Solving Word Problems

Our Algebra 1 tutorial software program contains over 60 topic areas. One of them is Solving Word Problems, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor algebra 1 software program.

General Explanation

In this lesson we'll learn to solve simple word problems. We'll begin by examining a problem stated in English. Then we'll convert the problem into an algebraic equation which we can solve.

Sample Problem

Sally is F times older than Joan. If Joan's age is 7, what is Sally's age?


We will begin by translating the words in the problem into symbols and an equation. After the problem is expressed as an equation, we can solve it to find the solution.
  1. Let's examine the first sentence:
    Sally is F times older than Joan.
    Now express the important quantities as variables:
    Let S stand for Sally's age
    Let J stand for Joan's age
    Now our sentence reads:
    S is F times older than J

  2. Next, to write an equation, look for the word 'is' and substitute an equals sign for it:
    S = F times older than J
  3. Next, look for words that can be translated into operations. In this case, the phrase 'times older than' implies multiplication. So, this sentence really means that Sally's age equals Joan's age multiplied by F. Now we can finish translating the sentence.
    S = FJ
  4. Last, replace J (Joan's age) with 7.
    S = 7F
    This is our final answer. When writing a term with multiplication, we generally place the constant (7) before the variable (F).