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Word Problems Calculators: (41) lessons

2 number word problems.

Free 2 number Word Problems Calculator - This calculator handles word problems in the format below: * Two numbers have a sum of 70 and a product of 1189 What are the numbers? * Two numbers have a sum of 70. Their difference 32

2 Unknown Word Problems

Free 2 Unknown Word Problems Calculator - Solves a word problem based on two unknown variables

Age Difference

Free Age Difference Calculator - Determines the ages for an age difference word problem.

Age Word Problems

Free Age Word Problems Calculator - Determines age in age word problems

Angle of Elevation

Free Angle of Elevation Calculator - Solves angle of elevation word problems

Free Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

Coin Combinations

Free Coin Combinations Calculator - Given a selection of coins and an amount, this determines the least amount of coins needed to reach that total.

Coin Total Word Problems

Free Coin Total Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value with a certain amount more or less of one coin than another

Coin Word Problems

Free Coin Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value

Collinear Points that form Unique Lines

Free Collinear Points that form Unique Lines Calculator - Solves the word problem, how many lines can be formed from (n) points no 3 of which are collinear.

Compare Raises

Free Compare Raises Calculator - Given two people with a salary and annual raise amount, this determines how long it takes for the person with the lower salary to catch the person with the higher salary.

Consecutive Integer Word Problems

Free Consecutive Integer Word Problems Calculator - Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.

Cost Revenue Profit

Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

Free Decay Calculator - Determines decay based on an initial mass and decay percentage and time.

Distance Catch Up

Free Distance Catch Up Calculator - Calculates the amount of time that it takes for a person traveling at one speed to catch a person traveling at another speed when one person leaves at a later time.

Distance Rate and Time

Free Distance Rate and Time Calculator - Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.

Find two numbers word problems

Free Find two numbers word problems Calculator - Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.

Inclusive Number Word Problems

Free Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions: 1) The Average of all numbers inclusive from A to B 2) The Count of all numbers inclusive from A to B 3) The Sum of all numbers inclusive from A to B

Free Map Scale Calculator - Solves map scale problems based on unit measurements

Markup Markdown

Free Markup Markdown Calculator - Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

Numbers Word Problems

Free Numbers Word Problems Calculator - Solves various basic math and algebra word problems with numbers

Free Overtime Calculator - Solves overtime wage problems

Percent Off Problem

Free Percent Off Problem Calculator - Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.

Percentage of the Pie Word Problem

Free Percentage of the Pie Word Problem Calculator - This takes two or three fractions of ownership in some good or object, and figures out what remaining fraction is left over.

Percentage Word Problems

Free Percentage Word Problems Calculator - Solves percentage word problems

Population Doubling Time

Free Population Doubling Time Calculator - Determines population growth based on a doubling time.

Population Growth

Free Population Growth Calculator - Determines population growth based on an exponential growth model.

Product of Consecutive Numbers

Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include: product of 2 consecutive integers product of 2 consecutive numbers product of 2 consecutive even integers product of 2 consecutive odd integers product of 2 consecutive even numbers product of 2 consecutive odd numbers product of two consecutive integers product of two consecutive odd integers product of two consecutive even integers product of two consecutive numbers product of two consecutive odd numbers product of two consecutive even numbers product of 3 consecutive integers product of 3 consecutive numbers product of 3 consecutive even integers product of 3 consecutive odd integers product of 3 consecutive even numbers product of 3 consecutive odd numbers product of three consecutive integers product of three consecutive odd integers product of three consecutive even integers product of three consecutive numbers product of three consecutive odd numbers product of three consecutive even numbers product of 4 consecutive integers product of 4 consecutive numbers product of 4 consecutive even integers product of 4 consecutive odd integers product of 4 consecutive even numbers product of 4 consecutive odd numbers product of four consecutive integers product of four consecutive odd integers product of four consecutive even integers product of four consecutive numbers product of four consecutive odd numbers product of four consecutive even numbers product of 5 consecutive integers product of 5 consecutive numbers product of 5 consecutive even integers product of 5 consecutive odd integers product of 5 consecutive even numbers product of 5 consecutive odd numbers product of five consecutive integers product of five consecutive odd integers product of five consecutive even integers product of five consecutive numbers product of five consecutive odd numbers product of five consecutive even numbers

Ratio Word Problems

Free Ratio Word Problems Calculator - Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.

