How to solve the word problems - Word и Excel - помощь в работе с программами

Download Article

You can solve many real world problems with the help of math. In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems can present a real challenge if you don’t know how to break them down and find the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.

1

Read the problem carefully.^[1] A common setback when trying to solve algebra word problems is assuming what the question is asking before you read the entire problem. In order to be successful in solving a word problem, you need to read the whole problem in order to assess what information is provided, and what information is missing.^[2]
2
Determine what you are asked to find. In many problems, what you are asked to find is presented in the last sentence. This is not always true, however, so you need to read the entire problem carefully.^[3] Write down what you need to find, or else underline it in the problem, so that you do not forget what your final answer means.^[4] In an algebra word problem, you will likely be asked to find a certain value, or you may be asked to find an equation that represents a value.
- For example, you might have the following problem: Jane went to a book shop and bought a book. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $10 less than three times the price of he first book. What was the price of the first book?
- In this problem, you are asked to find the price of the first book Jane purchased.
Advertisement
3
Summarize what you know, and what you need to know. Likely, the information you need to know is the same as what information you are asked to find. You also need to assess what information you already know. Again, underline or write out this information, so you can keep track of all the parts of the problem. For problems involving geometry, it is often helpful to draw a sketch at this point.^[5]
- For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second book cost $10 less than 3 times the price of the first book. You don’t know the price of the first book.
4

Assign variables to the unknown quantities. If you are being asked to find a certain value, you will likely only have one variable. If, however, you are asked to find an equation, you will likely have multiple variables. No matter how many variables you have, you should list each one, and indicate what they are equal to.^[6]
5
Look for keywords.^[7] Word problems are full of keywords that give you clues about what operations to use. Locating and interpreting these keywords can help you translate the words into algebra.^[8]
- Multiplication keywords include times, of, and factor.^[9]
- Division keywords include per, out of, and percent.^[10]
- Addition keywords include some, more, and together.^[11]
- Subtraction keywords include difference, fewer, and decreased.^[12]

1

Write an equation. Use the information you learn from the problem, including keywords, to write an algebraic description of the story.^[13]
2

Solve an equation for one variable. If you have only one unknown in your word problem, isolate the variable in your equation and find which number it is equal to. Use the normal rules of algebra to isolate the variable. Remember that you need to keep the equation balanced. This means that whatever you do to one side of the equation, you must also do to the other side.^[14]
3

Solve an equation with multiple variables. If you have more than one unknown in your word problem, you need to make sure you combine like terms to simplify your equation.
4

Interpret your answer. Look back to your list of variables and unknown information. This will remind you what you were trying to solve. Write a statement indicating what your answer means.^[15]

1
Solve the following problem. This problem has more than one unknown value, so its equation will have multiple variables. This means you cannot solve for a specific numerical value of a variable. Instead, you will solve to find an equation that describes a variable.
- Robyn and Billy run a lemonade stand. They are giving all the money that they make to a cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double whatever amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy will give to the shelter.
2

Read the problem carefully and determine what you are asked to find.^[16] You are asked to find how much money Robyn and Billy will give to the cat shelter.
3

Summarize what you know, and what you need to know. You know that Robyn and Billy will make money from selling cups of lemonade and from getting tips. You know that they will sell each cup for 75 cents. You also know that their mom and dad will double the amount they make in tips. You don’t know how many cups of lemonade they sell, or how much tip money they get.
4

Assign variables to the unknown quantities. Since you have three unknowns, you will have three variables. Let equal the amount of money they will give to the shelter. Let equal the number of cups they sell. Let equal the number of dollars they make in tips.
5

Look for keywords. Since they will “combine” their profits and tips, you know addition will be involved. Since their mom and dad will “double” their tips, you know you need to multiply their tips by a factor of 2.
6

Write an equation. Since you are writing an equation that describes the amount of money they will give to the shelter, the variable will be alone on one side of the equation.
7

Interpret your answer. The variable equals the amount of money Robyn and Billy will donate to the cat shelter. So, the amount they donate can be found by multiplying the number of cups of lemonade they sell by .75, and adding this product to the product of their tip money and 2.

Add New Question

Question

How do you solve an algebra word problem?

Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary’s College.

Academic Tutor

Expert Answer

Carefully read the problem and figure out what information you’re given and what that information should be used for. Once you know what you need to do with the values they’ve given you, the problem should be a lot easier to solve.
Question

If Deborah and Colin have $150 between them, and Deborah has $27 more than Colin, how much money does Deborah have?

Let x = Deborah’s money. Then (x — 27) = Colin’s money. That means that (x) + (x — 27) = 150. Combining terms: 2x — 27 = 150. Adding 27 to both sides: 2x = 177. So x = 88.50, and (x — 27) = 61.50. Deborah has $88.50, and Colin has $61.50, which together add up to $150.
Question

Karl is twice as old Bob. Nine years ago, Karl was three times as old as Bob. How old is each now?

