math folder** or in an **anchor chart** – and then in their math folder.

Kids can keep the keyword **poster sets** in their math notebooks or keep them in a **word problem journal**.

Their strategy for learning word problem keywords all depends on how they best absorb information.

Students may do well using a combination of these methods. Either way, all of these different strategies can be used to get them comfortable in identifying the route to solve math word equations.

### Math Word Problem Keywords Cheat Sheets & Teaching Aids:

Get a Clue Free Download – Check out these word problem clue word handouts and posters to help your students with word problems. There 5 pages in all that will be handy for your kids in trying to find the correct answer while using the correct operation.

Subtraction Keywords/Addition Keywords – Until your kids memorize keywords and what they mean, this freebie can help. Grab these simple black and white printable signs. They will help kids look for keywords like *larger numbers* for subtraction word problems or addition keywords like *in addition to*.

Words to Math – Keywords in math problems are essentially turning words into math. This graphic organizer printable is a quick reference for your students to use with numberless math word problems. Place them in a notebook chart or your homeschool classroom wall as a visual reminder.

Key Word Posters for Math Problems – Grab these word problem keyword handy reference posters for subtraction, addition, division, and multiplication. Each poster has its specific theme and specific words to solve all problem types. Kids will enjoy having practiced with these math key words posters.

Fun Key Word Sorting Activity – Your kids have now studied some keywords for problem solving in mathematical operations. Use this word problem sorting activity to test their knowledge in a fun engaging way. Add this fun activity to your test prep materials.

### Free Math Word Problems Keywords Cheat Sheet Download

You won’t want to miss our free cheat sheet download for different ways kids see keywords in various types of problems in mathematics. This math tool is everything your student needs and the perfect resource to reference keywords in math operations.

Math word problems are probably the first opportunity students get to understand how math relates to real world situations. The applications can be relevant in their real life experiences like going to the market.

*However, the benefit to word problems doesn’t stop there…*

With word problems, students develop their higher-order thinking and critical thinking skills.

Different types of word problems guide your students to applying math various math concepts at the same time. They have to know basic number sense, basic algebra skills, and even geometry when they attempt multiplication word problems.

If we do it the right way, kids won’t see word problems as a dreadful experience in math. Understanding word problems is a learning curve and doesn’t come easily to kids.

### Help For Math Struggles

Here are some resources to help you with a child struggling with math or if they seem to hate math.

Another important aspect of word problems is that they tell a parent/teacher if a child needs help in areas like reading comprehension or math number operations skills. This type of word math is a great evaluation of your student’s thinking processes.

We can, however, help make it a better experience for them by teaching it the right way.

Jeannette is a wife, mother and homeschooling mom. She has been mightily, saved by grace and is grateful for God’s sovereignty throughout her life’s journey. She has a Bachelor in English Education and her MBA. Jeannette is bi-lingual and currently lives in the Tongan Islands of the South Pacific. She posts daily freebies for homeschoolers!

Filed Under: Math Freebies for Homeschoolers

Sours: https://homeschoolgiveaways.com/2021/07/math-word-problem-keywords-cheat-sheets/## Solving Word Problems in Algebra

Inequality Word Problems

How are you with solving word problems in Algebra? Are you ready to dive into the "real world" of inequalities? I know that solving word problems in Algebra is probably not your favorite, but there's no point in learning the skill if you don't apply it.

I promise to make this as easy as possible. Pay close attention to the key words given below, as this will help you to write the inequality. Once the inequality is written, you can solve the inequality using the skills you learned in our past lessons.

I've tried to provide you with examples that could pertain to your life and come in handy one day. Think about others ways you might use inequalities in real world problems. I'd love to hear about them if you do!

Before we look at the examples let's go over some of the rules and key words for solving word problems in Algebra (or any math class).

### Word Problem Solving Strategies

- Read through the entire problem.
- Highlight the important information and key words that you need to solve the problem.
- Identify your variables.
- Write the equation or inequality.
- Solve.
- Write your answer in a complete sentence.
- Check or justify your answer.

I know it always helps too, if you have key words that help you to write the equation or inequality. Here are a few key words that we associate with inequalities! Keep these handy as a reference.

### Inequality Key Words

- at least - means greater than or equal to
- no more than - means less than or equal to
- more than - means greater than
- less than - means less than

Ok... let's put it into action and look at our examples.

### Example 1: Inequality Word Problems

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets.

- Write an inequality that represents Keith's situation.
- How many weeks can Keith withdraw money from his account? Justify your answer.

### Solution

**Step 1:** Highlight the important information in this problem.

Note: ** At least** is a key word that notes that this problem must be written as an inequality.

**Step 2**: Identify your variable. What don't you know? The question verifies that you don't know how many weeks.

Let w = the number of weeks

**Step 3: **Write your inequality.

500 - 25w __>__ 200

I know you are saying, "How did you get that inequality?"

I know the "at least" part is tricky. You would probably think that at least means less than.

But... he wants the amount in his account to be at least $200 which means $200 or greater. So, we must use the greater than or equal to symbol.

**Step 4**: Solve the inequality.

The number of weeks that Keith can withdraw money from his account is 12 weeks or less.

**Step 5: **Justify (prove your answer mathematically).

I'm going to prove that the largest number of weeks is 12 by substituting 12 into the inequality for w. You could also substitute any number less than 12.

Since 200 is equal to 200, my answer is correct. Any more than 12 weeks and his account balance would be less than $200. Any number of weeks less than 12 and his account would stay above $200.

That wasn't too bad, was it? Let's take a look at another example.

### Example 2: More Inequality Word Problems

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile. Katie has no more than $10 to spend on a ride.

- Write an inequality that represents Katie's situation.
- How many miles can Katie travel without exceeding her budget? Justify your answer.

### Solution

**Step 1: **Highlight the important information in this problem.

Note: No more than are key words that note that this problem must be written as an inequality.

**Step 2:** Identify your variable. What don't you know? The question verifies that you don't know the number of miles Katie can travel.

Let m = the number of miles

**Step 3: **Write the inequality.

0.65m + 1.75 __<__ 10

Are you thinking, "How did you write that inequality?"

The "no more than" can also be tricky. "No more than" means that you can't have more than something, so that means you must have less than!

**Step 4:** Solve the inequality.

Since this is a real world problem and taxi's usually charge by the mile, we can say that Katie can travel 12 miles or less before reaching her limit of $10.

**Step 5:** Justify (prove your answer mathematically).

Are you ready to try some on your own now? Yes... of course you are! Click here to move onto the word problem practice problems.

### Take a look at the questions that other students have submitted:

- Home >
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- Inequality Word Problems

Need More Help With Your Algebra Studies?

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Click here for more information on our affordable subscription options.

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## Word problems sheet math cheat

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