Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Contemporary Mathematics

5.3 Linear Inequalities in One Variable with Applications

Contemporary Mathematics5.3 Linear Inequalities in One Variable with Applications

Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index
A bar graph is titled, Mayoral Election Poll. The first bar represents Lugazi and reads 51 percent. The second bar represents Tsosi and reads 49 percent. There is a margin of error of plus or minus 4 percent.
Figure 5.5 These poll results, showing a margin of error at 4 percent, are an example of a real-world scenario that can be represented by linear inequalities.

Learning Objectives

After completing this section, you should be able to:

  1. Graph inequalities in one variable.
  2. Solve linear inequalities in one variable.
  3. Construct a linear inequality to solve applications.

In this section, we will study linear inequalities in one variable. Inequalities can be used when the possible values (answers) in a certain situation are numerous, not just a few, or when the exact value (answer) is not known but it is known to be within a range of possible values. There are many real-world scenarios that can be represented by linear inequalities. For example, consider the survey of the mayoral election in Figure 5.5 Surveys and polls are usually conducted with only a small group of people. The margin of error indicates a range of how the actual group of voters would vote given the results of the survey. This range can be expressed using inequalities.

Another example involves college tuition. Say a local community college charges $113 per credit hour. You budget $1,500 for tuition this fall semester. What are the number of credit hours that you could take this fall? Since this answer could be many different values, it can be expressed as an inequality.

Graphing Inequalities on the Number Line

In Algebraic Expressions, we introduced equality and the == symbol. In this section, we look at inequality and the symbols <<, >>, , and . The table below summarizes the symbols and their meaning.

Symbol Meaning
<< less than
>> greater than
less than or equal to
greater than or equal to

Suppose you had the inequality statement x>3x>3. What possible number or numbers would make the inequality x>3x>3 true? If you are thinking, "xx could be 4," that's correct, but xx could also be 5, 6, 37, 1 million, or even 3.001. The number of solutions is infinite; any number greater than 3 is a solution to the inequality x>3x>3.

Rather than trying to list all possible solutions, we show all the solutions to the inequality x>3x>3 on the number line. All the numbers to the right of 3 on the number line are shaded, to show that all numbers greater than 3 are solutions. At the number 3 itself, an open parenthesis is drawn, since the number 3 is not part of the solutions of x>3x>3.

We can also represent inequalities using interval notation. There is no upper end to the solution to this inequality. In interval notation, we express x>3x>3 as (3,)(3,). The symbol is read as "infinity." Infinity is not an actual number. Figure 5.6 shows both the number line and the interval notation for x>3x>3.

A number line ranges from negative 5 to 5, in increments of 1. An open parenthesis is marked at 3. The region to the right of the parenthesis is shaded on the number line. Text reads, (3, infinity).
Figure 5.6 The inequality x>3x>3 is graphed on this number line and written in interval notation.

We used the left parenthesis symbol to show that the endpoint of the inequality is not included. Parentheses are used when the endpoints are not included as a possible answer to the inequality. The notation for inequalities on a number line and in interval notation use the same symbols to express the endpoints of intervals.

The inequality x1x1 means all numbers less than or equal to 1. To illustrate that solution on a number line, we first put a bracket at x=1x=1; brackets are used when the endpoint is included. We then shade in all the numbers to the left of 1, to show that all numbers less than one are solutions. There is no lower end to those numbers. We write x1x1 in interval notation as ( ,1 ]( ,1 ]. The symbol is read as "negative infinity." Figure 5.7 shows both the number line and interval notation for x=1x=1.

A number line ranges from negative 5 to 5, in increments of 1. A close square bracket is marked at 1. The region to the left of the parenthesis is shaded on the number line. Text reads, x is less than or equal to 1, (negative infinity, 1).
Figure 5.7 The inequality x1x1 is graphed on this number line and written in interval notation.

Figure 5.8 summarizes the general representations in both number line form and interval notation of solutions for x>ax>a, x<ax<a, xaxa, and xaxa.

Four number lines. The first has an open parenthesis at a. The region to the right of the parenthesis is shaded. Text reads, x is greater than a, (a, infinity). Both have a left parenthesis. The second has an open square bracket at a. The region to the right of the bracket is shaded. Text reads, x is greater than or equal to a, (a, infinity). Both have a left bracket. The third has a close parenthesis at a. The region to the left of the parenthesis is shaded. Text reads, x is less than a, (negative infinity, a). Both have a right parenthesis. The fourth has a close square bracket at a. The region to the left of the bracket is shaded. Text reads, x is less than or equal to a, (negative infinity, a). Both have a right bracket.
Figure 5.8 Summary of representations in number line form and interval notation.

