Unveiling the Mystery: 21 is 28.8% of What Number?
Percentages are a fundamental part of everyday life, from calculating sales tax and discounts to understanding statistics and financial reports. Often, we encounter scenarios where we need to find the whole amount when only a percentage and its corresponding part are known. This article will delve into solving the problem: "21 is 28.8% of what number?" We'll break down the process step-by-step, making it accessible even for those who find percentages challenging.
1. Understanding the Problem
The statement "21 is 28.8% of what number?" can be translated into a mathematical equation. We can represent the unknown number as 'x'. The problem then becomes:
21 = 0.288 x
This equation states that 21 represents 28.8% (or 0.288 as a decimal) of an unknown number 'x'. Our goal is to solve for 'x'.
2. Converting Percentage to Decimal
Before we can solve the equation, we need to convert the percentage (28.8%) into its decimal equivalent. To do this, we divide the percentage by 100:
28.8% / 100 = 0.288
This means 28.8% is equal to 0.288. This decimal representation is crucial for performing the calculations needed to find 'x'.
3. Solving the Equation
Now, let's substitute the decimal equivalent into our equation:
21 = 0.288 x
To isolate 'x', we need to divide both sides of the equation by 0.288:
x = 21 / 0.288
Using a calculator, we find:
x ≈ 72.9167
Therefore, 21 is approximately 28.8% of 72.9167.
4. Practical Application: Real-World Examples
Let's consider a few real-world scenarios where this type of calculation is useful:
Sales: Imagine a store offering a 28.8% discount on an item, and the discount amount is $21. Using our calculation, we can determine the original price of the item was approximately $72.92.
Surveys: Suppose a survey shows that 28.8% of respondents (21 people) prefer a particular brand. We can use this information to estimate the total number of respondents in the survey, which is approximately 72.92 (rounding to 73). Note that in real-world scenarios, the final answer might not be a whole number as people are countable entities.
Finance: If you received $21 in interest, which represents 28.8% of your total investment, then your total investment was approximately $72.92.
5. Understanding the Approximation
It's important to note that our answer (72.9167) is an approximation. This is because we are dealing with percentages, which inherently involve rounding. Depending on the context, you might round the answer to a whole number (73) or to a more precise decimal value. The level of precision needed depends entirely on the application.
Actionable Takeaways:
Convert percentages to decimals before solving equations involving percentages.
Remember the fundamental equation: Part = Percentage × Whole
Use a calculator to simplify calculations.
Always consider the context and round your answer appropriately.
Frequently Asked Questions (FAQs):
1. Why do we divide by 0.288 instead of multiplying? We divide because we are trying to find the whole (x), and the 0.288 is multiplying the whole. Division is the inverse operation of multiplication, allowing us to isolate 'x'.
2. What if the percentage is a whole number like 30%? The process remains the same. Simply convert 30% to its decimal equivalent (0.30) and continue with the equation solving steps.
3. Can I use this method for any percentage problem? Yes, this method applies to any problem where you know a percentage and the corresponding part and need to find the whole.
4. What if I don't have a calculator? You can use long division to divide 21 by 0.288, although it will be more time-consuming.
5. How accurate does my answer need to be? The required accuracy depends on the context of the problem. In some cases, a whole number approximation is sufficient; in others, you might need more decimal places for precision.
Note: Conversion is based on the latest values and formulas.
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