How to solve Algebra Word Problems?

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: Translating the problem into equations with variables

Translating words to equations

We need to recognize some 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 descrihed 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

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.

Simplifying the equation	Isolate the variable (Transposition)
Addition Method (Opposite-Coefficient Method)	Substitution Method
Factoring Quadratic Equations	Quadratic Formula

Refer to our Algebra page for more information on solving equation techniques

Algebra Word Problems Videos

Age Word Problems I	Age Word Problems II
Coin Word Problems I	Coin Word Problems II
Digits Word Problems	Integer Word Problems I
Integer Word Problems II	Perimeter Word Problems I
Perimeter Word Problems II	Area Word Problems
Volume Word Problems	Angle Word Problems
Proportion Word Problems	Ratio Word Problems
Rate, Time, Distance Problems I	Rate, Time, Distance Problems II
Rate, Time, Distance Problems III	Simple Interest Word Problems
Compound Interest Word Problems I	Compound Interest Word Problems II
Investment Word Problems	Algebra Work Problems I
Algebra Work Problems II	Algebra Mixture Problems I
Algebra Mixture Problems II	Algebra Mixture Problems III

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

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?

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