Many students find solving algebra word problems difficult. The best way to approach word problems is to “divide and conquer”. Break the problem down into smaller bits and solve each bit at a time.
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.
Part 1: Translate the problem into equations with variables
Translating words to equations
How to recognize some common types of algebra word problems and how to solve them step by step:
usually compare the ages of people.
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
involve the computations for
of different quantities.
Another common type of average problems is the average speed
items with denominated values.
Similar word problems are Stamp Problems
Consecutive Integer Problems
The number sequences may be Even
, or some other simple
involve the relationship and manipulation of digits in numbers.
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
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
involve numerical representations of word problems.
The integer word problems may Involve 2 Unknowns
Involve More Than 2 Unknowns
involve calculations of simple interest.
deal with the lever principle described in word problems.
Lever problem may involve 2 Objects
or More than 2 Objects
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
involve proportional and inversely proportional relationships of various quantities.
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
Variation Word Problems may consist of Direct Variation Problems
, Inverse Variation Problems
or Joint Variation Problems
involve different people doing work together at different rates.
This may be for Two Persons
More Than Two Persons
Pipes Filling up a Tank
Refer to our Algebra page
for more Algebra Word Problems and algebra techniques.
Part 2: Solving the equations - finding the values of the variables for the equations.
Refer to our Algebra page
for more information on solving equation techniques
Algebra Word Problems with examples, videos and step-by-step solutions
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?
Example: One number is 4 times as large as another. Their sum is 45. Find the numbers.
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?
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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