Word problem solving examples

Related Pages
Math Word Problems
Singapore Math Word Problems
More Algebra Lessons

Here are some examples of mixed operations word problems. These problems are slightly more challenging,
but they also illustrate how helpful the block diagrams can be. The block diagrams or tape diagrams
(Common Core) can be used to help solve word problems that would usually require algebra.

Example:
Two bowls and three plates cost $1421. The cost of the plate is half the cost of the bowl. What is
the cost of the bowl?

Solution:
Step 1: Draw a block diagram to illustrate the number of bowls
and plates. (In this diagram, the bowls are shown as orange blocks and the plates as blue blocks.)

Step 2: Since a bowl costs twice as much as a plate, we can
replace one orange block (bowl) with two blue blocks (plate).

Step 3: Looking at the block diagram, find the cost of each plate.
7 blue blocks = 1421
1 blue block = 1421 ÷ 7 = 203
The cost of each plate is $203.
The cost of each bowl is 203 × 2 = $406.

Example:
A factory makes 4250 bars of chocolate. There were three kinds of chocolate bars – creamy,
milky and white. The number of white chocolate bars was 715 more than the number of milky chocolate
bars. The number of creamy chocolate bars was 5 times the number of milky chocolate bars. How many
creamy chocolate bars did the factory make?

Solution:
Step 1: Draw a block diagram to illustrate the different types of
chocolate bars. (In this diagram, the creamy chocolate bars are shown as orange blocks, the milky
chocolate bars as blue blocks and the white chocolate bars as red blocks.)

Step 2: Since the number of creamy chocolate bars was 5 times the
number of milky chocolate bars, we can replace one orange block (creamy) with 5 blue blocks (milky).
Since the number of white chocolate bars was 715 more than the number of milky chocolate bars, we
replace one red block with one blue block + 715.

Step 3: Looking at the block diagram, find the number of milky
chocolate bars (blue block)
4250 – 715 = 3535
7 blue blocks = 3535
1 blue block = 3535 ÷ 7 = 505
The number of milky chocolate bars made was 505.

Step 4: Calculate the number of creamy chocolate bars.
The number of creamy chocolate bars was 5 times the number of milky chocolate bars = 5 × 505 = 2525

How to solve word problems with four types of bar models — Comparing, Taking Out, Combining, Missing Part?

Examples:

1. Each week, Dwight calculated that he spends 2/3 of his allowance on food and 1/9 on video games.
   How much did he spend on food and video games?
2. Marvin bought 1/2 pound of gummy bears. He ate 1/3 pound on his way to school. How much of gummy bears
   does Marvin have left?
3. A recipe needs 7/8 teaspoons of salt and 2/5 teaspoons of sugar. How much more salt is needed than sugar?
4. For the last hour Mr. Negron was awake, he spent 4/8 of the hour making homework and 1/8 of the hour
   talking. He spent the rest of the hour watching TV. What fraction of the hour did he spend watching TV?

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Example:
Julian and Stacey need 8 liters of water to fill a tank. Stacey filled the tank with 3 11/12 liters of water.
Julian poured 1 2/5 liters less than Stacey into the tank. How much water is still needed to fill the tank?

• Show Video Lesson

How to solve part-whole word problems with bar modeling?

Examples:

1. Danika bought some nail polish for $51. This was 3/5 of her money. How much money did she have to begin with?
2. Henry bought 520 cookies for the math competition. If 3/4 were eaten, how many did he have left over?
3. Betsy made cupcakes to bring to work. After the Science Department ate 2/7 and the Math Department ate 64,
   she had 1/7 left. How many cupcakes did Betsy make?
4. Fran sold 108 chocolate chip and Snickerdoodle cookies at her lemonade stand. If she made 36 Snickerdoodle
   cookies, how many chocolate chip cookies did she make? How much money did she earn selling the chocolate chip
   cookies if she sold them in bags of 6 for $1.25 and she sold all of the bags.
5. Two lbs. of nactarines and one lb. of bananas cost $3.15. Two lbs. of nectarines and three lbs. of bananas
   cost $5.65. Find the cost of one lb. of bananas.
6. Two tennis balls and one racquet cost $75. Two tennis balls and three racquets cost $215. Find the cost of
   one racquet.
7. Carter raised money for a walk-a-thon. On Monday, he earned $0.75 per lap. On Tuesday, he earned $0.80 a
   lap and on Wednesday, he earned $0.95 a lap. If he walked 36 laps on Monday, 50% as many laps on Wednesday
   as on Monday, how much money did Carter earn for the walk-a-thon?

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How to solve comparison word problems with bar modeling?