Let x be Bob’s current age. Then Karl’s current age is 2x. Nine years ago Bob’s age was x-9, and Karl’s age was 2x-9. We’re told that nine years ago Karl’s age (2x-9) was three times Bob’s age (x-9). Therefore, 2x-9 = 3(x-9) = 3x-27. Subtract 2x from both sides, and add 27 to both sides: 18 = x. So Bob’s current age is 18, and Karl’s current age is 36, twice Bob’s current age. (Nine years ago Bob would have been 9, and Karl would have been 27, or three times Bob’s age then.)

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Video

Word problems can have more than one unknown and more the one variable.
The number of variables is always equal to the number of unknowns.
While solving word problems you should always read every sentence carefully and try to extract all the numerical information.

Show More Tips

References

About This Article

Article SummaryX

To solve word problems in algebra, start by reading the problem carefully and determining what you’re being asked to find. Next, summarize what information you know and what you need to know. Then, assign variables to the unknown quantities. For example, if you know that Jane bought 2 books, and the second book cost $80, which was $10 less than 3 times the price of the first book, assign x to the price of the 1st book. Use this information to write your equation, which is 80 = 3x — 10. To learn how to solve an equation with multiple variables, keep reading!

Did this summary help you?

Thanks to all authors for creating a page that has been read 56,462 times.

Reader Success Stories

James Carson

Sep 13, 2019

«I think this is amazing because it explains how and what you need to do.This helped me in algebra, and I recommend…» more

Did this article help you?

Источник

Related Pages
Basic Algebra
Combining Like Terms
Solving Equations
More Algebra Lessons

Step 1: Translate the problem into equations with variables

First, we need to translate the word problem into equation(s) with variables.
Then, we need to solve the equation(s) to find the solution(s) to the
word problems.

Translating words to equations

How to recognize some common types of algebra word problems and how to solve them step by step.

The following shows how to approach the common types of algebra word problems.

Age Problems usually compare the ages of people.
They may involve a single person, comparing his/her age in the past, present or future.
They may also compare the ages involving more than one person.

Average Problems involve the computations for
arithmetic mean or
weighted average of different quantities.
Another common type of average problems is the average speed computation.

Coin Problems deal with items with denominated values.
Similar word problems are Stamp Problems and
Ticket Problems.

Consecutive Integer Problems deal with consecutive numbers.
The number sequences may be Even or
Odd, or some other simple number sequences.

Digit Problems involve the relationship and manipulation of digits in numbers.

Distance Problems involve the distance an object travels at a rate over a period of time.
We can have objects that Travel at Different Rates, objects that
Travel in Different Directions or we may need to find the distance
Given the Total Time

Fraction Problems involve fractions or parts of a whole.

Geometry Word Problems deal with geometric figures and angles described in words.

This include geometry word problems Involving Perimeters,
Involving Areas and
Involving Angles

Integer Problems involve numerical representations of word problems.
The integer word problems may Involve 2 Unknowns or may
Involve More Than 2 Unknowns

Interest Problems involve calculations of simple interest.
Lever Problems deal with the lever principle described in word problems.
Lever problem may involve 2 Objects or More than 2 Objects

Mixture Problems involve items or quantities of different values that are
mixed together. This involve
Adding to a Solution,
Removing from a Solution,
Replacing a Solution,or Mixing Items of Different Values

Motion Word Problems are word problems that uses the distance, rate and time formula.

Number Sequence Problems use number sequences in the construction of word problems.
You may be asked to find the
Value of a Particular Term or the Pattern of a Sequence

Proportion Problems involve proportional and inversely proportional relationships of various quantities.

Ratio Problems require you to relate quantities of different items in certain
known ratios, or work out the ratios given certain quantities.
This could be Two-Term Ratios or
Three-Term Ratios

Symbol Problems

Variation Word Problems may consist of Direct Variation Problems,
Inverse Variation Problems or Joint Variation Problems

Work Problems involve different people doing work together at different rates.
This may be for Two Persons,
More Than Two Persons or
Pipes Filling up a Tank

For more Algebra Word Problems and Algebra techniques, go to our
Algebra page

Step 2: Solving the equations — finding the values of the variables for the equations

How to solve equations?

Algebra Word Problems with examples, videos and step-by-step solutions

Age Word Problems
Average Word Problems
Coin Word Problems
Consecutive Integer Word Problems
Digit Word Problems
Distance Word Problems
Fraction & Percent Word Problems
Geometry Word Problems
Integer Word Problems
Interest Word Problems
Lever Word Problems
Mixture Word Problems
Money & Coin Word Problems
Motion & Distance Word Problems
Number Sequence Word Problems
Proportion Word Problems
Word Problems using Quadratic Equations
Ratio Word Problems
Symbol Word Problems
Variation Word Problems
Work Word Problems
Ways to solve Word Problems

Have a look at the following videos for some introduction of how to solve algebra problems:

Example:
Angela sold eight more new cars this year than Carmen. If together they sold a total of 88 cars, how many cars did each of them sell?

