In a problem on percentages there are three quantities that are involved. These are the base, the amount, and the rate percent. Express the relation between them in the form of an equation and explain with examples how to find each one of them given the other two quantities

In a problem involving percentages, three quantities are typically involved: the base, the amount, and the rate percent. These quantities can be related to each other through a simple equation.

Let's break down each of the quantities:

1. Base: The base refers to the original value or the total quantity. It represents the whole, and the rate percent is typically calculated based on this value. In an equation, the base is denoted by the letter "B".

2. Amount: The amount is the result of applying the rate percent to the base. It represents the part or the fraction of the base. In an equation, the amount is denoted by the letter "A".

3. Rate percent: The rate percent is the percentage or proportion of the base that the amount represents. It is typically given as a percentage, and in an equation, the rate percent is denoted by the letter "R".

The equation that relates these three quantities is:

Amount (A) = Base (B) * (Rate percent (R) / 100)

To find each of these quantities given the other two, you can rearrange this equation:

1. To find the amount (A):
A = B * (R/100)
Example: If the base is 200 and the rate percent is 30%, then the amount can be calculated as:
A = 200 * (30/100) = 60

2. To find the base (B):
B = A / (R/100)
Example: If the amount is 60 and the rate percent is 30%, then the base can be calculated as:
B = 60 / (30/100) = 200

3. To find the rate percent (R):
R = (A / B) * 100
Example: If the amount is 60 and the base is 200, then the rate percent can be calculated as:
R = (60 / 200) * 100 = 30%

By using this equation and the given values of two quantities, you can calculate the third quantity in a percentage problem.