Rebound Ratio

Free Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Slope Word Problems

Free Slope Word Problems Calculator - Solves slope word problems

Solution Mixture

Free Solution Mixture Calculator - Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

Split Fund Interest

Free Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

Sum of Consecutive Numbers

Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include: sum of 2 consecutive integers sum of 2 consecutive numbers sum of 2 consecutive even integers sum of 2 consecutive odd integers sum of 2 consecutive even numbers sum of 2 consecutive odd numbers sum of two consecutive integers sum of two consecutive odd integers sum of two consecutive even integers sum of two consecutive numbers sum of two consecutive odd numbers sum of two consecutive even numbers sum of 3 consecutive integers sum of 3 consecutive numbers sum of 3 consecutive even integers sum of 3 consecutive odd integers sum of 3 consecutive even numbers sum of 3 consecutive odd numbers sum of three consecutive integers sum of three consecutive odd integers sum of three consecutive even integers sum of three consecutive numbers sum of three consecutive odd numbers sum of three consecutive even numbers sum of 4 consecutive integers sum of 4 consecutive numbers sum of 4 consecutive even integers sum of 4 consecutive odd integers sum of 4 consecutive even numbers sum of 4 consecutive odd numbers sum of four consecutive integers sum of four consecutive odd integers sum of four consecutive even integers sum of four consecutive numbers sum of four consecutive odd numbers sum of four consecutive even numbers sum of 5 consecutive integers sum of 5 consecutive numbers sum of 5 consecutive even integers sum of 5 consecutive odd integers sum of 5 consecutive even numbers sum of 5 consecutive odd numbers sum of five consecutive integers sum of five consecutive odd integers sum of five consecutive even integers sum of five consecutive numbers sum of five consecutive odd numbers sum of five consecutive even numbers

Sum of Five Consecutive Integers

Free Sum of Five Consecutive Integers Calculator - Finds five consecutive integers, if applicable, who have a sum equal to a number. Sum of 5 consecutive integers

Sum of Four Consecutive Integers

Free Sum of Four Consecutive Integers Calculator - Finds four consecutive integers, if applicable, who have a sum equal to a number. Sum of 4 consecutive integers

Sum of the First (n) Numbers

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n) * Whole Numbers * Natural Numbers * Even Numbers * Odd Numbers * Square Numbers * Cube Numbers * Fourth Power Numbers

Sum of Three Consecutive Integers

Free Sum of Three Consecutive Integers Calculator - Finds three consecutive integers, if applicable, who have a sum equal to a number. Sum of 3 consecutive integers

Free Sun Shadow Calculator - This solves for various components and scenarios of the sun shadow problem

Unit Savings

Free Unit Savings Calculator - A discount and savings word problem using 2 people and full prices versus discount prices.

Work Word Problems

Free Work Word Problems Calculator - Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.

solving equations word problems calculator

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solving equations word problems calculator

These calculators will solve three types of 'work' word problems . Also, it will provide a detailed explanation.

First worker can do the job in Days Hours Minutes and the second worker takes Days Hours Minutes . How long would it take the two workers together to finish the job?

If men can do a job in days, how many would it take to do the job in days?

A swimming pool has 2 inlet pipes. One fills the pool in hours, the other in hours. The outlet pipe empties the pool in hours. If the pool is at first empty and all three pipes are open, how many hours will it take to fill up the pool?

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Math Lesson 9.2.5 - Equations for solving Word Problems

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Welcome to our Math lesson on Equations for solving Word Problems , this is the fifth lesson of our suite of math lessons covering the topic of Word Problems Involving Equations , you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Using Other Types of Equations to Solve Word Problems

There are many types of equations besides the first - order equations with one variable. We will discuss a few examples where two other types of equations (second - order equations with one variable and first - order equations with two variables) are used in word problems. Let's present a short overview of these two types of equations.

Second - order equations with one variable

Second - order equations with one variable include equations that contain a single variable raised at the second power. In the next tutorials, we will see that the general form of these equations (otherwise known as 'quadratic equations') is

The left part of such equations is identical to the general form of quadratic expressions discussed in tutorial 6.4, where we explained how to factorise such expressions.

In this paragraph, however, we will consider only a simplified form of quadratic equations, where the coefficient b is 0. Therefore, the problems discussed here will require the use of the reduced quadratic equation

Let's consider an example to clarify this point.

