The number you are looking for is 300.
Understanding Percentages
A percentage is a way of expressing a number as a fraction of 100. For example, "15 percent" means 15 parts out of every 100. In this problem, we are given a part (45) and the percentage it represents (15%) of an unknown whole number. Our goal is to determine that whole number.
How to Calculate the Original Number
There are several straightforward methods to find the original number when a percentage of it is known. Both methods below yield the same correct answer by working backward from the given information.
Method 1: Using an Algebraic Equation
This method is precise and widely applicable for solving percentage problems.
- Define the Unknown: Let the unknown number be represented by the variable x.
- Formulate the Equation:
- "15 percent of a number" can be translated into a mathematical expression as
0.15 * x(since 15% is equivalent to the decimal 0.15). - "is 45" means it equals 45.
- Combining these, the equation becomes:
0.15 * x = 45.
- "15 percent of a number" can be translated into a mathematical expression as
- Solve for x: To isolate x, divide both sides of the equation by 0.15:
x = 45 / 0.15x = 300
Method 2: Calculating the Value of 1%
This approach breaks the problem down by first finding the value of one percent.
- Determine the Value of 1%: If 15% of the number is 45, then to find what 1% represents, divide the given value (45) by the percentage (15):
1% of the number = 45 / 15 = 3
- Calculate 100% of the Number: Since we've established that 1% of the number is 3, to find the full number (100%), multiply this value by 100:
100% of the number = 3 * 100 = 300
Both methods consistently show that the number is 300. Thus, when 15% of a number is 45, the number itself is 300.
Verification of the Answer
To ensure accuracy, you can always check your answer by performing the original calculation:
- Calculate 15% of 300:
0.15 * 300 = 45
Since 15% of 300 indeed equals 45, our calculated number is correct.
Summary of the Calculation
For quick reference, here's a table summarizing the components and the solution:
| Element | Value | Description |
|---|---|---|
| Given Percentage | 15% | The known percentage of the unknown number |
| Given Part Value | 45 | The numerical value corresponding to 15% |
| Formula Applied | Part / % | To find the whole (e.g., Number = 45 / 0.15) |
| Resulting Number | 300 | The calculated whole number |
Practical Applications
Understanding how to reverse percentage calculations is a valuable skill used in various real-world scenarios:
- Financial Management: Calculating an original price before a discount was applied, determining a total bill based on a tip amount, or finding the principal amount of a loan from the interest paid.
- Business Operations: Estimating total sales revenue from a known percentage of profit, or extrapolating overall production based on a sample's defect rate.
- Everyday Situations: Understanding the original cost of an item after a sale, or figuring out the total amount of a group's contribution if you only know a percentage.
These skills empower you to make informed decisions and better understand quantitative information in daily life and professional contexts.