Example 5.21

Graphing an Inequality

Graph the inequality x3x3 and write the solution in interval notation.

Your Turn 5.21

1.
Graph the inequality x < 2.5 and write the solution in interval notation.

Example 5.22

Graphing a Compound Inequality

Graph the inequality x>3x>3 and x<4x<4 and write the solution in interval notation.

Your Turn 5.22

1.
Graph the inequality x 0 and x 2.5 and write the solution in interval notation.

Who Knew?

Where Did the Inequality Symbols Come From?

The first use of the << symbol to represent "less than" and >> to represent "greater than" appeared in a mathematics book written by Englishman Thomas Harriot that was published in 1631. However, Harriot did not invent the symbols…the editor of the book did! Harriot used triangular symbols to represent less than and greater than; the editor, for reasons unknown, changed to symbols that are similar to the ones we use today. The symbols used to represent less than or equal to, and greater than or equal to ( and ) were first used in 1731 by French hydrologist and surveyor Pierre Bouguer. Interestingly, English mathematician John Wallis had used similar symbols as early as 1670, but he put the bar above the less than and greater than symbols instead of below them.

Solving Linear Inequalities

A linear inequality is much like a linear equation—but the equal sign is replaced with an inequality sign. A linear inequality is an inequality in one variable that can be written in one of the forms ax+b<c,ax+bc,ax+bc,ax+b<c,ax+bc,ax+bc, or ax+b>c,ax+b>c, where aa, bb, and cc are all real numbers.

When we solved linear equations, we were able to use the properties of equality to add, subtract, multiply, or divide both sides and still keep the equality. Similar properties hold true for inequalities. We can add or subtract the same quantity from both sides of an inequality and still keep the inequality. For example, we know that 2 is less than 4, i.e., 2<42<4. If we add 6 to both sides of this inequality, we still have a true statement:

2+6<4+68<102+6<4+68<10

The same would happen if we subtracted 6 from both sides of the inequality; the statement would stay true:

26<464<226<464<2

Notice that the inequality signs stayed the same. This leads us to the Addition and Subtraction Properties of Inequality.

FORMULA

For any numbers aa, bb, and cc, if a<ba<b, then a+c<b+ca+c<b+c and ac<bcac<bc.

For any numbers aa, bb, and cc, if a>ba>b, then a+c>b+ca+c>b+c and a-c>b-ca-c>b-c.

We can add or subtract the same quantity from both sides of an inequality and still keep the inequality the same. But what happens to an inequality when we divide or multiply both sides by a number? Let's first multiply and divide both sides by a positive number, starting with an inequality we know is true, 10<1510<15. We will multiply and divide this inequality by 5:

10<1510<1510(5)?15(5)105?15550?752?350<75(true)2<3(true)10<1510<1510(5)?15(5)105?15550?752?350<75(true)2<3(true)

The inequality signs stayed the same. Does the inequality stay the same when we divide or multiply by a negative number? Let's use our inequality 10<1510<15 to find out, multiplying it and dividing it by 55:

10<1510<1510(5)?15(5)105?15550?752?350>75(true)2>3(true)10<1510<1510(5)?15(5)105?15550?752?350>75(true)2>3(true)

Notice that when we filled in the inequality signs, the inequality signs reversed their direction in order to make it true! To summarize, when we divide or multiply an inequality by a positive number, the inequality sign stays the same. When we divide or multiply an inequality by a negative number, the inequality sign reverses. This gives us the Multiplication and Division Property of Inequality.

FORMULA

For any numbers aa, bb, and cc,

multiply or divide by a positive: if a<ba<b and c>0c>0 , then ac<bcac<bc and ac<bcac<bc
if a>ba>b and c>0c>0 , then ac>bcac>bc and ac>bcac>bc
multiply or divide by a negative: if a<ba<b and c<0c<0 , then ac>bcac>bc and ac>bcac>bc
if a>ba>b and c<0c<0 , then ac<bcac<bc and ac<bcac<bc

To summarize, when we divide or multiply an inequality by:

  • a positive number, the inequality sign stays the same.
  • a negative number, the inequality sign reverses.