The area of a square is 4 cm 2 more than that of a rectangle of dimensions 9 cm × 5 cm. What is the side length of the square?

The unknown in this problem is the side length of the square, which we denote by x . Since the area of a rectangle is the product of its dimensions and that of a square is the second power of the side length, we obtain the equation

Hence, the side length of the square is

(√49 can be 7 or - 7. However, we consider only the positive root, as the side length cannot be negative.)

First - order equations with two variables

First - order equations with two variables have the general form

where a and b are coefficients, c is a constant, while x and y are the two variables. For example, 3x - 2y - 6 = 0 is a first - order equation with two variables as it contains two variables x and y where both are in the first power (hence the name "first - order equation with two variables").

To solve first - order equations with two variables means finding the values of the two variables. However, since there are a lot of possible combinations that can give a true result, we must have some additional information about the relationship between the two variables. For example, in our example, we may take x = 4 and y = 3 as possible solutions, as 3 · 4 - 2 · 3 - 6 = 0 . Yet, we may also take x = 2 and y = 0 as possible solutions, as 3 · 2 - 2 · 0 - 6 = 0 . Both pairs of solutions are true. However, in a word problem, usually, there are only a couple of values that fit the description. Therefore, as said earlier, we must have some extra information about the relationship between the two variables. This extra information usually forms another first - order equation and we solve it as a system (we will explain systems of equations in the last two tutorials of this chapter). However, for now, it is sufficient to know that we express one of the variables in terms of the other variable and in this way, the original equation turns into a first - order equation with one variable, which we already know how to solve.

For example, if we have given that in a class there are 30 students where the boys vs girls ratio is B:G = 2:3 , we can write

This is a first - order equation (variables are written as B and G ) with two variables, as we can write it as

As we said earlier, it is impossible to find the correct value of the two variables only through this equation, as there are many combinations that fit the description. Therefore, we use the help of the other clue, which says that the total number of students in the class is 30. Hence, we have the other equation

available, which helps to express one of the variables (for example the girls G) in terms of the other variable in the first equation. Therefore, since G = 30 - B , we can substitute this expression in the first equation to obtain

Now, we have a first - order equation with one variable, which can be easily solved. Thus,

In this first - order equation with one variable we have a = 5 and b = -60 . Therefore, the root B that gives the number of boys in the class is

Hence, the number of girls in the class is

The perimeter of a rectangle is 12 cm more than that of an equilateral triangle with a 16 cm side length. Calculate the dimensions of the rectangle if its length is 2 cm more than its width.

We can express the rectangle's length by x and its width by y . Since the perimeter (the sum of all sides length) of a rectangle is calculated by the formula P = x + x + y + y = 2x + 2y , and given that an equilateral triangle has three equal sides, we have

This is a first - order equation with two variables. Therefore, we need some additional information to solve it. This additional information is already available. We know that length is 2 cm more than width, i.e. x = y + 2 . Therefore, we substitute x with its equivalent expression in the main equation to obtain

In this way, we obtained a first - order equation with one variable, where a = 2 and b = -28 . Therefore, we obtain for the variable y:

Hence, since x + y = 30 , we have

This too is a first - order equation with one variable, where a = 1 and b = -16 . Therefore, we obtain for the other variable x :

Hence, the length of the rectangle is 16 cm and the width is 14 cm.

More Word Problems Involving Equations Lessons and Learning Resources

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Enjoy the "Equations for solving Word Problems" math lesson? People who liked the "Word Problems Involving Equations lesson found the following resources useful:

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  • Equations Math tutorial: Word Problems Involving Equations . Read the Word Problems Involving Equations math tutorial and build your math knowledge of Equations
  • Equations Video tutorial: Word Problems Involving Equations . Watch or listen to the Word Problems Involving Equations video tutorial, a useful way to help you revise when travelling to and from school/college
  • Equations Revision Notes: Word Problems Involving Equations . Print the notes so you can revise the key points covered in the math tutorial for Word Problems Involving Equations
  • Equations Practice Questions: Word Problems Involving Equations . Test and improve your knowledge of Word Problems Involving Equations with example questins and answers
  • Check your calculations for Equations questions with our excellent Equations calculators which contain full equations and calculations clearly displayed line by line. See the Equations Calculators by iCalculator™ below.
  • Continuing learning equations - read our next math tutorial: Identities

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Equations Calculators by iCalculator™

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Praxis Core Math

Course: praxis core math   >   unit 1.

