Find The Whole.$15\%$ Of $\square$ Is 12.

Introduction

Mathematics is a fascinating subject that involves problem-solving, critical thinking, and logical reasoning. It is a universal language that helps us understand the world around us. In this article, we will delve into a mathematical puzzle that has been intriguing people for a long time. The puzzle states that "Find the whole. $15\%$ of $\square$ is 12." This seemingly simple problem requires a deep understanding of percentages, algebra, and logical reasoning. In this article, we will break down the solution step by step and provide a clear explanation of the mathematical concepts involved.

Understanding the Problem

The problem states that "Find the whole. $15\%$ of $\square$ is 12." This means that we need to find the value of $\square$ such that $15\%$ of it equals 12. To solve this problem, we need to understand the concept of percentages and how to work with them.

Percentages are a way of expressing a value as a fraction of 100. For example, $15\%$ means 15 out of 100, or $\frac{15}{100}$. When we say that $15\%$ of $\square$ is 12, we mean that $\frac{15}{100}$ of $\square$ equals 12.

Setting Up the Equation

To solve this problem, we need to set up an equation. Let's represent the value of $\square$ as $x$. Then, we can write the equation as:

$$\frac{15}{100} \times x = 12$$

This equation states that $15\%$ of $x$ equals 12.

Solving the Equation

To solve for $x$, we need to isolate the variable. We can do this by multiplying both sides of the equation by $\frac{100}{15}$, which is the reciprocal of $\frac{15}{100}$.

$$\frac{100}{15} \times \frac{15}{100} \times x = \frac{100}{15} \times 12$$

Simplifying the equation, we get:

$$x = \frac{100}{15} \times 12$$

Calculating the Value

Now that we have the equation, we can calculate the value of $x$. To do this, we need to multiply $\frac{100}{15}$ by 12.

$$x = \frac{100}{15} \times 12$$

$$x = \frac{1200}{15}$$

$$x = 80$$

Conclusion

In this article, we solved a mathematical puzzle that stated "Find the whole. $15\%$ of $\square$ is 12." We broke down the solution step by step and provided a clear explanation of the mathematical concepts involved. We set up an equation, solved for the variable, and calculated the value of $\square$. The final answer is $x = 80$.

Real-World Applications

This problem may seem like a simple mathematical puzzle, but it has real-world applications. For example, in business, understanding percentages is crucial for calculating profits, losses, and interest rates. In finance, percentages are used to calculate interest rates, investment returns, and credit scores. In everyday life, understanding percentages is essential for making informed decisions about personal finance, investments, and credit.

Tips and Tricks

Here are some tips and tricks for solving mathematical puzzles like this one:

• Read the problem carefully: Make sure you understand what the problem is asking for.
• Set up an equation: Write down the equation that represents the problem.
• Solve for the variable: Isolate the variable and solve for its value.
• Check your work: Make sure your solution makes sense and is consistent with the problem.

Final Thoughts

Mathematics is a fascinating subject that involves problem-solving, critical thinking, and logical reasoning. This article demonstrated how to solve a mathematical puzzle that stated "Find the whole. $15\%$ of $\square$ is 12." We broke down the solution step by step and provided a clear explanation of the mathematical concepts involved. We hope that this article has provided you with a deeper understanding of percentages and algebra, and has inspired you to explore the world of mathematics.

Introduction

In our previous article, we solved a mathematical puzzle that stated "Find the whole. $15\%$ of $\square$ is 12." We broke down the solution step by step and provided a clear explanation of the mathematical concepts involved. In this article, we will answer some of the most frequently asked questions about the puzzle.

Q&A

Q: What is the value of $\square$?

A: The value of $\square$ is 80.

Q: How do I solve the puzzle?

A: To solve the puzzle, you need to set up an equation that represents the problem. In this case, the equation is $\frac{15}{100} \times x = 12$. You then need to solve for the variable $x$ by isolating it and calculating its value.

Q: What is the concept of percentages?

A: Percentages are a way of expressing a value as a fraction of 100. For example, $15\%$ means 15 out of 100, or $\frac{15}{100}$. When we say that $15\%$ of $\square$ is 12, we mean that $\frac{15}{100}$ of $\square$ equals 12.

Q: How do I calculate percentages?

A: To calculate percentages, you need to multiply the value by the percentage as a decimal. For example, to calculate $15\%$ of 80, you would multiply 80 by $\frac{15}{100}$.

Q: What are some real-world applications of percentages?

A: Percentages have many real-world applications, including business, finance, and everyday life. For example, in business, understanding percentages is crucial for calculating profits, losses, and interest rates. In finance, percentages are used to calculate interest rates, investment returns, and credit scores.

Q: How do I check my work?

A: To check your work, you need to make sure that your solution makes sense and is consistent with the problem. You can do this by plugging your answer back into the original equation and checking that it is true.

Q: What are some tips and tricks for solving mathematical puzzles like this one?

A: Here are some tips and tricks for solving mathematical puzzles like this one:

• Read the problem carefully: Make sure you understand what the problem is asking for.
• Set up an equation: Write down the equation that represents the problem.
• Solve for the variable: Isolate the variable and solve for its value.
• Check your work: Make sure your solution makes sense and is consistent with the problem.

Conclusion

In this article, we answered some of the most frequently asked questions about the mathematical puzzle "Find the whole. $15\%$ of $\square$ is 12." We provided a clear explanation of the mathematical concepts involved and offered some tips and tricks for solving mathematical puzzles like this one. We hope that this article has provided you with a deeper understanding of percentages and algebra, and has inspired you to explore the world of mathematics.

Additional Resources

If you are interested in learning more about percentages and algebra, here are some additional resources that you may find helpful:

• Online tutorials: There are many online tutorials and resources available that can help you learn about percentages and algebra.
• Math textbooks: There are many math textbooks available that can provide you with a comprehensive understanding of percentages and algebra.
• Math apps: There are many math apps available that can help you practice and learn about percentages and algebra.

Final Thoughts

Mathematics is a fascinating subject that involves problem-solving, critical thinking, and logical reasoning. This article demonstrated how to solve a mathematical puzzle that stated "Find the whole. $15\%$ of $\square$ is 12." We hope that this article has provided you with a deeper understanding of percentages and algebra, and has inspired you to explore the world of mathematics.