Examples:

1. Alex, Sonia and Tini have a total of $580. Sonia has $120 more than Alex, and Toni has $190 more than Sonia.
   How much money does Toni have?
2. Trevor bought a ski jacket, gloves and helmet on clearance for $242 altogether. The jacket cost $71 more
   than the gloves while the gloves cost $27 less than the helmet. How much did the jacket cost?
3. A hard drive costs twice as much as a 64 GB jump drive and a 32 GB jump drive costs half as much as a 64 GB
   jump drive. If the hard drive costs $140, find the total cost.
4. Tracy earned 3/4 as much as Julie. Shannon earned 2/3 as much as Tracy. Julie earned $44. How much less
   did Shannon earn than Tracy?
5. Sadie spent twice as much money as Kim. Kim spent $150 less than Jason. Jason spent $45 more than Sadie.
   How much money did they spend altogether?
6. Harlis is five years younger than Janae. Sherry is three times as old as Janae. Together, Harlis’ and
   Janae’s total age is 20 years less than Sherry’s age. How old is Sherry?
7. Josh has 3/4 as many jelly beans as Lisa. Lisa has 4/5 as many jelly beans as Curt. If Curt has 28 more
   jelly beans than Josh, how many jelly beans do they have altogether?

• Show Video Lesson

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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After you finish this lesson, view all of our Pre-Algebra lessons and practice problems. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

Solving Word Problems

To solve a word problem using a system of equations, it is important to;
– Identify what we don’t know
– Declare variables
– Use sentences to create equations

An example on how to do this:

Mary and Jose each bought plants from the same store. Mary spent $188 on 7 cherry trees and 11 rose bushes. Jose spent $236 on 13 cherry trees and 11 rose bushes. Find the cost of one cherry tree and the cost of one rose bush.

Cost of a cherry tree:
Cost of a rose bush:
7 cherry trees and 11 rose bushes = $188

The y-values cancel each other out, so now you are left with only x-values and real numbers.

Then, you plug in your x-value into an original equation in order to find the y-value.

Cost of a cherry tree: $8
Cost of a rose bush: $12

Example 1

Three coffees and a cupcake cost a total of dollars. Two coffees and four cupcake cost a total of dollars. What is the individual price for a single coffee and a single cupcake?

Let’s solve this by following steps.

1. What we don’t know:

Cost of a single coffee

Cost of single cupcake

2. Declare variables:

Cost of a single coffee=

Cost of single cupcake=

3. Use sentences to create equations.

Three coffees and a cupcake cost a total of dollars.

Two coffees and four cupcake cost a total of dollars.

Now, we have a system of equations:

Let’s solve for one of the variables in one of the equations and then use that to substitute into the other.

Now, solve for the value of using the first equation.

Let’s solve the value of by substituting the value of to the bottom equation.

Distribute to each terms inside the parenthesis

Combine like terms

Now, let’s isolate the by subtracting on both sides.

Then divide both sides by ,

And we’ll have

Then, let’s plug the value of into one equation to get the value of .

Cost of a single coffee=

Cost of single cupcake=

Example 2

The senior class at High School A rented and filled vans and buses with students. High School B rented and filled vans and bus with students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

Let’s solve this by following steps.

1. What we don’t know:

Students in each van

Students in each bus

2. Declare variables:

Students in each van=

Students in each bus=

3. Use sentences to create equations.

High School A rented and filled 8 vans and 8 buses with 240 students.

High School B rented and filled 4 vans and 1 bus with 54 students.

Now, we have a system of equations:

Let’s solve for one of the variables in one of the equations and then use that to substitute into the other.

Now, solve for the value of using the second equation.

Let’s solve the value of by substituting the value of to the bottom equation.

Distribute to each terms inside the parenthesis

Combine like terms

Now, let’s isolate the by subtracting on both sides.

Then divide both sides by ,

And we’ll have

Then, let’s plug the value of into one equation to get the value of .

Students in each van=

Students in each bus=

Video-Lesson Transcript

To solve a word problem using system of equations, it is important to:
1. Identify what we don’t know
2. Declare variables.
3. Use sentences to create equations.

Let’s have an example:

Mary and Jose each bought plants from the same store. Mary spent on cherry trees and rose bushes. Jose spent on cherry trees and rose bushes. Find the cost of one cherry tree and the cost of one rose bush.

Let’s solve this by following steps above.

1. What we don’t know:
cost of a cherry tree
cost of a rose bush

2. Declare variables:
cost of a cherry tree :
cost of a rose bush :

3. Use sentences to create equations.

For Mary:
cherry trees and rose bushes

For Jose:
cherry trees and rose bushes

Now, we have a system of equations

We can solve this by process of substitution, elimination or fraction.