  • Algebraic properties | Lesson
  • Algebraic properties | Worked example
  • Solution procedures | Lesson
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  • Equivalent expressions | Lesson
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  • Creating expressions and equations | Lesson
  • Creating expressions and equations | Worked example

Algebraic word problems | Lesson

  • Algebraic word problems | Worked example
  • Linear equations | Lesson
  • Linear equations | Worked example
  • Quadratic equations | Lesson
  • Quadratic equations | Worked example

What are algebraic word problems?

What skills are needed.

  • Translating sentences to equations
  • Solving linear equations with one variable
  • Evaluating algebraic expressions
  • Solving problems using Venn diagrams

How do we solve algebraic word problems?

  • Define a variable.
  • Write an equation using the variable.
  • Solve the equation.
  • If the variable is not the answer to the word problem, use the variable to calculate the answer.

What's a Venn diagram?

  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
  • (Choice A)   $ 4 ‍   A $ 4 ‍  
  • (Choice B)   $ 5 ‍   B $ 5 ‍  
  • (Choice C)   $ 9 ‍   C $ 9 ‍  
  • (Choice D)   $ 14 ‍   D $ 14 ‍  
  • (Choice E)   $ 20 ‍   E $ 20 ‍  
  • (Choice A)   10 ‍   A 10 ‍  
  • (Choice B)   12 ‍   B 12 ‍  
  • (Choice C)   24 ‍   C 24 ‍  
  • (Choice D)   30 ‍   D 30 ‍  
  • (Choice E)   32 ‍   E 32 ‍  
  • (Choice A)   4 ‍   A 4 ‍  
  • (Choice B)   10 ‍   B 10 ‍  
  • (Choice C)   14 ‍   C 14 ‍  
  • (Choice D)   18 ‍   D 18 ‍  
  • (Choice E)   22 ‍   E 22 ‍  

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New SAT Math - Calculator : Solving Linear Equations in Word Problems

Study concepts, example questions & explanations for new sat math - calculator, all new sat math - calculator resources, example questions, example question #1 : solving linear equations in word problems.

Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling each shirt for $18 apiece. If each shirt cost her $10 apiece to make, how much profit does she make if she only sells 25 shirts at the reunion?

solving equations word problems calculator

This problem involves two seperate multiplication problems. Erin will make $450 at the reunion but supplies cost her $300 to make the shirts. So her profit is $150.

Example Question #2 : Solving Linear Equations In Word Problems

Write as an equation: 

"Ten added to the product of a number and three is equal to twice the number."

solving equations word problems calculator

The first expression:

"The product of a number and three" is three times this number, or 

solving equations word problems calculator

"Ten added to the product" is

solving equations word problems calculator

The second expression:

"Twice the number" is two times the number, or

solving equations word problems calculator

The desired equation is therefore

solving equations word problems calculator

Example Question #3 : Solving Linear Equations In Word Problems

Five-sevenths of the difference of a number and nine is equal to forty.

solving equations word problems calculator

"The difference of a number and nine" is the result of a subtraction of the two, so we write this as

solving equations word problems calculator

This is equal to forty, so write the equation as

solving equations word problems calculator

Example Question #1 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Write as an equation:

Twice the sum of a number and ten is equal to the difference of the number and one half.

solving equations word problems calculator

"The difference of the number and one half" is a subtraction of the two, or

solving equations word problems calculator

Set these equal, and the desired equation is

solving equations word problems calculator

Example Question #5 : Solving Linear Equations In Word Problems

solving equations word problems calculator

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

solving equations word problems calculator

We can substitute in our known values and solve for our unknown variable (i.e. length):

solving equations word problems calculator

Example Question #1 : Word Problems

solving equations word problems calculator

Example Question #8 : Solving Linear Equations In Word Problems

solving equations word problems calculator

Example Question #9 : Solving Linear Equations In Word Problems

solving equations word problems calculator

Example Question #10 : Solving Linear Equations In Word Problems

solving equations word problems calculator

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Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

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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:

subtraction

Multiplication.

double (2x)

triple (3x)

quadruple (4x)

divided into

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. 

Algebra word problem solutions

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!

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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?

solving equations word problems calculator

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.

solving equations word problems calculator

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!

  • Solving Equations
  • Algebra Word Problems

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    Math Word Problem Solutions. Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms. Word ...

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