Decoding The Percentage Puzzle 150% Of What Number Is 60

Delving into the world of percentages can sometimes feel like navigating a maze, but with a clear understanding of the fundamentals, even the most intricate problems can be solved with ease. In this article, we will dissect a classic percentage question: "150% of what number is 60?" This seemingly simple question provides a valuable opportunity to reinforce our understanding of percentages, their relationship to fractions and decimals, and the algebraic techniques used to solve them. By breaking down the problem step-by-step, we will not only arrive at the correct answer but also gain a deeper appreciation for the logic and reasoning that underpin percentage calculations. So, let's embark on this mathematical journey and unravel the mystery behind this percentage puzzle.

Understanding Percentages: The Foundation of Our Solution

At its core, a percentage is a way of expressing a number as a fraction of 100. The word "percent" itself comes from the Latin "per centum," meaning "out of one hundred." This fundamental concept is crucial for understanding and solving percentage problems. When we say "150%," we are essentially saying 150 out of every 100, or 1.5 in decimal form. This conversion from percentage to decimal (or fraction) is the first key step in translating the word problem into a mathematical equation. Recognizing that 150% is greater than 100% immediately tells us that the answer to our question will be a number smaller than 60, as we are looking for the original value that, when increased by 50%, becomes 60. This initial assessment of the problem helps us anticipate the solution and provides a check against potential errors in our calculations. Furthermore, understanding the concept of percentages extends beyond simple calculations; it is a fundamental skill applicable in various real-world scenarios, from calculating discounts and taxes to interpreting statistical data and financial reports. A firm grasp of percentages empowers us to make informed decisions and navigate the complexities of everyday life.

Translating Words into Equations: The Algebraic Approach

To effectively solve percentage problems, we need to translate the given information into a mathematical equation. This involves identifying the unknown quantity, representing it with a variable, and expressing the relationships between the known and unknown values using mathematical symbols. In our case, the question "150% of what number is 60?" can be translated as follows: Let 'x' represent the unknown number. The phrase "150% of" signifies multiplication, and "is" indicates equality. Therefore, we can rewrite the question as the equation: 1. 50% * x = 60. This seemingly simple translation is a powerful step, as it allows us to apply the tools of algebra to solve the problem. By representing the unknown quantity with a variable, we can manipulate the equation using algebraic operations to isolate the variable and find its value. This approach not only provides a systematic way to solve the problem but also enhances our problem-solving skills in mathematics and other disciplines. The ability to translate word problems into mathematical equations is a fundamental skill that empowers us to tackle a wide range of quantitative challenges.

Solving for the Unknown: Unraveling the Value of 'x'

Now that we have the equation 1. 50% * x = 60, the next step is to solve for 'x'. Before we proceed, it's crucial to express the percentage as a decimal. As discussed earlier, 150% is equivalent to 1.5. So, our equation becomes 1. 5 * x = 60. To isolate 'x', we need to perform the inverse operation of multiplication, which is division. We divide both sides of the equation by 1.5: (1.5 * x) / 1.5 = 60 / 1.5. This simplifies to x = 40. Therefore, the unknown number is 40. This step-by-step process of isolating the variable is a cornerstone of algebraic problem-solving. By applying the properties of equality, we can manipulate equations to reveal the value of the unknown. In this case, dividing both sides by 1.5 effectively "undoes" the multiplication, leaving 'x' by itself on one side of the equation. The result, x = 40, is the solution to our problem, indicating that 150% of 40 is indeed 60. This methodical approach not only provides the correct answer but also reinforces the underlying principles of algebra.

Verifying the Solution: Ensuring Accuracy and Understanding

Once we have a potential solution, it's essential to verify its accuracy. This step not only ensures that we have arrived at the correct answer but also deepens our understanding of the problem and the solution process. To verify our solution, we substitute the value of 'x' (which is 40) back into the original equation: 1. 50% * 40 = 60. Converting 150% to its decimal equivalent, 1.5, we have 1. 5 * 40 = 60. Performing the multiplication, we get 60 = 60, which confirms that our solution is correct. This verification process is a crucial step in any mathematical problem-solving endeavor. It allows us to catch potential errors, solidify our understanding, and build confidence in our results. By substituting the solution back into the original equation, we are essentially reversing the steps we took to solve the problem, ensuring that the answer aligns with the initial conditions. This practice not only enhances our accuracy but also fosters a deeper appreciation for the interconnectedness of mathematical concepts.

Real-World Applications: Percentages in Everyday Life

Understanding percentages is not just an academic exercise; it has practical applications in numerous real-world scenarios. From calculating discounts at the store to understanding interest rates on loans, percentages are an integral part of our daily lives. For instance, if a store is offering a 20% discount on an item, we can use percentages to determine the sale price. Similarly, when calculating tips at a restaurant, we use percentages to determine the appropriate amount to leave. In finance, percentages are used to express investment returns, interest rates, and inflation rates. Understanding these concepts allows us to make informed financial decisions and manage our money effectively. Furthermore, percentages are used extensively in statistics and data analysis, allowing us to interpret and compare data sets. For example, we might use percentages to compare the performance of different companies or to track changes in economic indicators. By mastering the fundamentals of percentages, we equip ourselves with a valuable tool for navigating the complexities of the modern world. The ability to understand and apply percentages empowers us to make informed decisions, solve practical problems, and become more financially literate.

Conclusion: Mastering Percentages for Mathematical Success

In conclusion, the question "150% of what number is 60?" serves as an excellent example of how to approach and solve percentage problems. By breaking down the problem into smaller, manageable steps, we can effectively translate the words into a mathematical equation, solve for the unknown variable, and verify our solution. This process not only provides the correct answer but also reinforces our understanding of percentages and their relationship to fractions, decimals, and algebra. Moreover, mastering percentages is essential for success in mathematics and various real-world applications. From calculating discounts to understanding financial concepts, percentages are an integral part of our daily lives. By developing a strong foundation in percentages, we equip ourselves with a valuable tool for problem-solving, decision-making, and financial literacy. Therefore, it is crucial to continue practicing and applying these concepts to further enhance our mathematical skills and confidence. The journey of learning percentages is a journey of empowerment, enabling us to navigate the quantitative aspects of the world with greater ease and understanding.