Checkpoint

Be careful to only reverse the inequality sign when you are multiplying and dividing by a negative. You do NOT reverse the inequality sign when you add or subtract a negative. For example, 2x<42x<4 is solved by dividing both sides of the inequality by 2 to get x<2x<2. You do NOT reverse the inequality sign because there is a negative 4. As another example, 2x+5<3x2x+5<3x is solved by adding 2x2x to both sides to get 5<5x5<5x. This does not reverse the inequality sign because we were not multiplying or dividing by a negative. We then divide both sides by 5 and get 1<x1<x.

Example 5.23

Solving a Linear Inequality Using One Operation

Solve 9y<549y<54, graph the solution on the number line, and write the solution in interval notation.

Your Turn 5.23

1.
Solve 13 m 65 , graph the solution on the number line, and write the solution in interval notation.

Example 5.24

Solving a Linear Inequality Using Multiple Operations

Solve the inequality 6y11y+176y11y+17, graph the solution on the number line, and write the solution in interval notation.

Your Turn 5.24

1.
Solve the inequality 8 p + 3 ( p 12 ) 7 p 28 , graph the solution on the number line, and write the solution in interval notation.

Solving Applications with Linear Inequalities

Many real-life situations require us to solve inequalities. The method we will use to solve applications with linear inequalities is very much like the one we used when we solved applications with equations. We will read the problem and make sure all the words are understood. Next, we will identify what we are looking for and assign a variable to represent it. We will restate the problem in one sentence to make it easy to translate into an inequality. Then, we will solve the inequality.

Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is not a whole number. In that case, we must round the algebraic solution to a whole number. The context of the application will determine whether we round up or down.

Example 5.25

Constructing a Linear Inequality to Solve an Application with Tablet Computers

A teacher won a mini grant of $4,000 to buy tablet computers for their classroom. The tablets they would like to buy cost $254.12 each, including tax and delivery. What is the maximum number of tablets the teacher can buy?

Your Turn 5.25

1.
Taleisha’s phone plan costs her $28.80 per month plus $0.20 per text message. How many text messages can she send/receive and keep her monthly phone bill no more than $50?

Example 5.26

Constructing a Linear Inequality to Solve a Tuition Application

The local community college charges $113 per credit hour. Your budget is $1,500 for tuition this fall semester. What number of credit hours could you take this fall?

Your Turn 5.26

1.
You are awarded a $500 scholarship! In addition to the $1,500 you have saved for tuition, you now have an additional $500 to spend on credit hours for fall semester. Now, how many credit hours could you take this fall semester? Assume the cost is still $113 per credit hour.

Example 5.27

Constructing a Linear Inequality to Solve an Application with Travel Costs

Brenda’s best friend is having a destination wedding and the event will last 3 days and 3 nights. Brenda has $500 in savings and can earn $15 an hour babysitting. She expects to pay $350 for airfare, $375 for food and entertainment, and $60 a night for her share of a hotel room. How many hours must she babysit to have enough money to pay for the trip?

Your Turn 5.27

1.
Malik is planning a 6-day summer vacation trip. He has $840 in savings, and he earns $45 per hour for tutoring. The trip will cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel. How many hours must he tutor to have enough money to pay for the trip?

Tech Check

The Desmos activities called "Inequalities on a Number Line" and "Compound Inequalities on a Number Line" are ways for students to develop and deepen their understanding of inequalities. Teachers will need a Desmos account to assign the activity for student use. Once they have assigned the activity to their students, teachers need to share the code for the activity with their students. Students will input the code to work on the activity.

