How To Solve Algebra Word Problems? (video lessons, examples, solutions) (2024)

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 theword 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 forarithmetic mean orweighted 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 andTicket Problems.

Consecutive Integer Problems deal with consecutive numbers.
The number sequences may be Even orOdd, 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 thatTravel in Different Directions or we may need to find the distanceGiven 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 andInvolving Angles

Integer Problems involve numerical representations of word problems.
The integer word problems may Involve 2 Unknowns or mayInvolve 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 aremixed together. This involveAdding 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 theValue 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 certainknown ratios, or work out the ratios given certain quantities.This could be Two-Term Ratios orThree-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 orPipes Filling up a Tank

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

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

  • How to solve equations?

    Simplifying the equation
    Isolate the variable (Transposition)
    Addition Method (Opposite-Coefficient Method)

    Substitution Method
    Factoring Quadratic Equations
    Quadratic Formula



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

  • Age Word Problems

    Age Problems
    Age Problems: Single Person
    More Than One Person
    Age Word Problems 1
    Age Word Problems 2

  • Average Word Problems

    Arithmetic Mean
    Weighted Average
    Average Speed

  • Coin Word Problems

    Problems involving Coins
    Stamp Problems
    Ticket Problems
    Coin Word Problems 1
    Coin Word Problems 2

  • Consecutive Integer Word Problems

    Consecutive Integers 1
    Consecutive Integers 2
    Consecutive Odd Integer
    Consecutive Even Integer
    Consecutive Integer Problems

  • Digit Word Problems

    Simple Digit Problems

    Digits Word Problems

  • Distance Word Problems

    Distance Problems
    Travel at Different Rates
    Travel in Different Directions
    Given Total Time

  • Fraction Problems
    Percent Word Problems

  • Geometry Word Problems

    Geometry Word Problems
    Involving Perimeters
    Involving Areas

    Involving Angles
    Angle Word Problems
    Perimeter Word Problems 1
    Perimeter Word Problems 2
    Perimeter Word Problems 3

    Area Word Problems
    Area of Rectangle Word Problems
    Area of Triangle Word Problems
    Area of Parallelogram Word Problems

    Volume Word Problems
    Volume Word Problems

    Geometry Word Problems using Quadratic Equations
    Pythagorean Theorem Word Problems
    Trigonometry Word Problems

  • Integer Word Problems

    Involving 2 Unknowns
    More Than 2 Unknowns
    Integer Word Problems 1
    Integer Word Problems 2

  • Interest Word Problems

    Interest Word Problems
    Simple Interest Word Problems
    Compound Interest Word Problems 1
    Compound Interest Word Problems 2
    Investment Word Problems

  • Lever Word Problems

    Involving 2 or More Objects

  • Mixture Word Problems

    Mixture Problems
    Adding to a Solution
    Remove from a Solution
    Replace a Solution
    Mix Items of Different Values
    Algebra Mixture Problems 1
    Algebra Mixture Problems 2
    Algebra Mixture Problems 3

  • Money Word Problems

  • Rate, Time, Distance Problems 1
    Rate, Time, Distance Problems 2
    Rate, Time, Distance Problems 3
    Motion Word Problems

  • Number Sequence Word Problems

    Number Sequence Problems
    Value of a Particular Term
    Pattern of a Sequence

  • Proportion Word Problems

    Proportion Problems
    Directly Proportional
    Inversely Proportional
    Proportion Word Problems

  • Word Problems using Quadratic Equations

    Quadratic Word Problems
    Quadratic Equations Word Problems
    Quadratic Problems in Geometry
    Projectile Motion

  • Ratio Word Problems

    Ratio Problems
    Two-Term Ratios
    Three-Term Ratios
    Ratio Word Problems

  • Symbol Word Problems

    Symbol Problems

  • Variation Word Problems

    Direct Variation Problems
    Inverse Variation Problems

    Variation Word Problems

  • Work Word Problems

    Work Problems
    Two Persons
    More Than Two Persons
    Pipes Filling up a Tank
    Algebra Work Problems 1
    Algebra Work Problems 2

  • Ways to solve Word Problems

    One Variable Word Problems
    Two-Variable Word Problems
    System of Equations 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 wantsthe top shelf to be half a foot shorter than the middle, and the bottom shelf to be half a footshorter 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 andproblem solver below to practice various math topics. Try the given examples, or type in your ownproblem and check your answer with the step-by-step explanations.



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How To Solve Algebra Word Problems? (video lessons, examples, solutions) (2024)
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