Show Video Lesson

Example:
One number is 4 times as large as another. Their sum is 45. Find the numbers.

Show Video Lesson

Example:
Devon is going to make 3 shelves for her father. She has a piece of lumber 12 feet long. She wants
the top shelf to be half a foot shorter than the middle, and the bottom shelf to be half a foot
shorter than twice the length of the top shelf. How long will each shelf be if she uses the entire 12 feet of wood?

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.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Источник

Step 1 – Read through the problem at least three times. The first reading should be a quick scan, and the next two readings should be done slowly to find answers to these questions:

What does the problem ask? (Usually located at the end)

Mark all information and underline all important words or phrases.

Step 2 – Draw a picture. Use arrows, circles, lines, whatever works for you. This makes the problem real.

A favorite word problem is something like, 1 train leaves Station A travelling at 100 km/hr and another train leaves Station B travelling at 60 km/hr. …

Draw a line, the two stations, and the two trains at either end.

Depending on the question, make a table with a blank portion to show information you don’t know.

Step 3 – Assign a single letter to represent each unknown.

You may want to note the unknown that each letter represents so you don’t get confused.

Step 4 – Translate the information into an equation.

Remember that the main problem with word problems is that they are not expressed in regular math equations. Your ability to identify correctly the variables and translate the information into an equation determines your ability to solve the problem.

Step 5 – Check the equation to see if it looks like regular equations that you are used to seeing and whether it looks sensible.

Does the equation appear to represent the information in the question? Take note that you may need to rewrite some formulas needed to solve the word problem equation.

Step 6 – Use algebra rules to solve the equation.

Simplify each side of the equation by removing parentheses and combining like terms.

Use addition or subtraction to isolate the variable term on one side of the equation. If a number crosses to the other side of the equation, the sign changes to the opposite — for example positive to negative.

Use multiplication or division to solve for the variable. What you to once side of the equation you must do for the other.

Where there are multiple unknowns you will need to use elimination or substitution methods to resolve all the equations.

Step 7 – Check your final answers to see if they make sense with the information given in the problem.

For example, if the word problem involves a discount, the final price should be less or if a product was taxed then the final answer has to cost more.

Источник

Word problems can be intimidating and overwhelming for children and parents alike. They require children to read at grade level while solving a complex puzzle. Empower your child to tackle those tricky problems by teaching a systematic approach for solving them. Whether it’s a one-step or multi-step word problem, the simple strategies listed below will take the guesswork out of the equation. 😉

3-Step System

1. Read: Read the problem and decide what the question is asking.

Read the problem 2 times or more.
Underline or circle key words, phrases, and numbers. Draw a line through irrelevant information.

2. Plan: Think about what the story is asking you to do. What information are you given, and what do you need to find out?

Draw a picture.
Circle or underline key words. (Use highlighters or crayons to color-code key numbers and phrases.)
Write out the question in your own words.

3. Solve: What strategy could you use to find the missing information: addition, subtraction, multiplication, or division?

Write a number sentence and solve.
Use counters.
Create charts.

Check your work by explaining your reasoning. Does your answer make sense?

Download this free strategy checklist from Math Fundamentals to help your child solve word problems.

Different Strategies to Solve Word Problems

Everyone learns in a different way. What makes sense to one individual often isn’t the easiest option for another. Incorporating different strategies to solve word problems can help your child discover what strategy works best for him or her. A few tips to use are:

1. Circle numbers in a story and underline key phrases.

Color coding is a fun method to incorporate to help children decide what operation the question is asking for. Assign a color to each operation and highlight the phrase that identifies it. For example, red links to addition and blue links to subtraction.

2. Incorporate a key word list.

Key word lists are best used for teaching younger children how to solve word problems. As math curriculum advances, children should not be dependent on a key word list to solve a problem. The questions get trickier.

Addition
In all
Together
Total
Altogether
Combine
Sum
Join

Subtraction
Difference
Fewer
How many more
How much more
Left
Remain
Less

3. Visuals

If your child is a visual learner, drawing a picture or using counters can help him or her understand what the problem is asking. Use number lines, charts, or counters or draw a picture.

4. Write your own word problem.
Knowing what is needed to write a word problem is the first step in identifying key words to solve a story. Take turns writing your own word problems with your child and exchange them to solve.

5. Stay organized.

It is important to write clearly and keep work space neat so children can read and follow their own computations. Many children need a separate piece of paper to allow them enough space to solve and understand their answer. Graphing paper is a great option to help students record neat work.

