As a network administrator, you must constantly monitor network traffic to ensure that employees can access the Internet and company resources to do their jobs. You may have to analyze comparisons between departments to see where the heaviest load is so you can compensate for any congestion that might be occurring. By using percentages, you can quickly compare the differences between departments and potentially even users to determine how the network is being utilized. This module discusses applications of percents. By the end of the module, you should be able to distinguish between the base, percent, and percentage, and calculate the percentage, the percent, and the base.
By the end of this lesson, you should be able to:
Review the flashcards to learn the key terms for this lesson.
Three basic types of percent problems are most common. Each type involves a base, a percent, and a percentage, and when they are translated from words to mathematical symbols, each becomes a multiplication statement. Examples of these types of problems are the following:
In Problem 1, the product is missing.
To solve the problem, you represent the missing product with P.
P = 30% ⋅ 50
Percentage
The missing product P is called the percentage. Percentage means part or portion.
In P = 30% ⋅ 50, P represents a particular part of 50.
In Problem 2, one of the factors is missing. Here the missing factor is represented with Q.
15 = Q ⋅ 50
Percent
The missing factor is the percent. Percent, you know, means per 100, or part of 100. In 15 = Q ⋅ 50, Q indicates what part of 50 is being taken or considered. Specifically, 15 = Q ⋅ 50 means that if 50 were to be divided into 100 equal parts, then Q indicates 15 are being considered.
In Problem 3, one of the factors is missing. Represent the missing factor with B.
15 = 30% ⋅ B
Base
The missing factor is the base. Some meanings of base are a source of supply or a starting place. In 15 = 30% ⋅ B, B indicates the amount of supply. Specifically, 15 = 30% ⋅ B indicates that 15 represents 30% of the total supply.
Each of these three types of problems is of the form (percentage) = (percent) ⋅ (base).
You can determine any one of the three values given the other two.
Example  
Problem 
What number is 30% of 50? 



Example  
Problem 
What number is 36% of 95? 



Example  
Problem 
15 is what percent of 50? 



Example  
Problem 
4.32 is what percent of 72? 



Example  
Problem 
15 is 30% of what number? 



Example  
Problem 
56.43 is 33% of what number? 



Using the three methods listed above you can now solve problems like these:
Example  
Problem 
Jeff has a coupon at an electronics store for 15% off any purchase of $100 or more. He wants to buy a 17inch monitor with a price tag of $220. Jeff wonders how much money the coupon will take off the $220 original price. 



Example  
Problem 
Evelyn bought some CDs at the local bookstore. Her total bill was $31.50, which included 5% tax. How much did the books cost before tax? 



Watch the following Khan Academy videos about how to solve percent problems. You will see additional examples that can help you better understand how to solve percent problems.
Math Video Toolkit: View the following Khan Academy video lessons. 
Now you get a chance to work out some problems. You will need to get out a piece of paper and a pencil to complete the practice problems. Study each of these problems carefully; you will see similar problems on the lesson knowledge check. Select the following link to complete the practice activity. Translating Problems with Percent Practice Problems Once you complete the practice activity, check to see how well you did by selecting the following link: Solutions: Translating Problems with Percent Practice Problems 
Each of these three types of problems is of the form (percentage) = (percent) ⋅ (base). You can determine any one of the three values given the other two.
Now that you have read over the lesson carefully attempted the practice exercises, it is time for a knowledge check. Please note that this is a graded part of this lesson so be sure you have prepared yourself before starting. 
Resource:
“Ratios and Rates: Applications of Percents” by Ellis, W., & Burzynski, D. © 2010 retrieved from http://cnx.org/content/m35007/1.2/ is used under a Creative Commons Attribution http://creativecommons.org/licenses/by/3.0/. This is an adaption of the lesson titled, “Translating Problems with Percent,” by the National Information Security and Geospatial Technologies Consortium (NISGTC) is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0.