© 2010 Pearson Prentice Hall. All rights reserved.
CHAPTER 6
Algebra: Equations and Inequalities
© 2010 Pearson Prentice Hall. All rights reserved. 2
6.3
Applications of Linear Equations
© 2010 Pearson Prentice Hall. All rights reserved.3
Objectives
1. Use linear equations to solve problems.
2. Solve a formula for a variable.
© 2010 Pearson Prentice Hall. All rights reserved.4
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.
© 2010 Pearson Prentice Hall. All rights reserved. 5
Algebraic Translations of English Phrases
Addition Subtraction Multiplication Divisionsum
more than
increased by
minus
decreased by
subtracted from
difference between
less than
fewer than
times
product of
percent of a number
multiplied by
twice
divided by
quotient
reciprocal
© 2010 Pearson Prentice Hall. All rights reserved.6
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.
© 2010 Pearson Prentice Hall. All rights reserved.7
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 degreex + 41 = the average yearly salary of a man with a bachelor’s degree or more.
© 2010 Pearson Prentice Hall. All rights reserved.8
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.
( 3) ( 41) 188
3 44 188
3 144
48
x x x
x
x
x
© 2010 Pearson Prentice Hall. All rights reserved.9
Example 2: continued
The average salary with some college = 48The average salary with an associate degree = x + 3
= 48 + 3 = 51The average salary with a bachelor’s degree or more
= x + 41 = 48 + 41 = 89.
Some college = $48 thousand per yearAssociate degree = $51 thousandBachelor’s degree = $89 thousandStep 5: Check the proposed solution in the wording
of the problem. The solution checks.
© 2010 Pearson Prentice Hall. All rights reserved.10
Example 6: Solving a Formula for One of its Variables
The total price of an article purchased on a monthly deferred payment plan isdescribed 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 onepays. Solve the formula for p.
T – D = D – D + pm
T – D = pm
T – D = pm m m
T – D = p m