Understanding the Percentage Problem

The question asks us to find a specific number. We are given a piece of information about this number: 32% of it is equal to 80. This is a common type of percentage problem where a part of a whole is given as a percentage, and we need to find the whole (the original number).

Setting up the Equation for Percentages

To solve this, we can represent the unknown number with a variable, let's say \(x\). The phrase "32% of a number" can be translated into a mathematical expression. In mathematics, "of" often means multiplication, and a percentage can be written as a decimal or a fraction.

32% as a decimal is \(32 \div 100 = 0.32\).

So, "32% of \(x\)" can be written as \(0.32 \times x\), or simply \(0.32x\).

The problem states that "32% of a number is 80". This gives us the equation:

\[0.32x = 80\]

Solving for the Unknown Number

Now, we need to solve the equation \(0.32x = 80\) for \(x\). To isolate \(x\), we need to divide both sides of the equation by 0.32.

\[x = \frac{80}{0.32}\]

Performing the division:

\[x = 250\]

Step-by-Step Calculation

Let's break down the calculation:

1. Identify the given information: 32% of the number is 80.
2. Let the unknown number be \(x\).
3. Translate the percentage into a decimal or fraction: \(32\% = 0.32\).
4. Formulate the equation: \(0.32x = 80\).
5. Solve for \(x\) by dividing 80 by 0.32: \(x = \frac{80}{0.32}\).
6. Calculate the result: \(x = 250\).

Conclusion: The Found Number

Therefore, the number of which 32% is 80 is 250. We can check this: 32% of 250 is \(0.32 \times 250 = 80\), which matches the information given in the problem.

Percentage Problem Revision

Additional Information on Percentages

Percentages are a fundamental concept in mathematics used widely in everyday life, finance, statistics, and many other fields. Understanding how to work with percentages is crucial for various calculations.

• Percentage Increase/Decrease: Used to calculate how much a quantity has changed relative to its original value.
• Profit and Loss Percentages: Commonly used in business to express profit or loss as a percentage of the cost price.
• Simple and Compound Interest: Interest rates are typically expressed as percentages.
• Discounts and Taxes: Often calculated as a percentage of the original price.

Problems like "P% of X is Y" can always be solved by setting up the equation \( (P/100) \times X = Y \) and solving for the unknown variable (\(P\), \(X\), or \(Y\)).