CHAPTER 6
Algebra: Equations and
Inequalities
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6.3
Applications of Linear Equations
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2
Objectives
1. Use linear equations to solve problems.
2. Solve a formula for a variable.
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Strategy for Solving Word Problems
Step 1 Read the problem carefully several times until you can state in
your own words what is given and what the problem is looking
for. Let x (or any variable) represent one of the quantities in the
problem.
Step 2 If necessary, write expressions for any other unknown
quantities in the problem in terms of x.
Step 3 Write an equation in x that models the verbal conditions of
the problem.
Step 4 Solve the equation and answer the problem’s question.
Step 5 Check the solution in the original wording of the problem, not
in the equation obtained from the words.
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Algebraic Translations of English Phrases
Addition Subtraction
Multiplication Division
sum
minus
more than
decreased by
increased by subtracted from
difference between
less than
fewer than
times
product of
percent of a number
multiplied by
twice
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divided by
quotient
reciprocal
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Example 1: Education Pays Off
This graph shows the average yearly earnings in the United States
by highest educational attainment.
The average yearly salary of a man with an associate degree
exceeds that of a man with some college by $3 thousand. The
average yearly salary of a man with a
bachelor’s degree or more exceeds
that of a man with some college by
$41 thousand. Combined, three men
with these educational attainments
earn $188 thousand. Find the average
yearly salary of men with each of
these levels of education.
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Example 2: continued
Step 1: Let x represent one of the unknown
quantities.
Let x = the average yearly salary of a man with
some college.
Step 2: Represent the other unknown quantities
in terms of x.
x + 3 = the average yearly salary of a man with
an associate degree
x + 41 = the average yearly salary of a man with
a bachelor’s degree or more.
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Example 2: continued
Step 3: Write an equation in x that models the
conditions.
x + (x + 3) + (x + 41) = 188
Step 4: Solve the equation and answer the
question.
x  ( x  3)  ( x  41)  188
3 x  44  188
3 x  144
x  48
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Example 2: continued
The average salary with some college = 48
The average salary with an associate degree = x +
3 = 48 + 3 = 51
The average salary with a bachelor’s degree or
more = x + 41 = 48 + 41 = 89.
Some college = $48 thousand per year
Associate degree = $51 thousand
Bachelor’s degree = $89 thousand
Step 5: Check the proposed solution in the
wording of the problem. The solution checks.
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Example 6: Solving a Formula for One of its Variables
The total price of an article
purchased on a monthly
deferred payment plan is
described by the following
formula:
T is the total price, D is the
down payment, p is the
monthly payment, and m is
the number of months one
pays.
Solve the formula for p.
T – D = D – D + pm
T – D = pm
T – D = pm
m
m
T–D=p
m
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