Since the value of is the same for both equations, let’s do the process of elimination.

First, let’s multiply the first equation by

Here we’ll have a negated equation

Let’s do the process of elimination now

We’ll have

Then, let’s isolate by dividing both sides by

Now, we have

Remember, our declared variable?

cost of a cherry tree :

Since

Now we can say that

cost of a cherry tree :

Now, let’s solve for the value of by getting one equation and plugging the value of .

Let’s use the first equation to plug in

Let’s isolate by subtracting on both sides of the equation

Then divide by

And we get

Now, we know that cost of a rose bush is .

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).

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

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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:

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1. Home

>

2. Inequalities

>

3. 
   Inequality Word Problems

Now that we’ve practiced turning words into linear equations, let’s actually solve a couple of word problems. This is usually a three-step process:

1. Find the linear equation being described.
2. Figure out what question is being asked, and answer that question.
3. Check your answer.

The fourth step, «take a nap,» is totally optional.

Sample Problem

Jenna works at a retail shop. Yes, she still works there, even after all her thievery, but she’ll tell you it has nothing to do with her old man owning the joint. She still makes $10 per hour, plus $3 for each item she sells.

1. How much does Jenna make in one hour if she sells 5 items during that hour?
2. How many items would Jenna need to sell in an hour to make $43 during that hour?

This word problem is describing a line with an equation we found earlier: y = 3x + 10, which describes the amount of cash (y) she makes in an hour if she sells x items.

Since we’ve found the linear equation, now we can answer the questions.

1. How much does Jenna make in one hour if she sells 5 items during that hour?

Since x is the number of items Jenna sells during one hour, we’ve got x = 5.

Then y = 3(5) + 10 = 25, which means Jenna would be paid $25. This amount doesn’t include tips. Yeah, she makes tips, too. What can we say, this girl knows how to turn a buck.

2. How many items would Jenna need to sell in an hour to make $43 during that hour?

Since y is the amount Jenna is paid, if Jenna makes $43, we want to have y = 43. Plug that into our equation:

43 = 3x + 10

We can solve this equation for x to find:

Since x is the number of items Jenna sells during an hour, in order to make $43 Jenna must sell 11 items. Given her foolproof sales technique of breaking down into tears whenever someone decides not to buy something, she shouldn’t have any problem hitting that mark.

Let’s check that this is correct, though: If Jenna sells 11 items she’ll make 3(11) + 10 dollars, which is indeed $43.

Sample Problem

Marcio spent $7 per day. Knowing Marcio, he probably spent it on Lotto scratchers. After five days, he had $8 left. How much money did Marcio start with?

First, we need to come up with a linear equation. The amount of money Marcio has depends on how many days have passed. Let’s have x be the number of days that have passed, and y be the amount of money Marcio has.

The statement «after five days, he had $8 left» tells us that the point (5, is on the graph. It also tells us he «shockingly» hasn’t struck it rich yet, or he probably would have given up on these silly things by now.

Since Marcio is spending $7 per day, the slope of the line is -7. We can use this information to find an equation for the line. Let’s use point-slope form, since we have a point and a slope. We find the equation:

y – 8 = -7(x – 5)

Now we can worry about answering the question. The amount of money Marcio started with is the amount of money he had when 0 days had passed. Oh, to go back in time and have all that hard-earned cashola back, eh, Marcio?

We want to find the y-intercept of the line, since that’s the point where x = 0 days. We can do this by rearranging our point-slope equation into slope-intercept form.

The y-intercept is 43, which means Marcio started with $43. Hey…that’s how much Jenna made from selling her 11 items. These two might be in cahoots…

Let’s make sure we’re right. If Marcio started with $43 and spent $7 per day, after 5 days he would have 43 – 5(7) = 43 – 35, which is indeed 8 dollars.

Word problems that involve a linear equation can give us the information we need to write that equation in several different ways. We could be told two points on the line, or a point and a slope, or the y-intercept and the slope, or both intercepts. We could be given a treasure map that will lead us to the information we need, although those problems are more rare. Word problems can ask questions about the intercepts of the line or the slope. They can provide one coordinate of a point on the line and then ask for the other coordinate.

Come to think of it, they ask us for a whole lot of stuff without giving much back in return. We’re in a one-sided relationship and should probably get out of it. We’ll see what our therapist has to say about this on Tuesday.

After we find the line described by the word problem, the trick, as usual, is to figure out what the question is actually asking. Don’t be distracted by any of its mumbo-jumbo.

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. Read the Entire Word Problem

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. What exactly is the question?

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

• Circle any numbers you’ll use.

• Lightly cross out any information you don’t need.

• Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd Grade Math Task Cards Bundle has word problems in almost every one of its 30 task card sets.

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

Thanks so much for stopping by!

A Picture is Worth a Thousand Words

“Today, we are going to solve math word problems.” When students hear this from their math teacher, their faces drop, sweat starts to form on their foreheads and they refuse to make eye contact. As a math teacher, I understand. I understand the anxiety and want to make the learning process with word problems more enjoyable. This is where reading, writing and, math collide and the real world of math begins. Let’s talk about how to solve word problems with pictures.

When students struggle with word problems in school, they also have difficulty tackling them for homework. Most students want the “one-size-fits-all” formula for word problems but unfortunately, that does not exist. However, drawing a picture will help students visualize the problem and will start advancing their learning stage from the concrete to the abstract. Let’s take a look at how to solve a word problem using pictures:

Steps for Solving Word Problems using Pictures

1. Read the entire problem: Get all the facts – Underline key word
2. Answer the question: What am I looking for?
3. Draw a picture or diagram: Visualize as a real world situation
4. Solve the problem: Set up the equation and solve
5. Check your solution: Is this answer reasonable?

Word Problem Examples – Example A

Cody has 6 pencils on his desk, Jonah has 4 more than Cody and Vinny has three less pencils than Jonah. How many pencils are there in all?

• Read the entire problem  √
• What am I looking for? How many pencils do Cody, Jonah and Vinny have altogether?  √
• Draw a picture or diagram √

• Solve the problem    √

      6 + 10 + 7 = 23 pencils

• Check your solution  √

      This answer is reasonable

Example B

There are 3 fish tanks labeled   X, Y, and Z. Y weighs 6 times as much as X and twice as much as Z. If Z is 36 lbs. heavier than X, find the total weight of X, Y and Z.

• Read the entire problem  √
• What am I looking for?  What is thetotal weight of fish tanks X, Y and Z?  √
• Draw a picture or diagram √

• Solve the problem    √

18 + 108 + 54 = 180 pounds

• Check your solution  √

      This answer is reasonable

Visualizing a word problem with pictures is a strategy that will help motivate many students to begin the process of solving them.  This works especially for students that may become bored by the excess amount of words instead of numbers or for those students who become overwhelmed by the information and want to break it down into a simpler form.   Another benefit of using pictures when solving word problems involves communicating the results.  The pictures act as justification for answers, make the problems easier to understand and therefore, secure the learning process.

Meet our Guest Blogger: Jan Rowe

Jan is one of Educational Connections’ top tutors. She has twelve years of classroom teaching experience and holds a Virginia and Florida teaching license in middle school mathematics and elementary education. Jan has been with Educational Connections for over a year, working with over twenty students. Her tutoring goal is to help each student understand their learning style so they can improve the speed and quality of that learning. When she is not tutoring or teaching, Jan loves to play scrabble, go hiking and play Frisbee with her new puppy.

 Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in the cartoon below?

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts, like the student in the cartoon below. Read the positive thoughts and say them out loud.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-Solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then, you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.

We list the steps we took to solve the previous example.

Translate word problems into expressions

One of the first steps to solving word problems is converting an English sentence into a mathematical sentence. In the table below, words or phrases commonly associated with mathematical operators are categorized. Word problems often contain these or similar words, so it’s good to see what mathematical operators are associated with them.

Addition [latex]+[/latex]	Subtraction [latex]-[/latex]	Multiplication [latex]times[/latex]	Variable ?	Equals [latex]=[/latex]
More than	Less than	Double	A number	Is
Together	In the past	Product	Often, a value for which no information is given.	The same as
Sum	Slower than	times	After how many hours?
Total	The remainder of		How much will it cost?
In the future	Difference
Faster than

Some examples follow:

• “[latex]xtext{ is }5[/latex]” becomes [latex]x=5[/latex]
• “Three more than a number” becomes [latex]x+3[/latex]
• “Four less than a number” becomes [latex]x-4[/latex]
• “Double the cost” becomes [latex]2cdottext{ cost }[/latex]
• “Groceries and gas together for the week cost $250” means [latex]text{ groceries }+text{ gas }=250[/latex]
• “The difference of [latex]9[/latex] and a number” becomes [latex]9-x[/latex]. Notice how [latex]9[/latex] is first in the sentence and the expression.

Let’s practice translating a few more English phrases into algebraic expressions.

In this example video, we show how to translate more words into mathematical expressions.

For another review of how to translate algebraic statements into words, watch the following video.

The power of algebra is how it can help you model real situations in order to answer questions about them.  Let’s use this approach with another example.

In the video that follows, we show another example of how to translate a sentence into a mathematical expression using a problem solving method.

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

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