This chapter covers ways of setting up word problems and solving for
Given a word problem, write equations and SOLVE for
Basic Approach to Solving Algebraic Word Problems
Algebra is used to solve problems in science, industry, business, and the home. Algebraic
equations can be used to describe laws of motion, pressures of gases, electric circuits, and nuclear
facility operations. They can be applied to problems about the ages of people, the cost of
articles, football scores, and other everyday matters. The basic approach to solving problems in
these apparently dissimilar fields is the same. First, condense the available information into
algebraic equations, and, second, solve the equations. Of these two basic steps, the first is
frequently the most difficult to master because there are no clearly defined rules such as those
that exist for solving equations.
Algebraic word problems should not be read with the objective of immediately determining the
answer because only in the simpler problems is this possible. Word problems should be initially
read to identify what answer is asked for and to determine which quantity or quantities, if known,
will give this answer. All of these quantities are called the unknowns in the problem.
Recognizing all of the unknowns and writing algebraic expressions to describe them is often the
most difficult part of solving word problems. Quite often, it is possible to identify and express
the unknowns in several different ways and still solve the problem. Just as often, it is possible
to identify and express the unknowns in several ways that appear different but are actually the
In writing algebraic expressions for the various quantities given in word problems, it is helpful
to look for certain words that indicate mathematical operations. The words "sum" and "total"
signify addition; the word "difference" signifies subtraction; the words "product," "times," and
"multiples of" signify multiplication; the words "quotient," "divided by," "per," and "ratio" signify
division; and the words "same as" and "equal to" signify equality. When quantities are connected
by these words and others like them, these quantities can be written as algebraic expressions.
Sometimes you may want to write equations initially using words. For example, Bob is 30 years
older than Joe. Express Bobs age in terms of Joes.
Bobs age = Joes age plus 30 years