Check Your Understanding

For the following exercises, choose the correct interval notation for the graph.
22.
A number line ranges from negative 1 to 2, in increments of 1. A close parenthesis is marked at 1. The region to the left of the parenthesis is shaded on the number line.
  1. [ 1 , )
  2. ( 1 , 1 )
  3. ( , 1 )
  4. ( , 1 )
  5. ( , 1 )
23.
A number line ranges from negative 6 to negative 3, in increments of 1. An open square bracket is marked at negative 5. The region to the right of the square bracket is shaded on the number line.
  1. ( 5 , )
  2. [ 5 , )
  3. [ 5 , )
  4. [ 5 , 3 )
  5. [ 5 , 3 ]
24.
A number line ranges from 0 to 3, in increments of 1. An open square bracket is marked at 1.5. The region to the right of the square bracket is shaded on the number line.
  1. ( 1 , )
  2. [ 1 , )
  3. [ 3 2 , )
  4. ( 3 2 , )
  5. ( , 3 2 )
25.
A number line ranges from negative 5 to 4, in increments of 1. An open parenthesis is marked at negative 4 and a close parenthesis is marked at 3. The region within the parentheses is shaded on the number line.
  1. ( 4 , 3 )
  2. ( 3 , 4 )
  3. [ , )
  4. [ 4 , 3 ]
  5. [ 3 , 4 ]
26.
[ 4 , ) is the solution for which inequality?
  1. 4 x 0
  2. 4 x 0
  3. 6 x < 24
  4. 6 x > 24
  5. 6 x 24
27.
( , 3 ) is the solution for which inequality?
  1. 6 x < 18
  2. 6 x > 18
  3. 6 x 18
  4. 6 x 18
  5. 6 x 18
28.
( 2 , ) is the solution for which inequality?
  1. 4 x > 8
  2. 4 x + 3 > 11
  3. 4 x 3 > 11
  4. 4 x 8
  5. 4 x + 3 5
29.
( , 9 ) is the solution for which inequality?
  1. 9 x < 0
  2. 3 x 27
  3. 3 x + 14 > 13
  4. 3 x 14 > 13
  5. 3 x 27
For the following exercises, choose the equation that best models the situation.
30.
Renaldo is hauling boxes of lawn chairs. Each box is the same size, 8 cubic feet. Renaldo’s truck has a capacity of 764 cubic feet. How many boxes of lawn chairs can Renaldo put in his truck?
  1. 8 < 764 x
  2. 8 x < 764
  3. 8 > 764 x
  4. 8 x > 764
  5. None of these
31.
Bernadette babysits the neighbor’s kids, making on average $50 a night. How many nights will she have to babysit in order to earn enough money to buy a used car, whose cost is $8,120?
  1. 50 < 8,120x
  2. 50 x < 8,120
  3. 50 < 8,120x
  4. 50 x > 8,120
  5. None of these
For the following exercises, graph the inequality on a number line and write the interval notation.
1 .
x > 3
2 .
x 0.5
3 .
x 1 3
4 .
x < 7 3
5 .
2 < x < 0
6 .
5 x < 3
7 .
0 x 3.5
8 .
4 < x < 2
9 .
5 < x 2
10 .
3.75 x 0
For the following exercises, solve the inequality, graph the solution on the number line, and write the solution in interval notation.
11 .
6 y < 48
12 .
40 < 5 8 k
13 .
7 s < 28
14 .
9 4 g 36
15 .
8 v 96
16 .
b 10 30
17 .
7 d > 105
18 .
18 < q 6
19 .
5 u 8 u 21
20 .
9 p > 14 p 18
21 .
9 y + 5 ( y + 3 ) < 4 y 35
22 .
4 k ( k 2 ) 7 k 26
For the following exercises, construct a linear inequality to solve the application.
23 .
The elevator in Yehire’s apartment building has a sign that says the maximum weight is 2,100 pounds. If the average weight of one person is 150 pounds, how many people can safely ride the elevator?
24 .
Arleen got a $20 gift card for the coffee shop. Her favorite iced drink costs $3.79. What is the maximum number of drinks she can buy with the gift card?
25 .
Ryan charges his neighbors $17.50 to wash their car. How many cars must he wash next summer if his goal is to earn at least $1,500?
26 .
Kimuyen needs to earn $4,150 per month in order to pay all her expenses. Her sales job pays her $3,475 per month plus 4 percent of her total sales. What is the minimum Kimuyen’s total sales must be in order for her to pay all her expenses?
27 .
Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her $66,500 plus 15 percent of her total sales. What would her total sales need to be for her salary on the second offer to be higher than the first?
28 .
Kiyoshi’s phone plan costs $17.50 per month plus $0.15 per text message. What is the maximum number of text messages Kiyoshi can use so the phone bill is no more than $56.60?
29 .
Kellen wants to rent a banquet room in a restaurant for her cousin’s baby shower. The restaurant charges $350 for the banquet room plus $32.50 per person for lunch. How many people can Kellen have at the shower if she wants the maximum cost to be $1,500?
30 .
Noe installs and configures software on home computers. He charges $125 per job. His monthly expenses are $1,600. How many jobs must he work in order to make a profit of at least $2,400?
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/contemporary-mathematics/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/contemporary-mathematics/pages/1-introduction
Citation information

© Dec 21, 2023 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.