Problem 74 - Introductory Algebra for College Students

Question

What does the percent formula, \(A=P B,\) describe? Give an example of how the formula is used.

Step-by-Step Solution

Answer

The percent formula \(A = P B\) is used to calculate the amount represented by a certain percentage of a base quantity. For example, if we apply the formula to find 25% of 100 apples, we get 25 apples.

Step 1: Understanding the Percent Formula

The percent formula, denoted as \(A = P B\), is used to calculate the amounts of percentages. In this formula, 'A' denotes the resulting amount (the part of the base indicated by the percent), 'P' is the percent expressed in decimal form and 'B' represents the base amount (the entire amount or original quantity). The percent value is converted to a decimal by dividing it by 100.

Step 2: Applying the Percent Formula

Let's illustrate the use of our formula with an example. Suppose we have a group of 100 apples (which is our base quantity, \(B\)) and we want to find out 25% of this amount (this is our percentage, \(P\), as a decimal it equals \(0.25\). So, we substitute our values into the percent formula \(A = P B\) and get \(A = 0.25 * 100\).

Step 3: Calculate the Result

By doing the calculation in the previous step \(25 * 100\) we get \(A\) as 25. So, 25% of 100 apples is 25 apples.