2.2: Applications using Linear Inequalities

SECTION 2.2 Learning Objective

2.2:  Applications Using Linear Inequalities

  • Solve applications using linear inequalities

 

Solve applications using linear inequalities

This section will discuss several types of applications. No matter how simple or complex the application is, the following steps will help to translate and solve the problem.

  1. Read through the entire problem 
  2. Organize the information 
  3. Write the inequality 
  4. Solve the inequality
  5. Check the answer

Look for key words and phrases. The following table gives some common translations for inequalities.

Words or Phrase Symbol
Is less than <
Is more than >
At least
At most
Minimum
Maximum
No more than
No less than
Below is a video example of an application problem involving linear inequalities.

Example 1

Maria’s job provides a yearly base salary of $25,000 plus a commission of 7% of her sales. If her goal is to earn a yearly income of at least $39,000, what will her total sales need to be to achieve that goal?

Here is another similar example:

Example 2

Leslie wants to rent a car for the day. The rental company charges a daily rate of $18.95 plus 19 cents for each mile driven. If Leslie only has $50 to spend on the car rental, what is the maximum number of miles she can drive? Round the answer to the nearest mile.

 

Example 3

Leslie found a second rental company that charges 75 cents per mile with no additional fee.  Recall the first rental company (from Example 2) charged $18.95 plus 19 cents for each mile driven.  How many miles can she drive so that the second rental company is a better deal?  Round down to the nearest whole mile.

 

In order to do the next example, you need to know how to find the average of a set of numbers.  Recall that to find an average, you need to first add all the numbers together.  Then you divide that sum by the number of values in your set.

Example 4

A student has scores of 85, 65, and 82 on his first three tests. He needs an average of at least 80 to earn a grade of B in the class. What is the minimum score that the student needs on the fourth test to ensure a grade of B?