Download this free sample word problem from Math Fundamentals, grade 1.

How to solve a two-step word problem

In a two-step word problem children are being asking to solve two related equations. These can get tricky for children to understand when they transition from one-step to two-step problems. Help your child understand his or her relationships within two-step word problems with these strategies:

1. Circle important information.

Circle numbers and important phrases that ask questions. The number sentences needed to solve these equations are hidden in those asking questions. Identify the first and second questions needed to solve.

2. Distinguish the two parts of the problem.

First identify the first step of the first part of the word problem. Write a number sentence and solve.

3. Use the answer from the first-step solution to the whole problem.

Use the answer from the first question to help you solve the next equation. What operation does the second question require?

Check your work by explaining your reasoning. What was the question answered? Is the answer reasonable for the question being asked?

Download this free sample two-strategy word problem from Math Fundamentals, grade 2

Download this free sample multi-strategy word problem from Math Fundamentals, grade 4

Evan-Moor’s Math Fundamentals is a great resource for training students how to solve word problems in 3 simple steps. It provides step-by-step directions for solving questions and guides children with helpful visuals and key phrases.

Check out Daily Word Problems for consistent practice solving word problems.

For more fun math tips and strategies check out our Math- Ideas, Activities and Lessons Pinterest Board.

Save these tips and Pin It now!

Heather Foudy is a certified elementary teacher with over 7 years’ experience as an educator and volunteer in the classroom. She enjoys creating lessons that are meaningful and creative for students. She is currently working for Evan-Moor’s marketing and communications team and enjoys building learning opportunities that are both meaningful and creative for students and teachers alike.

Источник

The techniques and methods we apply to solve word problems in math will vary from problem to problem.

The techniques and methods we apply to solve a word problem in a particular topic in math will not work for another word problem found in some other topic.

For example, the methods we apply to solve the word problems in algebra will not work for the word problems in trigonometry.

Because, in algebra, we will solve most of the problems without any diagram. But, in trigonometry, for each word problem, we have to draw a diagram. Without diagram, always it is bit difficult to solve word problems in trigonometry.

Even though we have different techniques to solve word problems in different topics of math, let us see the steps which are most commonly used.

The following steps would be useful to solve word problems in Mathematics.

Step 1 :

Understanding the question is more important than any other thing. That is, always it is very important to understand the information given in the question rather than solving.

Step 2 :

If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily.

Step 3 :

Once we understand the given information clearly, solving the word problem would not be a challenging work.

Step 4 :

When we try to solve the word problems, we have to introduce «x» or «y» or some other alphabet for unknown value (=answer for our question). Finally we have to get value for the alphabet which was introduced for the unknown value.

Step 5 :

If it is required, we have to draw picture for the given information. Drawing picture for the given information will give us a clear understanding about the question.

Step 6 :

Using the alphabet introduced for unknown value, we have to translate the English statement (information) given in the question as mathematical equation.

In translation, we have to translate the following English words as the corresponding mathematical symbols.

of —-> x (multiplication)

am, is, are, was, were, will be, would be —-> = (equal)

Step 7 :

Once we have translated the English Statement (information) given in the question as mathematical equation correctly, 90% of the work will be over. The remaining 10% is just getting the answer. That is solving for the unknown.

Example :

The age of a man is three times the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man.

Answer :

Step 1 :

Let us understand the given information. There are two information given in the question.

1. The age of a man is three times the sum of the ages of his two sons. (At present)

2. After 5 years, his age would be double the sum of their ages. (After 5 years)

Step 2 :

Target of the question :

Present age of the man = ?

Step 3 :

Introduce required variables for the information given in the question.

Let x be the present age of the man.

Let y be the sum of present ages of two sons.

Clearly, the value of x to be found.

Because that is the target of the question.

Step 4 :

Translate the given information as mathematical equation using x and y.

First information :

The age of a man is three times the sum of the ages of his two sons.

Translation :

The Age of a man —-> x

is —-> =

Three times sum of the ages of his two sons —-> 3y

Equation related to the first information using x and y is

x = 3y —-(1)

Second Information :

After 5 years, his age would be double the sum of their ages.

Translation :

Age of the man after 5 years —-> (x + 5)

Sum of the ages of his two sons after 5 years is

y + 5 + 5 = y + 10

(Because there are two sons, 5 is added twice)

Double the sum of ages of two sons —-> 2(y + 10)

would be —-> =

Equations related to the second information using x and y is

x + 5 = 2(y + 10) —-(2)

Step 5 :

Solve equations (1) & (2).

From (1), substitute 3y for x in (2).

3y + 5 = 2(y + 10)

3y + 5 = 2y + 20

y = 15

Substitute 15 for y in (1).

x = 3(15)

x = 45

So, the present age of the man is 45 years.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

Источник