- Define the original amount as \(x\).
- Represent the \(15.25\%\) increase as the equation \(1.1525x = 96.81\).
- Divide the total by \(1.1525\) to find the original amount \(x\).
- The original amount is \(\boxed{84}\).
Explanation
- Understanding the Problem and Setting Up the Equation
We are given that an original amount, let's call it \(x\), is increased by \(15.25\%\) to result in a final value of \(96.81\). A \(15.25\%\) increase means that we add \(15.25\%\) of the original amount to the original amount itself. Mathematically, this is expressed as:
\[x + 0.1525x = 96.81\]
Combining like terms, we get:
\[1.1525x = 96.81\]
Our objective is to determine the value of the original amount \(x\).
- Solving for the Original Amount
To isolate \(x\), we need to divide both sides of the equation by \(1.1525\):
\[x = \frac{96.81}{1.1525}\]
Performing the division:
\[x = 84\]
Thus, the original amount was \(84\).
Examples
In daily life, this calculation is useful for determining original prices before a sales tax is applied or before a tip is added. For example, if you see a bill amount of \(\$96.81\) that includes a \(15.25\%\) surcharge (like a specific service fee or combined tax), you can work backward to find the base price of the items by dividing the total by \(1 + (\text{percentage}/100)\). This ensures you understand the true cost of goods or services before the additional fees.